%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO223+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:06:02 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO223+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 14:41:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(unorthogonal_lines_type, type, (
% 0.20/0.43 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.43 tff(orthogonal_through_point_type, type, (
% 0.20/0.43 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_A_1_type, type, (
% 0.20/0.43 tptp_fun_A_1: $i)).
% 0.20/0.43 tff(tptp_fun_L_0_type, type, (
% 0.20/0.43 tptp_fun_L_0: $i)).
% 0.20/0.43 tff(parallel_through_point_type, type, (
% 0.20/0.43 parallel_through_point: ( $i * $i ) > $i)).
% 0.20/0.43 tff(convergent_lines_type, type, (
% 0.20/0.43 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.43 tff(apart_point_and_line_type, type, (
% 0.20/0.43 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.43 tff(intersection_point_type, type, (
% 0.20/0.43 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.43 tff(distinct_lines_type, type, (
% 0.20/0.43 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.43 tff(1,assumption,(convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), introduced(assumption)).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.43 tff(7,plain,(
% 0.20/0.43 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[6])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.43 tff(11,plain,(~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(12,assumption,(~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), introduced(assumption)).
% 0.20/0.43 tff(13,assumption,(~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))), introduced(assumption)).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(17,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.43 tff(19,plain,(
% 0.20/0.43 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43 inference(skolemize,[status(sab)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(26,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.43 tff(28,plain,(
% 0.20/0.43 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.43 inference(skolemize,[status(sab)],[27])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (convergent_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.43 tff(39,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.44 tff(42,plain,(
% 0.20/0.44 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[41])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[49, 43, 33])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (convergent_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[50, 13])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.44 tff(57,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')).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.44 tff(60,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[59])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[64, 61, 51])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.44 tff(71,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')).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.44 tff(74,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[73])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[78, 75, 51])).
% 0.20/0.44 tff(80,assumption,(~distinct_lines(L!0, parallel_through_point(L!0, A!1))), introduced(assumption)).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.44 tff(86,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')).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.44 tff(89,plain,(
% 0.20/0.44 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[88])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | distinct_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | distinct_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[96, 90, 33, 13, 80])).
% 0.20/0.44 tff(98,plain,(distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (distinct_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 13])).
% 0.20/0.44 tff(100,assumption,(distinct_lines(L!0, L!0)), introduced(assumption)).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(104,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart2')).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.44 tff(106,plain,(
% 0.20/0.44 ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.44 inference(skolemize,[status(sab)],[105])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(L!0, L!0))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[108, 107, 100])).
% 0.20/0.44 tff(110,plain,(~distinct_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(111,assumption,(distinct_lines(L!0, parallel_through_point(L!0, A!1))), introduced(assumption)).
% 0.20/0.44 tff(112,assumption,(~distinct_lines(L!0, L!0)), introduced(assumption)).
% 0.20/0.44 tff(113,assumption,(~distinct_lines(parallel_through_point(L!0, A!1), L!0)), introduced(assumption)).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.45 tff(119,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.20/0.45 tff(122,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[121])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(L!0, A!1), L!0) | distinct_lines(L!0, L!0) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(parallel_through_point(L!0, A!1), L!0) | distinct_lines(L!0, L!0) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(L!0, A!1), L!0) | distinct_lines(L!0, L!0) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(parallel_through_point(L!0, A!1), L!0) | distinct_lines(L!0, L!0) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 123, 113, 112, 111])).
% 0.20/0.45 tff(128,plain,(distinct_lines(L!0, L!0) | distinct_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (distinct_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[128, 110])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (distinct_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[129, 99])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(134,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.45 tff(136,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.45 inference(skolemize,[status(sab)],[135])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (~convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.45 tff(145,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.20/0.45 tff(148,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[147])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ((convergent_lines(parallel_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0))) <=> (convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0))),
% 0.20/0.45 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), parallel_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, parallel_through_point(L!0, A!1)), L!0)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 149, 139, 130, 79, 65])).
% 0.20/0.45 tff(157,plain,(convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))) <=> (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[163, 43, 157, 12, 11])).
% 0.20/0.46 tff(165,plain,(convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[166, 22])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))) | convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 ((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[168, 139])).
% 0.20/0.46 tff(170,assumption,(~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))), introduced(assumption)).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[175])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((convergent_lines(M, N) & unorthogonal_lines(M, N)) <=> (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), rewrite((convergent_lines(L, N) & unorthogonal_lines(L, N)) <=> (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))), trans(monotonicity(rewrite((convergent_lines(L, M) & unorthogonal_lines(L, M)) <=> (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> (~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), rewrite((~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), rewrite(((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))), (((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))))), rewrite(((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))), (((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N)))) <=> ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.46 tff(182,axiom,(![L: $i, M: $i, N: $i] : ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.20/0.46 tff(185,plain,(
% 0.20/0.46 ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[184])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[189])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[190, 188])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.46 tff(194,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[193, 187, 174, 172, 169, 167])).
% 0.20/0.46 tff(195,plain,((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 ((~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[197, 165])).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 (^[A: $i, L: $i] : refl((~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> (~apart_point_and_line(A, orthogonal_through_point(L, A))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(202,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.20/0.46 tff(203,plain,
% 0.20/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.47 tff(204,plain,(
% 0.20/0.47 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[203])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[208, 20])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[210])).
% 0.20/0.47 tff(212,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(213,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.47 tff(215,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[214])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 ((~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))) <=> (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(220,axiom,(~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[221, 219])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[222, 219])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.20/0.47 tff(225,plain,(
% 0.20/0.47 distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.47 inference(skolemize,[status(sab)],[224])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (^[A: $i, L: $i, M: $i, N: $i] : refl((apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.47 tff(228,plain,
% 0.20/0.47 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(229,plain,
% 0.20/0.47 (^[A: $i, L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(A, L) | apart_point_and_line(A, M)) <=> (apart_point_and_line(A, M) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> ((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)))), rewrite(((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> ((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)))), rewrite(((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))))), rewrite((distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 (![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[229])).
% 0.20/0.47 tff(231,axiom,(![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.20/0.47 tff(234,plain,(
% 0.20/0.47 ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[233])).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(237,plain,
% 0.20/0.47 ((apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(238,plain,
% 0.20/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[237])).
% 0.20/0.47 tff(239,plain,
% 0.20/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[238, 236])).
% 0.20/0.47 tff(240,plain,
% 0.20/0.47 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(241,plain,
% 0.20/0.47 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.47 tff(242,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[241, 235, 225, 218, 209, 207, 198])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------