%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO191+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:05:51 AM UTC 2025
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO191+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:40:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(convergent_lines_type, type, (
% 0.19/0.45 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.45 tff(tptp_fun_X_3_type, type, (
% 0.19/0.45 tptp_fun_X_3: $i)).
% 0.19/0.45 tff(distinct_lines_type, type, (
% 0.19/0.45 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.45 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.45 tptp_fun_Y_2: $i)).
% 0.19/0.45 tff(distinct_points_type, type, (
% 0.19/0.45 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.45 tff(intersection_point_type, type, (
% 0.19/0.45 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.45 tff(tptp_fun_V_0_type, type, (
% 0.19/0.45 tptp_fun_V_0: $i)).
% 0.19/0.45 tff(tptp_fun_U_1_type, type, (
% 0.19/0.45 tptp_fun_U_1: $i)).
% 0.19/0.45 tff(apart_point_and_line_type, type, (
% 0.19/0.45 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.45 tff(parallel_through_point_type, type, (
% 0.19/0.45 parallel_through_point: ( $i * $i ) > $i)).
% 0.19/0.45 tff(unorthogonal_lines_type, type, (
% 0.19/0.45 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.45 tff(orthogonal_through_point_type, type, (
% 0.19/0.45 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(4,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.45 tff(6,plain,(
% 0.19/0.45 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.45 inference(skolemize,[status(sab)],[5])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (~convergent_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.45 tff(15,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.45 tff(18,plain,(
% 0.19/0.45 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.45 inference(skolemize,[status(sab)],[17])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1)) | convergent_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1)) | convergent_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1)) | convergent_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1)) | convergent_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (~distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(27,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.45 tff(29,plain,(
% 0.19/0.45 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.45 inference(skolemize,[status(sab)],[28])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (~unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (^[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))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.45 tff(40,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')).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.45 tff(43,plain,(
% 0.19/0.45 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[42])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 ((unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1))) <=> (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (~convergent_lines(U!1, U!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[51, 45, 32])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))) <=> (~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (((convergent_lines(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(intersection_point(X, Y), U) | apart_point_and_line(intersection_point(X, Y), V))) => (apart_point_and_line(intersection_point(U, V), X) | apart_point_and_line(intersection_point(U, V), Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(56,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((convergent_lines(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(intersection_point(X, Y), U) | apart_point_and_line(intersection_point(X, Y), V))) => (apart_point_and_line(intersection_point(U, V), X) | apart_point_and_line(intersection_point(U, V), Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[59, 54])).
% 0.19/0.46 tff(61,plain,(
% 0.19/0.46 ~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[60])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[61, 53])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.19/0.46 inference(or_elim,[status(thm)],[62])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (convergent_lines(U!1, V!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[63])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.46 tff(70,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')).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.46 tff(73,plain,(
% 0.19/0.46 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[72])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[77, 74, 64])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.46 tff(84,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.19/0.46 tff(87,plain,(
% 0.19/0.46 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[86])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)) | convergent_lines(U!1, U!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)) | convergent_lines(U!1, U!1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 ((convergent_lines(U!1, U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1))) <=> (apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)) | convergent_lines(U!1, U!1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(U!1, U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)) | convergent_lines(U!1, U!1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(U!1, U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)) | convergent_lines(U!1, U!1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(U!1, U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, U!1)) | convergent_lines(U!1, U!1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (~distinct_lines(U!1, U!1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[94, 88, 78, 52])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.46 tff(101,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.19/0.46 tff(104,plain,(
% 0.19/0.46 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[103])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.46 tff(106,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(U!1, U!1) | distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(U!1, U!1) | distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 ((distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))))) <=> (distinct_lines(U!1, U!1) | distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(U!1, U!1) | distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(U!1, U!1) | distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(U!1, U!1) | distinct_lines(parallel_through_point(U!1, intersection_point(X!3, Y!2)), U!1) | (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (~distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[111, 105, 95, 23])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(116,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.46 tff(118,plain,(
% 0.19/0.46 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[117])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(121,plain,
% 0.19/0.46 (~apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.47 tff(127,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/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.19/0.47 tff(130,plain,(
% 0.19/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[129])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 ((distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))) <=> ((~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[134, 132])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | apart_point_and_line(intersection_point(X!3, Y!2), parallel_through_point(U!1, intersection_point(X!3, Y!2))) | distinct_lines(U!1, parallel_through_point(U!1, intersection_point(X!3, Y!2)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[137, 131, 121, 112])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.19/0.47 inference(and_elim,[status(thm)],[63])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (apart_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.19/0.47 tff(141,assumption,(~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))), introduced(assumption)).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[142])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[145])).
% 0.19/0.47 tff(147,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')).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.19/0.47 tff(150,plain,(
% 0.19/0.47 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[149])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[154, 151, 64])).
% 0.19/0.47 tff(156,assumption,(apart_point_and_line(intersection_point(X!3, Y!2), V!0)), introduced(assumption)).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.47 tff(159,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[160])).
% 0.19/0.47 tff(162,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.19/0.47 tff(165,plain,(
% 0.19/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[164])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))) <=> (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.48 tff(173,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[172, 166, 156, 155, 141])).
% 0.19/0.48 tff(174,plain,(distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[174, 140])).
% 0.19/0.48 tff(176,plain,
% 0.19/0.48 (convergent_lines(X!3, Y!2)),
% 0.19/0.48 inference(and_elim,[status(thm)],[63])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(178,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(179,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.48 tff(180,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[179, 74, 176])).
% 0.19/0.48 tff(181,plain,
% 0.19/0.48 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(182,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(183,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.19/0.48 tff(184,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[183, 151, 176])).
% 0.19/0.48 tff(185,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.19/0.48 inference(or_elim,[status(thm)],[62])).
% 0.19/0.48 tff(186,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.19/0.48 inference(or_elim,[status(thm)],[62])).
% 0.19/0.48 tff(187,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(188,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.48 tff(189,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(190,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[189])).
% 0.19/0.48 tff(191,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(192,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(193,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[192])).
% 0.19/0.48 tff(194,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')).
% 0.19/0.48 tff(195,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.19/0.48 tff(196,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.19/0.48 tff(197,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[196])).
% 0.19/0.48 tff(198,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.19/0.48 tff(199,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[198, 188])).
% 0.19/0.48 tff(200,plain,
% 0.19/0.48 (((~![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(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!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(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(201,plain,
% 0.19/0.48 ((apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))) <=> (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(202,plain,
% 0.19/0.48 (((~![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(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!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(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[201])).
% 0.19/0.48 tff(203,plain,
% 0.19/0.48 (((~![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(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!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(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[202, 200])).
% 0.19/0.48 tff(204,plain,
% 0.19/0.48 ((~![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(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(205,plain,
% 0.19/0.48 ((~![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(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.48 tff(206,plain,
% 0.19/0.48 ((~distinct_lines(Y!2, X!3)) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[205, 199, 186, 185, 184, 180])).
% 0.19/0.48 tff(207,plain,
% 0.19/0.48 (~distinct_lines(Y!2, X!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[206, 175])).
% 0.19/0.48 tff(208,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(209,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[208])).
% 0.19/0.48 tff(210,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(211,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(212,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.48 tff(213,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')).
% 0.19/0.48 tff(214,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.48 tff(215,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.19/0.48 tff(216,plain,(
% 0.19/0.48 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[215])).
% 0.19/0.48 tff(217,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.19/0.49 tff(218,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!3, Y!2)) | distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!3, Y!2)) | distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(219,plain,
% 0.19/0.49 ((distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2))) <=> ((~convergent_lines(X!3, Y!2)) | distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(220,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!3, Y!2)) | distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.49 tff(221,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!3, Y!2)) | distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3))),
% 0.19/0.49 inference(transitivity,[status(thm)],[220, 218])).
% 0.19/0.49 tff(222,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(223,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!3, Y!2)) | distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.49 tff(224,plain,
% 0.19/0.49 (distinct_lines(Y!2, X!3) | convergent_lines(X!3, X!3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[223, 217, 176])).
% 0.19/0.49 tff(225,plain,
% 0.19/0.49 (convergent_lines(X!3, X!3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[224, 207])).
% 0.19/0.49 tff(226,plain,
% 0.19/0.49 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(227,plain,
% 0.19/0.49 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.49 tff(228,plain,
% 0.19/0.49 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(229,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.49 tff(230,plain,
% 0.19/0.49 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.19/0.49 tff(231,plain,(
% 0.19/0.49 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.49 inference(skolemize,[status(sab)],[230])).
% 0.19/0.49 tff(232,plain,
% 0.19/0.49 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.19/0.49 tff(233,plain,
% 0.19/0.49 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!3, X!3))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(234,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[233, 232, 225])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------