%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO196+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 05:05:53 AM UTC 2025
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO196+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:42:41 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(incident_point_and_line_type, type, (
% 0.18/0.40 incident_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.18/0.40 tptp_fun_Y_2: $i)).
% 0.18/0.40 tff(intersection_point_type, type, (
% 0.18/0.40 intersection_point: ( $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_V_0_type, type, (
% 0.18/0.40 tptp_fun_V_0: $i)).
% 0.18/0.40 tff(tptp_fun_U_1_type, type, (
% 0.18/0.40 tptp_fun_U_1: $i)).
% 0.18/0.40 tff(apart_point_and_line_type, type, (
% 0.18/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.40 tff(distinct_points_type, type, (
% 0.18/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_X_3_type, type, (
% 0.18/0.40 tptp_fun_X_3: $i)).
% 0.18/0.40 tff(distinct_lines_type, type, (
% 0.18/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(convergent_lines_type, type, (
% 0.18/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(unorthogonal_lines_type, type, (
% 0.18/0.40 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(orthogonal_through_point_type, type, (
% 0.18/0.40 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.18/0.40 tff(1,assumption,(~convergent_lines(V!0, U!1)), introduced(assumption)).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(5,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.40 tff(7,plain,(
% 0.18/0.40 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.40 inference(skolemize,[status(sab)],[6])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (~unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.40 tff(18,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.40 tff(21,plain,(
% 0.18/0.40 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[20])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), 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(X!3, U!1)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 ((unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | (~convergent_lines(U!1, U!1))) <=> (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), 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(X!3, U!1)), U!1) | (~convergent_lines(U!1, U!1))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[25])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), 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(X!3, U!1)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[26, 24])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(X!3, U!1)), U!1) | (~convergent_lines(U!1, U!1))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (~convergent_lines(U!1, U!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[29, 23, 10])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((((convergent_lines(X, Y) & convergent_lines(U, V)) & incident_point_and_line(intersection_point(X, Y), U)) & incident_point_and_line(intersection_point(X, Y), V)) => (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(33,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : ((((convergent_lines(X, Y) & convergent_lines(U, V)) & incident_point_and_line(intersection_point(X, Y), U)) & incident_point_and_line(intersection_point(X, Y), V)) => (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.18/0.40 tff(38,plain,(
% 0.18/0.40 ~((~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & incident_point_and_line(intersection_point(X!3, Y!2), U!1) & incident_point_and_line(intersection_point(X!3, Y!2), V!0))) | (incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[37])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & incident_point_and_line(intersection_point(X!3, Y!2), U!1) & incident_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.18/0.40 inference(or_elim,[status(thm)],[38])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (convergent_lines(U!1, V!0)),
% 0.18/0.40 inference(and_elim,[status(thm)],[39])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.40 tff(46,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.40 tff(49,plain,(
% 0.18/0.40 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[48])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | convergent_lines(U!1, U!1) | convergent_lines(V!0, U!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | convergent_lines(U!1, U!1) | convergent_lines(V!0, U!1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 ((convergent_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0))) <=> ((~convergent_lines(U!1, V!0)) | convergent_lines(U!1, U!1) | convergent_lines(V!0, U!1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(53,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | convergent_lines(U!1, U!1) | convergent_lines(V!0, U!1)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[52])).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | convergent_lines(U!1, U!1) | convergent_lines(V!0, U!1))),
% 0.18/0.41 inference(transitivity,[status(thm)],[53, 51])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | convergent_lines(U!1, U!1) | convergent_lines(V!0, U!1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[56, 50, 40, 30, 1])).
% 0.18/0.41 tff(58,plain,(convergent_lines(V!0, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(62,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.41 tff(64,plain,(
% 0.18/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.41 inference(skolemize,[status(sab)],[63])).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.41 tff(66,plain,
% 0.18/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(V!0, V!0))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (~convergent_lines(V!0, V!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.18/0.41 tff(68,assumption,(~distinct_lines(U!1, V!0)), introduced(assumption)).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.41 tff(74,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.18/0.41 tff(77,plain,(
% 0.18/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[76])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(U!1, V!0) | convergent_lines(V!0, V!0) | (~convergent_lines(V!0, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(U!1, V!0) | convergent_lines(V!0, V!0) | (~convergent_lines(V!0, U!1)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(U!1, V!0) | convergent_lines(V!0, V!0) | (~convergent_lines(V!0, U!1)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(81,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(U!1, V!0) | convergent_lines(V!0, V!0) | (~convergent_lines(V!0, U!1))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[81, 78, 68, 67, 58])).
% 0.18/0.41 tff(83,plain,(distinct_lines(U!1, V!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.18/0.41 tff(89,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.18/0.41 tff(92,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[91])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) <=> incident_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) <=> incident_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (incident_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.18/0.41 inference(and_elim,[status(thm)],[39])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 ((apart_point_and_line(intersection_point(X!3, Y!2), V!0) <=> incident_point_and_line(intersection_point(X!3, Y!2), V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | (~incident_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 ((apart_point_and_line(intersection_point(X!3, Y!2), V!0) <=> incident_point_and_line(intersection_point(X!3, Y!2), V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(intersection_point(X!3, Y!2), U!1) <=> incident_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (~(apart_point_and_line(intersection_point(X!3, Y!2), U!1) <=> incident_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[100, 93])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 (incident_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.18/0.41 inference(and_elim,[status(thm)],[39])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 ((apart_point_and_line(intersection_point(X!3, Y!2), U!1) <=> incident_point_and_line(intersection_point(X!3, Y!2), U!1)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | (~incident_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 ((apart_point_and_line(intersection_point(X!3, Y!2), U!1) <=> incident_point_and_line(intersection_point(X!3, Y!2), U!1)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.18/0.41 tff(111,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.18/0.41 tff(114,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[113])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (((~![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 ((~![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))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[118, 115, 40])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[120])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[123])).
% 0.18/0.41 tff(125,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.18/0.41 tff(128,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[127])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (((~![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 ((~![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))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[132, 129, 40])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[134])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(137,plain,
% 0.18/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[136])).
% 0.18/0.42 tff(138,plain,
% 0.18/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(139,plain,
% 0.18/0.42 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(140,plain,
% 0.18/0.42 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[139])).
% 0.18/0.42 tff(141,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.18/0.42 tff(143,plain,
% 0.18/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.18/0.42 tff(144,plain,(
% 0.18/0.42 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[143])).
% 0.18/0.42 tff(145,plain,
% 0.18/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.18/0.42 tff(146,plain,
% 0.18/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[145, 135])).
% 0.18/0.42 tff(147,plain,
% 0.18/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(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), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(U!1, V!0)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(148,plain,
% 0.18/0.42 ((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), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, V!0)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))) <=> (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(U!1, V!0)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(149,plain,
% 0.18/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!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), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, V!0)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))) <=> ((~![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), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(U!1, V!0))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[148])).
% 0.18/0.42 tff(150,plain,
% 0.18/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!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), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, V!0)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))) <=> ((~![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), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(U!1, V!0)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[149, 147])).
% 0.18/0.42 tff(151,plain,
% 0.18/0.42 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!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), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(U!1, V!0)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(152,plain,
% 0.18/0.42 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(U!1, V!0))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.18/0.42 tff(153,plain,
% 0.18/0.42 ((~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(U!1, V!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[152, 146, 133, 119, 105, 99])).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[153, 83])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 (convergent_lines(X!3, Y!2)),
% 0.18/0.42 inference(and_elim,[status(thm)],[39])).
% 0.18/0.42 tff(156,plain,
% 0.18/0.42 (((~![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(157,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(158,plain,
% 0.18/0.42 ((~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.18/0.42 tff(159,plain,
% 0.18/0.42 (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[158, 129, 155])).
% 0.18/0.42 tff(160,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(161,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[160])).
% 0.18/0.42 tff(162,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(163,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(164,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[163])).
% 0.18/0.42 tff(165,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/sandbox/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.18/0.42 tff(166,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.42 tff(167,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.18/0.42 tff(168,plain,(
% 0.18/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[167])).
% 0.18/0.43 tff(169,plain,
% 0.18/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.18/0.43 tff(170,plain,
% 0.18/0.43 (((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(171,plain,
% 0.18/0.43 ((distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> (apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(172,plain,
% 0.18/0.43 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[171])).
% 0.18/0.43 tff(173,plain,
% 0.18/0.43 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[172, 170])).
% 0.18/0.43 tff(174,plain,
% 0.18/0.43 ((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(175,plain,
% 0.18/0.43 ((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.43 tff(176,plain,
% 0.18/0.43 (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[175, 169, 159, 154])).
% 0.18/0.43 tff(177,plain,
% 0.18/0.43 (((~![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(178,plain,
% 0.18/0.43 ((~![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)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(179,plain,
% 0.18/0.43 ((~![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))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.18/0.43 tff(180,plain,
% 0.18/0.43 (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[179, 115, 155])).
% 0.18/0.43 tff(181,plain,
% 0.18/0.43 (((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(182,plain,
% 0.18/0.43 ((distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3))) <=> (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(183,plain,
% 0.18/0.43 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.43 tff(184,plain,
% 0.18/0.43 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[183, 181])).
% 0.18/0.43 tff(185,plain,
% 0.18/0.43 ((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(186,plain,
% 0.18/0.43 ((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.18/0.43 tff(187,plain,
% 0.18/0.43 (~apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[186, 169, 180, 154])).
% 0.18/0.43 tff(188,assumption,(apart_point_and_line(intersection_point(U!1, V!0), X!3) <=> incident_point_and_line(intersection_point(U!1, V!0), X!3)), introduced(assumption)).
% 0.18/0.43 tff(189,plain,
% 0.18/0.43 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(intersection_point(U!1, V!0), X!3) <=> incident_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(190,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[189, 93, 188])).
% 0.18/0.43 tff(191,plain,(~(apart_point_and_line(intersection_point(U!1, V!0), X!3) <=> incident_point_and_line(intersection_point(U!1, V!0), X!3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(192,plain,
% 0.18/0.43 ((apart_point_and_line(intersection_point(U!1, V!0), X!3) <=> incident_point_and_line(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | incident_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(193,plain,
% 0.18/0.43 (apart_point_and_line(intersection_point(U!1, V!0), X!3) | incident_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.18/0.43 tff(194,plain,
% 0.18/0.43 (incident_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[193, 187])).
% 0.18/0.43 tff(195,plain,
% 0.18/0.43 ((~(~((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2))))) <=> ((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(196,plain,
% 0.18/0.43 ((incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2)) <=> (~((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(197,plain,
% 0.18/0.43 ((~(incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> (~(~((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[196])).
% 0.18/0.43 tff(198,plain,
% 0.18/0.43 ((~(incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> ((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[197, 195])).
% 0.18/0.43 tff(199,plain,
% 0.18/0.43 (~(incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 0.18/0.43 inference(or_elim,[status(thm)],[38])).
% 0.18/0.43 tff(200,plain,
% 0.18/0.43 ((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.18/0.43 tff(201,plain,
% 0.18/0.43 (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[200, 194])).
% 0.18/0.43 tff(202,plain,
% 0.18/0.43 ((apart_point_and_line(intersection_point(U!1, V!0), Y!2) <=> incident_point_and_line(intersection_point(U!1, V!0), Y!2)) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | incident_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(203,plain,
% 0.18/0.43 (apart_point_and_line(intersection_point(U!1, V!0), Y!2) <=> incident_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[202, 201, 176])).
% 0.18/0.43 tff(204,plain,
% 0.18/0.43 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) <=> incident_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(205,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[204, 93, 203])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------