%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO217+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:00 AM UTC 2025
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO217+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:41:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% 0.11/0.39 tff(convergent_lines_type, type, (
% 0.11/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.11/0.39 tff(tptp_fun_L_2_type, type, (
% 0.11/0.39 tptp_fun_L_2: $i)).
% 0.11/0.39 tff(tptp_fun_M_1_type, type, (
% 0.11/0.39 tptp_fun_M_1: $i)).
% 0.11/0.39 tff(distinct_lines_type, type, (
% 0.11/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.11/0.39 tff(tptp_fun_N_0_type, type, (
% 0.11/0.39 tptp_fun_N_0: $i)).
% 0.11/0.39 tff(unorthogonal_lines_type, type, (
% 0.11/0.39 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.11/0.39 tff(orthogonal_through_point_type, type, (
% 0.11/0.39 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.11/0.39 tff(intersection_point_type, type, (
% 0.11/0.39 intersection_point: ( $i * $i ) > $i)).
% 0.11/0.39 tff(apart_point_and_line_type, type, (
% 0.11/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.39 tff(parallel_lines_type, type, (
% 0.11/0.39 parallel_lines: ( $i * $i ) > $o)).
% 0.11/0.39 tff(1,plain,
% 0.11/0.39 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(2,plain,
% 0.11/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.39 tff(3,plain,
% 0.11/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.11/0.39 tff(5,plain,
% 0.11/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.39 tff(6,plain,(
% 0.11/0.39 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.11/0.39 inference(skolemize,[status(sab)],[5])).
% 0.11/0.39 tff(7,plain,
% 0.11/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.39 tff(8,plain,
% 0.11/0.39 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(9,plain,
% 0.11/0.39 (~unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.39 tff(10,plain,
% 0.11/0.39 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(11,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.39 tff(12,plain,
% 0.11/0.39 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(13,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.39 tff(14,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(15,plain,
% 0.11/0.39 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(16,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.39 tff(17,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.11/0.39 tff(18,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.39 tff(20,plain,(
% 0.11/0.39 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[19])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 ((unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0))) <=> (unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0)))),
% 0.11/0.40 inference(transitivity,[status(thm)],[25, 23])).
% 0.11/0.40 tff(27,plain,
% 0.11/0.40 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(28,plain,
% 0.11/0.40 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(N!0, intersection_point(M!1, N!0)), N!0) | (~convergent_lines(N!0, N!0))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.40 tff(29,plain,
% 0.11/0.40 (~convergent_lines(N!0, N!0)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[28, 22, 9])).
% 0.11/0.40 tff(30,plain,
% 0.11/0.40 (^[X: $i, Y: $i] : refl((~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(31,plain,
% 0.11/0.40 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.40 tff(32,plain,
% 0.11/0.40 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(33,plain,
% 0.11/0.40 (^[X: $i, Y: $i] : trans(rewrite((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))), rewrite((~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))), ((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.40 tff(35,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.40 tff(38,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[37])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))) | (~(convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (~(convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 ((~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 ((~![L: $i, M: $i, N: $i] : ((parallel_lines(L, M) & parallel_lines(L, N)) => parallel_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(44,axiom,(~![L: $i, M: $i, N: $i] : ((parallel_lines(L, M) & parallel_lines(L, N)) => parallel_lines(M, N))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[47, 42])).
% 0.21/0.40 tff(49,plain,(
% 0.21/0.40 ~((~(parallel_lines(L!2, M!1) & parallel_lines(L!2, N!0))) | parallel_lines(M!1, N!0))),
% 0.21/0.40 inference(skolemize,[status(sab)],[48])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (~parallel_lines(M!1, N!0)),
% 0.21/0.40 inference(or_elim,[status(thm)],[49])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 ((convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0)) | convergent_lines(M!1, N!0) | parallel_lines(M!1, N!0)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 ((convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0)) | convergent_lines(M!1, N!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (convergent_lines(M!1, N!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[52, 41])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.40 tff(59,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')).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.40 tff(62,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[61])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(M!1, N!0)) | (~apart_point_and_line(intersection_point(M!1, N!0), N!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(M!1, N!0)) | (~apart_point_and_line(intersection_point(M!1, N!0), N!0)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(M!1, N!0)) | (~apart_point_and_line(intersection_point(M!1, N!0), N!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(M!1, N!0)) | (~apart_point_and_line(intersection_point(M!1, N!0), N!0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (~apart_point_and_line(intersection_point(M!1, N!0), N!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[66, 63, 53])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.40 tff(73,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')).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.40 tff(76,plain,(
% 0.21/0.40 ![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)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[75])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0)) | convergent_lines(N!0, N!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)))) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0)) | convergent_lines(N!0, N!0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ((convergent_lines(N!0, N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0))) <=> (apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0)) | convergent_lines(N!0, N!0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (((~![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(N!0, N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!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)))) | (apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0)) | convergent_lines(N!0, N!0)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (((~![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(N!0, N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!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)))) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0)) | convergent_lines(N!0, N!0))),
% 0.21/0.40 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((~![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(N!0, N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(M!1, N!0), N!0) | (~distinct_lines(N!0, N!0)) | convergent_lines(N!0, N!0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (~distinct_lines(N!0, N!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[83, 77, 67, 29])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))) | (~(convergent_lines(L!2, N!0) <=> parallel_lines(L!2, N!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (~(convergent_lines(L!2, N!0) <=> parallel_lines(L!2, N!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[85, 39])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (parallel_lines(L!2, M!1) & parallel_lines(L!2, N!0)),
% 0.21/0.40 inference(or_elim,[status(thm)],[49])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (parallel_lines(L!2, N!0)),
% 0.21/0.40 inference(and_elim,[status(thm)],[87])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 ((convergent_lines(L!2, N!0) <=> parallel_lines(L!2, N!0)) | (~convergent_lines(L!2, N!0)) | (~parallel_lines(L!2, N!0))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 ((convergent_lines(L!2, N!0) <=> parallel_lines(L!2, N!0)) | (~convergent_lines(L!2, N!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 (~convergent_lines(L!2, N!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[90, 86])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.40 tff(97,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.21/0.40 tff(100,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.40 inference(skolemize,[status(sab)],[99])).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!2, N!0)) | convergent_lines(L!2, N!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!2, N!0)) | convergent_lines(L!2, N!0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!2, N!0)) | convergent_lines(L!2, N!0))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!2, N!0)) | convergent_lines(L!2, N!0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (~distinct_lines(L!2, N!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.41 tff(111,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')).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.41 tff(114,plain,(
% 0.21/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[113])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (~distinct_lines(N!0, L!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[118, 115, 105, 84])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.41 tff(125,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')).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.21/0.41 tff(128,plain,(
% 0.21/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[127])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 ((distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[131])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.21/0.41 inference(transitivity,[status(thm)],[132, 130])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[135, 129, 53])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 (convergent_lines(M!1, L!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[136, 119])).
% 0.21/0.41 tff(138,assumption,(convergent_lines(M!1, M!1)), introduced(assumption)).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(142,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.41 tff(144,plain,(
% 0.21/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(skolemize,[status(sab)],[143])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(M!1, M!1))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[146, 145, 138])).
% 0.21/0.41 tff(148,plain,(~convergent_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))) | (~(convergent_lines(L!2, M!1) <=> parallel_lines(L!2, M!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(150,plain,
% 0.21/0.41 (~(convergent_lines(L!2, M!1) <=> parallel_lines(L!2, M!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[149, 39])).
% 0.21/0.41 tff(151,plain,
% 0.21/0.41 (parallel_lines(L!2, M!1)),
% 0.21/0.41 inference(and_elim,[status(thm)],[87])).
% 0.21/0.41 tff(152,plain,
% 0.21/0.41 ((convergent_lines(L!2, M!1) <=> parallel_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~parallel_lines(L!2, M!1))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(153,plain,
% 0.21/0.41 ((convergent_lines(L!2, M!1) <=> parallel_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.41 tff(154,plain,
% 0.21/0.41 (~convergent_lines(L!2, M!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.21/0.41 tff(155,plain,
% 0.21/0.41 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(156,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(157,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.41 tff(158,plain,
% 0.21/0.41 (~distinct_lines(L!2, M!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[157, 101, 154])).
% 0.21/0.41 tff(159,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(160,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(161,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.41 tff(162,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[161, 129, 158, 148, 137])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------