%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO209+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:57 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO209+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 14:41:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(convergent_lines_type, type, (
% 0.12/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_N_0_type, type, (
% 0.12/0.37 tptp_fun_N_0: $i)).
% 0.12/0.37 tff(tptp_fun_M_1_type, type, (
% 0.12/0.37 tptp_fun_M_1: $i)).
% 0.12/0.37 tff(tptp_fun_L_2_type, type, (
% 0.12/0.37 tptp_fun_L_2: $i)).
% 0.12/0.37 tff(apart_point_and_line_type, type, (
% 0.12/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_A_3_type, type, (
% 0.12/0.37 tptp_fun_A_3: $i)).
% 0.12/0.37 tff(distinct_lines_type, type, (
% 0.12/0.37 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))) <=> (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![A: $i, L: $i, M: $i, N: $i] : (((((apart_point_and_line(A, L) & (~apart_point_and_line(A, M))) & (~apart_point_and_line(A, N))) & (~convergent_lines(M, L))) & (~convergent_lines(N, L))) => (~distinct_lines(M, N)))) <=> (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,axiom,(~![A: $i, L: $i, M: $i, N: $i] : (((((apart_point_and_line(A, L) & (~apart_point_and_line(A, M))) & (~apart_point_and_line(A, N))) & (~convergent_lines(M, L))) & (~convergent_lines(N, L))) => (~distinct_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,(
% 0.12/0.37 ~((~distinct_lines(M!1, N!0)) | (~(apart_point_and_line(A!3, L!2) & (~apart_point_and_line(A!3, M!1)) & (~apart_point_and_line(A!3, N!0)) & (~convergent_lines(M!1, L!2)) & (~convergent_lines(N!0, L!2)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (apart_point_and_line(A!3, L!2) & (~apart_point_and_line(A!3, M!1)) & (~apart_point_and_line(A!3, N!0)) & (~convergent_lines(M!1, L!2)) & (~convergent_lines(N!0, L!2))),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~convergent_lines(N!0, L!2)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~convergent_lines(M!1, L!2)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.37 tff(17,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/GEO008+0.ax','apart6')).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.37 tff(20,plain,(
% 0.12/0.37 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[23])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[24, 22])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (~convergent_lines(M!1, N!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[27, 21, 11, 10])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (~apart_point_and_line(A!3, N!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (~apart_point_and_line(A!3, M!1)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (distinct_lines(M!1, N!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.37 tff(37,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')).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.37 tff(40,plain,(
% 0.12/0.37 ![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)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[39])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (((~![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)))) | ((~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, 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)))) | (~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 ((convergent_lines(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, N!0))) <=> ((~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (((~![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(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, 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)))) | ((~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (((~![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(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, 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)))) | (~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0))),
% 0.12/0.37 inference(transitivity,[status(thm)],[44, 42])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~![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(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, N!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[47, 41, 31, 30, 29, 28])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------