%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO205+3 : TPTP v9.0.0. Released v4.0.0.
% 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 05:05:56 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO205+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:41:47 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(convergent_lines_type, type, (
% 0.13/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_X_2_type, type, (
% 0.13/0.40 tptp_fun_X_2: $i)).
% 0.13/0.40 tff(unorthogonal_lines_type, type, (
% 0.13/0.40 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.13/0.40 tff(orthogonal_through_point_type, type, (
% 0.13/0.40 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.13/0.40 tff(intersection_point_type, type, (
% 0.13/0.40 intersection_point: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.40 tptp_fun_Y_1: $i)).
% 0.13/0.40 tff(distinct_lines_type, type, (
% 0.13/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.13/0.40 tff(apart_point_and_line_type, type, (
% 0.13/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.40 tptp_fun_Z_0: $i)).
% 0.13/0.40 tff(equal_lines_type, type, (
% 0.13/0.40 equal_lines: ( $i * $i ) > $o)).
% 0.13/0.40 tff(equal_points_type, type, (
% 0.13/0.40 equal_points: ( $i * $i ) > $o)).
% 0.13/0.40 tff(distinct_points_type, type, (
% 0.13/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.40 tff(20,plain,(
% 0.20/0.40 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, X!2))) <=> ((~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, X!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, X!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2))),
% 0.20/0.40 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, X!2)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(X!2, Y!1)), X!2)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~convergent_lines(X!2, X!2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[28, 22, 9])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : trans(rewrite((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), rewrite((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), ((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.40 tff(35,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.40 tff(38,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[37])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))) | (~(distinct_lines(Y!1, Z!0) <=> equal_lines(Y!1, Z!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (~(distinct_lines(Y!1, Z!0) <=> equal_lines(Y!1, Z!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & equal_lines(Y, Z))) | (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & equal_lines(Y, Z))) | (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, Z: $i] : ((convergent_lines(X, Y) & equal_lines(Y, Z)) => (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & equal_lines(Y, Z))) | (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(44,axiom,(~![X: $i, Y: $i, Z: $i] : ((convergent_lines(X, Y) & equal_lines(Y, Z)) => (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & equal_lines(Y, Z))) | (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & equal_lines(Y, Z))) | (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & equal_lines(Y, Z))) | (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & equal_lines(Y, Z))) | (convergent_lines(X, Z) & equal_points(intersection_point(X, Y), intersection_point(X, Z))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[47, 42])).
% 0.20/0.40 tff(49,plain,(
% 0.20/0.40 ~((~(convergent_lines(X!2, Y!1) & equal_lines(Y!1, Z!0))) | (convergent_lines(X!2, Z!0) & equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[48])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (convergent_lines(X!2, Y!1) & equal_lines(Y!1, Z!0)),
% 0.20/0.40 inference(or_elim,[status(thm)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (equal_lines(Y!1, Z!0)),
% 0.20/0.40 inference(and_elim,[status(thm)],[50])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ((distinct_lines(Y!1, Z!0) <=> equal_lines(Y!1, Z!0)) | (~distinct_lines(Y!1, Z!0)) | (~equal_lines(Y!1, Z!0))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((distinct_lines(Y!1, Z!0) <=> equal_lines(Y!1, Z!0)) | (~distinct_lines(Y!1, Z!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (~distinct_lines(Y!1, Z!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 41])).
% 0.20/0.40 tff(55,assumption,(~convergent_lines(X!2, Z!0)), introduced(assumption)).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (convergent_lines(X!2, Y!1)),
% 0.20/0.40 inference(and_elim,[status(thm)],[50])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.40 tff(62,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.40 tff(65,plain,(
% 0.20/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, Z!0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1))) <=> (convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, Z!0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, Z!0)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, Z!0))),
% 0.20/0.40 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, Z!0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[72, 66, 56, 55, 54])).
% 0.20/0.40 tff(74,plain,(convergent_lines(X!2, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.41 tff(80,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.41 tff(83,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[82])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 84, 74])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.41 tff(94,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.41 tff(97,plain,(
% 0.20/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[96])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 98, 54, 88])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : trans(rewrite((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))), rewrite((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))), ((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.41 tff(108,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.41 tff(111,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[110])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))) | (~(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) <=> equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (~(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) <=> equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~(~((~convergent_lines(X!2, Z!0)) | (~equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~convergent_lines(X!2, Z!0)) | (~equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ((convergent_lines(X!2, Z!0) & equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) <=> (~((~convergent_lines(X!2, Z!0)) | (~equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ((~(convergent_lines(X!2, Z!0) & equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> (~(~((~convergent_lines(X!2, Z!0)) | (~equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~(convergent_lines(X!2, Z!0) & equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> ((~convergent_lines(X!2, Z!0)) | (~equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[117, 115])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (~(convergent_lines(X!2, Z!0) & equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[49])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ((~convergent_lines(X!2, Z!0)) | (~equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (~equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 74])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) <=> equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) <=> equal_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[123, 114])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.41 tff(130,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.41 tff(133,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[132])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[137, 134, 74])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.41 tff(142,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[141, 134, 56])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.41 tff(146,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[145, 84, 56])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 (^[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_lines(U, V)) | (~distinct_points(X, Y))) <=> (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_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 (![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_lines(U, V)) | (~distinct_points(X, Y))) <=> ![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.41 tff(149,plain,
% 0.20/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))), 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_lines(U, V)) | (~distinct_points(X, Y)))) <=> (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_lines(U, V)) | (~distinct_points(X, Y)))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[149])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 (![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)))) <=> ![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(152,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(153,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[152])).
% 0.20/0.42 tff(154,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/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.20/0.42 tff(157,plain,(
% 0.20/0.42 ![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))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[156])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), 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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 ((apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.42 tff(163,plain,
% 0.20/0.42 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.20/0.42 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.42 tff(164,plain,
% 0.20/0.42 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(165,plain,
% 0.20/0.42 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.42 tff(166,plain,
% 0.20/0.42 (~distinct_lines(Y!1, X!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[165, 159, 146, 142, 138, 124, 102])).
% 0.20/0.42 tff(167,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(168,plain,
% 0.20/0.42 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(169,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[168])).
% 0.20/0.42 tff(170,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(transitivity,[status(thm)],[169, 167])).
% 0.20/0.42 tff(171,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(172,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.42 tff(173,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[172, 66, 56, 166, 29])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------