%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO214+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO214+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 14:45:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(unorthogonal_lines_type, type, (
% 0.12/0.39 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_L_1_type, type, (
% 0.12/0.39 tptp_fun_L_1: $i)).
% 0.12/0.39 tff(convergent_lines_type, type, (
% 0.12/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_M_0_type, type, (
% 0.12/0.39 tptp_fun_M_0: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!1, L!1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~convergent_lines(L!1, L!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))) | convergent_lines(L!1, L!1)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.12/0.39 tff(12,assumption,(convergent_lines(M!0, M!0)), introduced(assumption)).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(M!0, M!0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[13, 7, 12])).
% 0.12/0.39 tff(15,plain,(~convergent_lines(M!0, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 ((~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))) <=> (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![L: $i, M: $i] : (unorthogonal_lines(L, M) => unorthogonal_lines(M, L))) <=> (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,axiom,(~![L: $i, M: $i] : (unorthogonal_lines(L, M) => unorthogonal_lines(M, L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.12/0.39 tff(23,plain,(
% 0.12/0.39 ~((~unorthogonal_lines(L!1, M!0)) | unorthogonal_lines(M!0, L!1))),
% 0.12/0.39 inference(skolemize,[status(sab)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (~unorthogonal_lines(M!0, L!1)),
% 0.12/0.39 inference(or_elim,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,(
% 0.12/0.39 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.12/0.39 inference(skolemize,[status(sab)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (convergent_lines(M!0, L!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 31, 24])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.39 tff(41,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')).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.12/0.39 tff(44,plain,(
% 0.12/0.39 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[43])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!0, L!1)) | convergent_lines(M!0, M!0) | convergent_lines(L!1, M!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!0, L!1)) | convergent_lines(M!0, M!0) | convergent_lines(L!1, M!0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1))) <=> ((~convergent_lines(M!0, L!1)) | convergent_lines(M!0, M!0) | convergent_lines(L!1, M!0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!0, L!1)) | convergent_lines(M!0, M!0) | convergent_lines(L!1, M!0)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!0, L!1)) | convergent_lines(M!0, M!0) | convergent_lines(L!1, M!0))),
% 0.12/0.39 inference(transitivity,[status(thm)],[48, 46])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!0, L!1)) | convergent_lines(M!0, M!0) | convergent_lines(L!1, M!0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (convergent_lines(L!1, M!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[51, 45, 35, 15])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1))) | unorthogonal_lines(M!0, L!1)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[53, 24])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (unorthogonal_lines(L!1, M!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[23])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((convergent_lines(M, N) & unorthogonal_lines(M, N)) <=> (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), rewrite((convergent_lines(L, N) & unorthogonal_lines(L, N)) <=> (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))), trans(monotonicity(rewrite((convergent_lines(L, M) & unorthogonal_lines(L, M)) <=> (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> (~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), rewrite((~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), rewrite(((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.40 tff(63,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')).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.40 tff(66,plain,(
% 0.19/0.40 ![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))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0))) <=> ((~unorthogonal_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[71, 69])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 68, 55, 54, 52, 11])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------