%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO213+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:05:58 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO213+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:42:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(convergent_lines_type, type, (
% 0.20/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_M_1_type, type, (
% 0.20/0.41 tptp_fun_M_1: $i)).
% 0.20/0.41 tff(tptp_fun_L_2_type, type, (
% 0.20/0.41 tptp_fun_L_2: $i)).
% 0.20/0.41 tff(distinct_lines_type, type, (
% 0.20/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_N_0_type, type, (
% 0.20/0.41 tptp_fun_N_0: $i)).
% 0.20/0.41 tff(unorthogonal_lines_type, type, (
% 0.20/0.41 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(convergent_lines(M!1, M!1)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(M!1, M!1))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.41 tff(11,plain,(~convergent_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(12,assumption,(distinct_lines(N!0, N!0)), introduced(assumption)).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart2')).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,(
% 0.20/0.41 ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(skolemize,[status(sab)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(N!0, N!0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.20/0.41 tff(22,plain,(~distinct_lines(N!0, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(23,assumption,(distinct_lines(N!0, L!2)), introduced(assumption)).
% 0.20/0.41 tff(24,assumption,(~distinct_lines(N!0, N!0)), introduced(assumption)).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))) <=> (~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (distinct_lines(L, N) | unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,axiom,(~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (distinct_lines(L, N) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.20/0.41 tff(33,plain,(
% 0.20/0.41 ~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[32])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~distinct_lines(L!2, N!0)),
% 0.20/0.41 inference(or_elim,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.41 tff(41,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')).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.41 tff(44,plain,(
% 0.20/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[43])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((~![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)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 45, 35, 24, 23])).
% 0.20/0.41 tff(50,plain,(distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (~distinct_lines(N!0, L!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[50, 22])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (~unorthogonal_lines(M!1, N!0)),
% 0.20/0.41 inference(or_elim,[status(thm)],[34])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(56,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,(
% 0.20/0.41 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(skolemize,[status(sab)],[57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (convergent_lines(M!1, N!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[62, 59, 52])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.42 tff(69,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')).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.42 tff(72,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[71])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (((~![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)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~![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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![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)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (convergent_lines(M!1, L!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[80, 51])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!2, L!2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~convergent_lines(L!2, L!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[82, 8])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~![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(L!2, L!2) | (~convergent_lines(L!2, N!0)))) <=> ((~![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(L!2, L!2) | (~convergent_lines(L!2, N!0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~![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(L!2, L!2) | (~convergent_lines(L!2, N!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~![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(L!2, L!2) | (~convergent_lines(L!2, N!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (~convergent_lines(L!2, N!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 73, 51, 83])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))) | unorthogonal_lines(M!1, N!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 52])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (unorthogonal_lines(L!2, M!1)),
% 0.20/0.42 inference(or_elim,[status(thm)],[34])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (^[L: $i, M: $i, N: $i] : refl(((~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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (^[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)) | (~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(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![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)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.42 tff(100,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')).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.42 tff(103,plain,(
% 0.20/0.42 ![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))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[102])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))) <=> ((~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (((~![L: $i, M: $i, N: $i] : ((~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!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (((~![L: $i, M: $i, N: $i] : ((~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!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~![L: $i, M: $i, N: $i] : ((~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!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 ((~convergent_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[111, 105, 92, 91])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (~convergent_lines(L!2, M!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[112, 89])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.42 tff(119,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')).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.20/0.42 tff(122,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[121])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[126, 123, 113, 81, 11])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------