%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO217+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:59 AM UTC 2025
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO217+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n008.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Thu Jun 19 14:41:48 EDT 2025
% 0.11/0.34 % 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_N_0_type, type, (
% 0.11/0.39 tptp_fun_N_0: $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_M_1_type, type, (
% 0.11/0.39 tptp_fun_M_1: $i)).
% 0.11/0.39 tff(1,plain,
% 0.11/0.39 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(2,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.39 tff(3,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(4,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.11/0.39 tff(5,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.39 tff(6,plain,(
% 0.11/0.39 ![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(skolemize,[status(sab)],[5])).
% 0.11/0.39 tff(7,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.39 tff(8,plain,
% 0.11/0.39 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(N!0, N!0))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(9,plain,
% 0.11/0.39 (~distinct_lines(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 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(11,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.39 tff(12,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(13,plain,
% 0.11/0.39 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(14,plain,
% 0.11/0.39 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.39 tff(15,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.11/0.39 tff(16,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.39 tff(17,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.39 tff(18,plain,(
% 0.11/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.39 inference(skolemize,[status(sab)],[17])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.11/0.39 tff(20,plain,
% 0.11/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(N!0, N!0)) | distinct_lines(N!0, N!0))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(N!0, N!0)) | distinct_lines(N!0, N!0))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(N!0, N!0)) | distinct_lines(N!0, N!0))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(N!0, N!0)) | distinct_lines(N!0, N!0)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (~convergent_lines(N!0, N!0)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 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] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(26,axiom,(~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.11/0.39 tff(30,plain,
% 0.11/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.11/0.39 tff(31,plain,(
% 0.11/0.39 ~((~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0)))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[30])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 ((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0))),
% 0.11/0.39 inference(or_elim,[status(thm)],[31])).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 (~convergent_lines(L!2, N!0)),
% 0.11/0.39 inference(and_elim,[status(thm)],[32])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.39 tff(39,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.11/0.39 tff(42,plain,(
% 0.11/0.39 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[41])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 ((convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2))) <=> (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[45])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.11/0.39 inference(transitivity,[status(thm)],[46, 44])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (~convergent_lines(N!0, L!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[49, 43, 33, 23])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(M!1, M!1))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 (~distinct_lines(M!1, M!1)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[51, 7])).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (~convergent_lines(M!1, M!1)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[55, 19, 52])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (~convergent_lines(L!2, M!1)),
% 0.11/0.39 inference(and_elim,[status(thm)],[32])).
% 0.11/0.39 tff(58,plain,
% 0.11/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(59,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(60,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.40 tff(61,plain,
% 0.11/0.40 (~convergent_lines(M!1, L!2)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[60, 43, 57, 56])).
% 0.11/0.40 tff(62,plain,
% 0.11/0.40 (convergent_lines(M!1, N!0)),
% 0.11/0.40 inference(or_elim,[status(thm)],[31])).
% 0.11/0.40 tff(63,plain,
% 0.11/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(64,plain,
% 0.11/0.40 ((convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(65,plain,
% 0.11/0.40 (((~![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, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[64])).
% 0.11/0.40 tff(66,plain,
% 0.11/0.40 (((~![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, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.11/0.40 inference(transitivity,[status(thm)],[65, 63])).
% 0.11/0.40 tff(67,plain,
% 0.11/0.40 ((~![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)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(68,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.40 tff(69,plain,
% 0.11/0.40 (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[68, 43, 62])).
% 0.11/0.40 tff(70,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[69, 61, 50])).
% 0.11/0.40 % SZS output end Proof
% 0.11/0.40 % E exiting
%------------------------------------------------------------------------------