%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO201+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:05:54 AM UTC 2025
% Result : Theorem 0.10s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO201+3 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n010.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Jun 19 14:42:41 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.38 % SZS status Theorem
% 0.10/0.38 % SZS output start Proof
% 0.10/0.38 tff(distinct_lines_type, type, (
% 0.10/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.10/0.38 tff(tptp_fun_X_1_type, type, (
% 0.10/0.38 tptp_fun_X_1: $i)).
% 0.10/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.10/0.38 tptp_fun_Y_0: $i)).
% 0.10/0.38 tff(convergent_lines_type, type, (
% 0.10/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.10/0.38 tff(unorthogonal_lines_type, type, (
% 0.10/0.38 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.10/0.38 tff(orthogonal_through_point_type, type, (
% 0.10/0.38 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.10/0.38 tff(intersection_point_type, type, (
% 0.10/0.38 intersection_point: ( $i * $i ) > $i)).
% 0.10/0.38 tff(equal_points_type, type, (
% 0.10/0.38 equal_points: ( $i * $i ) > $o)).
% 0.10/0.38 tff(distinct_points_type, type, (
% 0.10/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.10/0.38 tff(apart_point_and_line_type, type, (
% 0.10/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.10/0.38 tff(1,plain,
% 0.10/0.38 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(2,plain,
% 0.10/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.10/0.38 tff(3,plain,
% 0.10/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.10/0.38 tff(5,plain,
% 0.10/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.10/0.38 tff(6,plain,(
% 0.10/0.38 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.10/0.38 inference(skolemize,[status(sab)],[5])).
% 0.10/0.38 tff(7,plain,
% 0.10/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.10/0.38 tff(8,plain,
% 0.10/0.38 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1))),
% 0.10/0.38 inference(quant_inst,[status(thm)],[])).
% 0.10/0.38 tff(9,plain,
% 0.10/0.38 (~unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1)),
% 0.10/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.10/0.38 tff(10,plain,
% 0.10/0.38 (^[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))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(11,plain,
% 0.10/0.38 (![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)))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.10/0.38 tff(12,plain,
% 0.10/0.38 (^[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)))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(13,plain,
% 0.10/0.38 (![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)))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.10/0.38 tff(14,plain,
% 0.10/0.38 (![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)))))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(15,plain,
% 0.10/0.38 (^[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))))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(16,plain,
% 0.10/0.38 (![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)))))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.10/0.38 tff(17,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.10/0.38 tff(18,plain,
% 0.10/0.38 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.10/0.38 tff(19,plain,
% 0.10/0.38 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.10/0.38 tff(20,plain,(
% 0.10/0.38 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.10/0.38 inference(skolemize,[status(sab)],[19])).
% 0.10/0.38 tff(21,plain,
% 0.10/0.38 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.10/0.38 tff(22,plain,
% 0.10/0.38 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.10/0.38 tff(23,plain,
% 0.10/0.38 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(X!1, X!1)) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!1, X!1)) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(24,plain,
% 0.10/0.38 ((unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | (~convergent_lines(X!1, X!1))) <=> ((~convergent_lines(X!1, X!1)) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(25,plain,
% 0.10/0.38 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | (~convergent_lines(X!1, X!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(X!1, X!1)) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1)))),
% 0.10/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.10/0.38 tff(26,plain,
% 0.10/0.38 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | (~convergent_lines(X!1, X!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!1, X!1)) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1))),
% 0.10/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.10/0.38 tff(27,plain,
% 0.10/0.38 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1) | (~convergent_lines(X!1, X!1)))),
% 0.10/0.38 inference(quant_inst,[status(thm)],[])).
% 0.10/0.38 tff(28,plain,
% 0.10/0.38 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!1, X!1)) | unorthogonal_lines(orthogonal_through_point(X!1, intersection_point(X!1, Y!0)), X!1)),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.10/0.38 tff(29,plain,
% 0.10/0.38 (~convergent_lines(X!1, X!1)),
% 0.10/0.38 inference(unit_resolution,[status(thm)],[28, 22, 9])).
% 0.10/0.38 tff(30,plain,
% 0.10/0.38 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(31,plain,
% 0.10/0.38 ((~![X: $i, Y: $i] : (convergent_lines(X, Y) => equal_points(intersection_point(X, Y), intersection_point(Y, X)))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(32,axiom,(~![X: $i, Y: $i] : (convergent_lines(X, Y) => equal_points(intersection_point(X, Y), intersection_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.10/0.38 tff(33,plain,
% 0.10/0.38 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.10/0.38 tff(34,plain,
% 0.10/0.38 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.10/0.38 tff(35,plain,
% 0.10/0.38 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.10/0.38 tff(36,plain,
% 0.10/0.38 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.10/0.38 tff(37,plain,(
% 0.10/0.38 ~((~convergent_lines(X!1, Y!0)) | equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.10/0.38 inference(skolemize,[status(sab)],[36])).
% 0.10/0.38 tff(38,plain,
% 0.10/0.38 (convergent_lines(X!1, Y!0)),
% 0.10/0.38 inference(or_elim,[status(thm)],[37])).
% 0.10/0.38 tff(39,plain,
% 0.10/0.38 (^[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))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(40,plain,
% 0.10/0.38 (![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)))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.10/0.38 tff(41,plain,
% 0.10/0.38 (![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)))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(42,plain,
% 0.10/0.38 (^[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)))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(43,plain,
% 0.10/0.39 (![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)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.10/0.39 tff(44,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.10/0.39 tff(45,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.10/0.39 tff(46,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.10/0.39 tff(47,plain,(
% 0.10/0.39 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[46])).
% 0.10/0.39 tff(48,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.10/0.39 tff(49,plain,
% 0.10/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(50,plain,
% 0.10/0.39 ((distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0))) <=> ((~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(51,plain,
% 0.10/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1)))),
% 0.10/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.10/0.39 tff(52,plain,
% 0.10/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.10/0.39 inference(transitivity,[status(thm)],[51, 49])).
% 0.10/0.39 tff(53,plain,
% 0.10/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(54,plain,
% 0.10/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.10/0.39 tff(55,plain,
% 0.10/0.39 (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[54, 48, 38])).
% 0.10/0.39 tff(56,plain,
% 0.10/0.39 (distinct_lines(Y!0, X!1)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[55, 29])).
% 0.10/0.39 tff(57,plain,
% 0.10/0.39 (^[X: $i, Y: $i] : refl((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(58,plain,
% 0.10/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.10/0.39 tff(59,plain,
% 0.10/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(60,plain,
% 0.10/0.39 (^[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)))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(61,plain,
% 0.10/0.39 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.10/0.39 tff(62,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.10/0.39 tff(63,plain,
% 0.10/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.10/0.39 tff(64,plain,
% 0.10/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.10/0.39 tff(65,plain,(
% 0.10/0.39 ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[64])).
% 0.10/0.39 tff(66,plain,
% 0.10/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.10/0.39 tff(67,plain,
% 0.10/0.39 ((~![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))) | (~(distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(68,plain,
% 0.10/0.39 (~(distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.10/0.39 tff(69,plain,
% 0.10/0.39 (~equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.10/0.39 inference(or_elim,[status(thm)],[37])).
% 0.10/0.39 tff(70,plain,
% 0.10/0.39 ((distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) | equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.10/0.39 inference(tautology,[status(thm)],[])).
% 0.10/0.39 tff(71,plain,
% 0.10/0.39 ((distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.10/0.39 tff(72,plain,
% 0.10/0.39 (distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.10/0.39 tff(73,plain,
% 0.10/0.39 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(74,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.10/0.39 tff(75,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(76,plain,
% 0.10/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(77,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.10/0.39 tff(78,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.10/0.39 tff(79,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.10/0.39 tff(80,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.10/0.39 tff(81,plain,(
% 0.10/0.39 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[80])).
% 0.10/0.39 tff(82,plain,
% 0.10/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.10/0.39 tff(83,plain,
% 0.10/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(84,plain,
% 0.10/0.39 ((convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0))) <=> ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(85,plain,
% 0.10/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)))),
% 0.10/0.39 inference(monotonicity,[status(thm)],[84])).
% 0.10/0.39 tff(86,plain,
% 0.10/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.10/0.39 inference(transitivity,[status(thm)],[85, 83])).
% 0.10/0.39 tff(87,plain,
% 0.10/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(88,plain,
% 0.10/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.10/0.39 tff(89,plain,
% 0.10/0.39 (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[88, 82, 38])).
% 0.10/0.39 tff(90,plain,
% 0.10/0.39 (convergent_lines(Y!0, X!1)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[89, 29])).
% 0.10/0.39 tff(91,plain,
% 0.10/0.39 (^[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))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(92,plain,
% 0.10/0.39 (![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)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[91])).
% 0.10/0.39 tff(93,plain,
% 0.10/0.39 (![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)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(94,plain,
% 0.10/0.39 (^[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))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(95,plain,
% 0.10/0.39 (![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)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[94])).
% 0.10/0.39 tff(96,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.10/0.39 tff(97,plain,
% 0.10/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.10/0.39 tff(98,plain,
% 0.10/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.10/0.39 tff(99,plain,(
% 0.10/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[98])).
% 0.10/0.39 tff(100,plain,
% 0.10/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.10/0.39 tff(101,plain,
% 0.10/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(102,plain,
% 0.10/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(103,plain,
% 0.10/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.10/0.39 tff(104,plain,
% 0.10/0.39 ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[103, 100])).
% 0.10/0.39 tff(105,plain,
% 0.10/0.39 (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[104, 90])).
% 0.10/0.39 tff(106,plain,
% 0.10/0.39 (^[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))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(107,plain,
% 0.10/0.39 (![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)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[106])).
% 0.10/0.39 tff(108,plain,
% 0.10/0.39 (![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)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(109,plain,
% 0.10/0.39 (^[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))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(110,plain,
% 0.10/0.39 (![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)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[109])).
% 0.10/0.39 tff(111,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.10/0.39 tff(112,plain,
% 0.10/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.10/0.39 tff(113,plain,
% 0.10/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.10/0.39 tff(114,plain,(
% 0.10/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[113])).
% 0.10/0.39 tff(115,plain,
% 0.10/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.10/0.39 tff(116,plain,
% 0.10/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(117,plain,
% 0.10/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(118,plain,
% 0.10/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.10/0.39 tff(119,plain,
% 0.10/0.39 ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.10/0.39 tff(120,plain,
% 0.10/0.39 (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[119, 90])).
% 0.10/0.39 tff(121,plain,
% 0.10/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(122,plain,
% 0.10/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(123,plain,
% 0.10/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1))),
% 0.10/0.40 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.10/0.40 tff(124,plain,
% 0.10/0.40 (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)),
% 0.10/0.40 inference(unit_resolution,[status(thm)],[123, 115, 38])).
% 0.10/0.40 tff(125,plain,
% 0.10/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)))),
% 0.10/0.40 inference(rewrite,[status(thm)],[])).
% 0.10/0.40 tff(126,plain,
% 0.10/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)))),
% 0.10/0.40 inference(quant_inst,[status(thm)],[])).
% 0.10/0.40 tff(127,plain,
% 0.10/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0))),
% 0.10/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.10/0.40 tff(128,plain,
% 0.10/0.40 (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)),
% 0.10/0.40 inference(unit_resolution,[status(thm)],[127, 100, 38])).
% 0.10/0.40 tff(129,plain,
% 0.10/0.40 (^[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))))),
% 0.10/0.40 inference(bind,[status(th)],[])).
% 0.10/0.40 tff(130,plain,
% 0.10/0.40 (![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)))),
% 0.10/0.40 inference(quant_intro,[status(thm)],[129])).
% 0.10/0.40 tff(131,plain,
% 0.10/0.40 (^[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)))))),
% 0.10/0.40 inference(bind,[status(th)],[])).
% 0.10/0.40 tff(132,plain,
% 0.10/0.40 (![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)))),
% 0.10/0.40 inference(quant_intro,[status(thm)],[131])).
% 0.10/0.40 tff(133,plain,
% 0.10/0.40 (![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))))),
% 0.10/0.40 inference(rewrite,[status(thm)],[])).
% 0.10/0.40 tff(134,plain,
% 0.10/0.40 (^[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))))))),
% 0.10/0.40 inference(bind,[status(th)],[])).
% 0.10/0.40 tff(135,plain,
% 0.10/0.40 (![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))))),
% 0.10/0.40 inference(quant_intro,[status(thm)],[134])).
% 0.10/0.40 tff(136,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.18/0.40 tff(137,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.40 tff(138,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.18/0.40 tff(139,plain,(
% 0.18/0.40 ![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))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[138])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 (((~![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!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!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!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(143,plain,
% 0.18/0.40 ((apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) <=> (apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(144,plain,
% 0.18/0.40 (((~![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(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!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!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[143])).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 (((~![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(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!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!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[144, 142])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 ((~![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(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(147,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[147, 141, 128, 124, 120, 105, 72, 56])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------