%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO193+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:05:52 AM UTC 2025
% Result : Theorem 0.72s 0.89s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO193+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 14:39:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.72/0.89 % SZS status Theorem
% 0.72/0.89 % SZS output start Proof
% 0.72/0.89 tff(convergent_lines_type, type, (
% 0.72/0.89 convergent_lines: ( $i * $i ) > $o)).
% 0.72/0.89 tff(tptp_fun_X_2_type, type, (
% 0.72/0.89 tptp_fun_X_2: $i)).
% 0.72/0.89 tff(unorthogonal_lines_type, type, (
% 0.72/0.89 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.72/0.89 tff(orthogonal_through_point_type, type, (
% 0.72/0.89 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.72/0.89 tff(intersection_point_type, type, (
% 0.72/0.89 intersection_point: ( $i * $i ) > $i)).
% 0.72/0.89 tff(tptp_fun_Z_0_type, type, (
% 0.72/0.89 tptp_fun_Z_0: $i)).
% 0.72/0.89 tff(tptp_fun_Y_1_type, type, (
% 0.72/0.89 tptp_fun_Y_1: $i)).
% 0.72/0.89 tff(line_connecting_type, type, (
% 0.72/0.89 line_connecting: ( $i * $i ) > $i)).
% 0.72/0.89 tff(distinct_lines_type, type, (
% 0.72/0.89 distinct_lines: ( $i * $i ) > $o)).
% 0.72/0.89 tff(distinct_points_type, type, (
% 0.72/0.89 distinct_points: ( $i * $i ) > $o)).
% 0.72/0.89 tff(apart_point_and_line_type, type, (
% 0.72/0.89 apart_point_and_line: ( $i * $i ) > $o)).
% 0.72/0.89 tff(1,plain,
% 0.72/0.89 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(2,plain,
% 0.72/0.89 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1])).
% 0.72/0.89 tff(3,plain,
% 0.72/0.89 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.72/0.89 tff(5,plain,
% 0.72/0.89 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.72/0.89 tff(6,plain,(
% 0.72/0.89 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.72/0.89 inference(skolemize,[status(sab)],[5])).
% 0.72/0.89 tff(7,plain,
% 0.72/0.89 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.72/0.89 tff(8,plain,
% 0.72/0.89 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(9,plain,
% 0.72/0.89 (~unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.72/0.89 tff(10,plain,
% 0.72/0.89 (^[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))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(11,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[10])).
% 0.72/0.89 tff(12,plain,
% 0.72/0.89 (^[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)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(13,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[12])).
% 0.72/0.89 tff(14,plain,
% 0.72/0.89 (![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)))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(15,plain,
% 0.72/0.89 (^[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))))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(16,plain,
% 0.72/0.89 (![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)))))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[15])).
% 0.72/0.89 tff(17,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.72/0.89 tff(18,plain,
% 0.72/0.89 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.72/0.89 tff(19,plain,
% 0.72/0.89 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.72/0.89 tff(20,plain,(
% 0.72/0.89 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.72/0.89 inference(skolemize,[status(sab)],[19])).
% 0.72/0.89 tff(21,plain,
% 0.72/0.89 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.72/0.89 tff(22,plain,
% 0.72/0.89 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.72/0.89 tff(23,plain,
% 0.72/0.89 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(24,plain,
% 0.72/0.89 ((unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | (~convergent_lines(X!2, X!2))) <=> ((~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(25,plain,
% 0.72/0.89 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | (~convergent_lines(X!2, X!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2)))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[24])).
% 0.72/0.89 tff(26,plain,
% 0.72/0.89 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | (~convergent_lines(X!2, X!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2))),
% 0.72/0.89 inference(transitivity,[status(thm)],[25, 23])).
% 0.72/0.89 tff(27,plain,
% 0.72/0.89 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2) | (~convergent_lines(X!2, X!2)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(28,plain,
% 0.72/0.89 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(X!2, X!2)) | unorthogonal_lines(orthogonal_through_point(X!2, intersection_point(orthogonal_through_point(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), intersection_point(X!2, Y!1)), Z!0)), X!2)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.72/0.89 tff(29,plain,
% 0.72/0.89 (~convergent_lines(X!2, X!2)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[28, 22, 9])).
% 0.72/0.89 tff(30,assumption,(~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))), introduced(assumption)).
% 0.72/0.89 tff(31,plain,
% 0.72/0.89 ((~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))) <=> (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(32,plain,
% 0.72/0.89 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Z, Y), X) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Z, Y), X) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(33,plain,
% 0.72/0.89 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(Z, Y), X)))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Z, Y), X) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(34,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(Z, Y), X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.72/0.89 tff(35,plain,
% 0.72/0.89 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Z, Y), X) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.72/0.89 tff(36,plain,
% 0.72/0.89 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Z, Y), X) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.72/0.89 tff(37,plain,
% 0.72/0.89 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Z, Y), X) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.72/0.89 tff(38,plain,
% 0.72/0.89 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Z, Y), X) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.72/0.89 tff(39,plain,(
% 0.72/0.89 ~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.72/0.89 inference(skolemize,[status(sab)],[38])).
% 0.72/0.89 tff(40,plain,
% 0.72/0.89 (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.72/0.89 tff(41,plain,
% 0.72/0.89 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)),
% 0.72/0.89 inference(or_elim,[status(thm)],[40])).
% 0.72/0.89 tff(42,plain,
% 0.72/0.89 (convergent_lines(Z!0, Y!1)),
% 0.72/0.89 inference(and_elim,[status(thm)],[41])).
% 0.72/0.89 tff(43,plain,
% 0.72/0.89 (^[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))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(44,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[43])).
% 0.72/0.89 tff(45,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(46,plain,
% 0.72/0.89 (^[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))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(47,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[46])).
% 0.72/0.89 tff(48,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')).
% 0.72/0.89 tff(49,plain,
% 0.72/0.89 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.72/0.89 tff(50,plain,
% 0.72/0.89 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.72/0.89 tff(51,plain,(
% 0.72/0.89 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[50])).
% 0.72/0.89 tff(52,plain,
% 0.72/0.89 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.72/0.89 tff(53,plain,
% 0.72/0.89 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(54,plain,
% 0.72/0.89 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(55,plain,
% 0.72/0.89 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.72/0.89 tff(56,plain,
% 0.72/0.89 (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.72/0.89 tff(57,plain,
% 0.72/0.89 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.72/0.89 inference(or_elim,[status(thm)],[40])).
% 0.72/0.89 tff(58,plain,
% 0.72/0.89 (^[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))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(59,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[58])).
% 0.72/0.89 tff(60,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(61,plain,
% 0.72/0.89 (^[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)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(62,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[61])).
% 0.72/0.89 tff(63,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')).
% 0.72/0.89 tff(64,plain,
% 0.72/0.89 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.72/0.89 tff(65,plain,
% 0.72/0.89 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.72/0.89 tff(66,plain,(
% 0.72/0.89 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[65])).
% 0.72/0.89 tff(67,plain,
% 0.72/0.89 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.72/0.89 tff(68,plain,
% 0.72/0.89 (((~![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!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) <=> ((~![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!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(69,plain,
% 0.72/0.89 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(70,plain,
% 0.72/0.89 (((~![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!2, Y!1), intersection_point(Z!0, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!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(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[69])).
% 0.72/0.89 tff(71,plain,
% 0.72/0.89 (((~![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!2, Y!1), intersection_point(Z!0, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!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(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[70, 68])).
% 0.72/0.89 tff(72,plain,
% 0.72/0.89 ((~![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!2, Y!1), intersection_point(Z!0, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(73,plain,
% 0.72/0.89 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.72/0.89 tff(74,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[73, 67, 57, 56, 30])).
% 0.72/0.89 tff(75,plain,(distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(76,plain,
% 0.72/0.89 (^[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))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(77,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[76])).
% 0.72/0.89 tff(78,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(79,plain,
% 0.72/0.89 (^[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))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(80,plain,
% 0.72/0.89 (![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)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[79])).
% 0.72/0.89 tff(81,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')).
% 0.72/0.89 tff(82,plain,
% 0.72/0.89 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.72/0.89 tff(83,plain,
% 0.72/0.89 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.72/0.89 tff(84,plain,(
% 0.72/0.89 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[83])).
% 0.72/0.89 tff(85,plain,
% 0.72/0.89 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.72/0.89 tff(86,plain,
% 0.72/0.89 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(87,plain,
% 0.72/0.89 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(88,plain,
% 0.72/0.89 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.72/0.89 tff(89,plain,
% 0.72/0.89 (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[88, 85, 42])).
% 0.72/0.89 tff(90,plain,
% 0.72/0.89 (convergent_lines(X!2, Y!1)),
% 0.72/0.89 inference(and_elim,[status(thm)],[41])).
% 0.72/0.89 tff(91,plain,
% 0.72/0.89 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(92,plain,
% 0.72/0.89 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(93,plain,
% 0.72/0.89 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.72/0.89 tff(94,plain,
% 0.72/0.89 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[93, 52, 90])).
% 0.72/0.90 tff(95,plain,
% 0.72/0.90 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(96,plain,
% 0.72/0.90 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(97,plain,
% 0.72/0.90 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.72/0.90 tff(98,plain,
% 0.72/0.90 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[97, 85, 90])).
% 0.72/0.90 tff(99,plain,
% 0.72/0.90 (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.72/0.90 inference(or_elim,[status(thm)],[40])).
% 0.72/0.90 tff(100,plain,
% 0.72/0.90 (^[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))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(101,plain,
% 0.72/0.90 (![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)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[100])).
% 0.72/0.90 tff(102,plain,
% 0.72/0.90 (^[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)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(103,plain,
% 0.72/0.90 (![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)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[102])).
% 0.72/0.90 tff(104,plain,
% 0.72/0.90 (![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))))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(105,plain,
% 0.72/0.90 (^[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))))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(106,plain,
% 0.72/0.90 (![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))))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[105])).
% 0.72/0.90 tff(107,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')).
% 0.72/0.90 tff(108,plain,
% 0.72/0.90 (![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))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.72/0.90 tff(109,plain,
% 0.72/0.90 (![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))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.72/0.90 tff(110,plain,(
% 0.72/0.90 ![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))))),
% 0.72/0.90 inference(skolemize,[status(sab)],[109])).
% 0.72/0.90 tff(111,plain,
% 0.72/0.90 (![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)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.72/0.90 tff(112,plain,
% 0.72/0.90 (![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)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.72/0.90 tff(113,plain,
% 0.72/0.90 (((~![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(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, X!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(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(114,plain,
% 0.72/0.90 ((apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) <=> (apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(115,plain,
% 0.72/0.90 (((~![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(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[114])).
% 0.72/0.90 tff(116,plain,
% 0.72/0.90 (((~![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(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[115, 113])).
% 0.72/0.90 tff(117,plain,
% 0.72/0.90 ((~![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(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(118,plain,
% 0.72/0.90 ((~![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(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.72/0.90 tff(119,plain,
% 0.72/0.90 ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[118, 112, 99, 98, 94, 89])).
% 0.72/0.90 tff(120,plain,
% 0.72/0.90 (~distinct_lines(Y!1, X!2)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[119, 75])).
% 0.72/0.90 tff(121,plain,
% 0.72/0.90 (^[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))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(122,plain,
% 0.72/0.90 (![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)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[121])).
% 0.72/0.90 tff(123,plain,
% 0.72/0.90 (![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)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(124,plain,
% 0.72/0.90 (^[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)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(125,plain,
% 0.72/0.90 (![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)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[124])).
% 0.72/0.90 tff(126,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')).
% 0.72/0.90 tff(127,plain,
% 0.72/0.90 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.72/0.90 tff(128,plain,
% 0.72/0.90 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.72/0.90 tff(129,plain,(
% 0.72/0.90 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[128])).
% 0.72/0.90 tff(130,plain,
% 0.72/0.90 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.72/0.90 tff(131,plain,
% 0.72/0.90 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(132,plain,
% 0.72/0.90 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(133,plain,
% 0.72/0.90 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[132])).
% 0.72/0.90 tff(134,plain,
% 0.72/0.90 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.72/0.90 inference(transitivity,[status(thm)],[133, 131])).
% 0.72/0.90 tff(135,plain,
% 0.72/0.90 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(136,plain,
% 0.72/0.90 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.72/0.90 tff(137,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[136, 130, 90, 120, 29])).
% 0.72/0.90 % SZS output end Proof
% 0.72/0.90 % E exiting
%------------------------------------------------------------------------------