%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO199+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:54 AM UTC 2025
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO199+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 14:41:03 EDT 2025
% 0.19/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(distinct_lines_type, type, (
% 0.19/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_X_2_type, type, (
% 0.19/0.41 tptp_fun_X_2: $i)).
% 0.19/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.41 tptp_fun_Y_1: $i)).
% 0.19/0.41 tff(convergent_lines_type, type, (
% 0.19/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.41 tff(apart_point_and_line_type, type, (
% 0.19/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.41 tptp_fun_Z_0: $i)).
% 0.19/0.41 tff(intersection_point_type, type, (
% 0.19/0.41 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.41 tff(distinct_points_type, type, (
% 0.19/0.41 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,assumption,(~distinct_lines(Y!1, X!2)), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(5,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.41 tff(7,plain,(
% 0.19/0.41 ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.41 inference(skolemize,[status(sab)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(X!2, X!2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (~distinct_lines(X!2, X!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 ((~![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(Y, X), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,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(Y, X), Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.19/0.41 tff(18,plain,(
% 0.19/0.41 ~((~apart_point_and_line(intersection_point(Y!1, X!2), 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(X!2, Y!1), Z!0)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.19/0.41 inference(or_elim,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (convergent_lines(X!2, Y!1)),
% 0.19/0.41 inference(and_elim,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.41 tff(26,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.41 tff(29,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.41 inference(skolemize,[status(sab)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (distinct_lines(X!2, Y!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.41 tff(40,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.41 tff(43,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[42])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((distinct_lines(Y!1, X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1))) <=> (distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2))),
% 0.19/0.41 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[50, 44, 34, 10, 1])).
% 0.19/0.41 tff(52,plain,(distinct_lines(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(53,assumption,(~convergent_lines(Y!1, X!2)), introduced(assumption)).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, X!2)) | distinct_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, X!2)) | distinct_lines(X!2, X!2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, X!2)) | distinct_lines(X!2, X!2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, X!2)) | distinct_lines(X!2, X!2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (~convergent_lines(X!2, X!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 30, 10])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.41 tff(63,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.41 tff(66,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, X!2) | convergent_lines(Y!1, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, X!2) | convergent_lines(Y!1, X!2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, X!2) | convergent_lines(Y!1, X!2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, X!2) | convergent_lines(Y!1, X!2)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, X!2) | convergent_lines(Y!1, X!2))),
% 0.19/0.42 inference(transitivity,[status(thm)],[70, 68])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, X!2) | convergent_lines(Y!1, X!2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[73, 67, 20, 57, 53])).
% 0.19/0.42 tff(75,plain,(convergent_lines(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(76,assumption,(distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2))), introduced(assumption)).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(80,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.42 tff(82,plain,(
% 0.19/0.42 ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[84, 83, 76])).
% 0.19/0.42 tff(86,plain,(~distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.42 tff(92,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.42 tff(95,plain,(
% 0.19/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[94])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 ((~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[99, 96, 86])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[100, 75])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[106, 83])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~(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(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[113, 108])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[116, 96, 20, 107])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ((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(X!2, Y!1), Y!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 ((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(X!2, Y!1), X!2))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.19/0.43 inference(and_elim,[status(thm)],[19])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.19/0.43 inference(or_elim,[status(thm)],[18])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.43 tff(129,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq1')).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.43 tff(132,plain,(
% 0.19/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[131])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 (((~![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(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, 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(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 ((distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0))) <=> ((~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 (((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[136, 134])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 ((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 ((~![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(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[139, 133, 123, 122])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 (^[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_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_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[141])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, 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) | (~(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_points(X, Y)) | (~distinct_lines(U, V)))))), 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_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_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_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_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.43 tff(148,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.19/0.43 tff(151,plain,(
% 0.19/0.43 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[150])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[152, 142])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), 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_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(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) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, 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_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, 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_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.19/0.43 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 ((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[159, 153, 140])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[160, 121, 119, 105, 103, 52])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------