%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO214+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO214+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 14:41:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(convergent_lines_type, type, (
% 0.19/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_M_0_type, type, (
% 0.19/0.42 tptp_fun_M_0: $i)).
% 0.19/0.42 tff(tptp_fun_L_1_type, type, (
% 0.19/0.42 tptp_fun_L_1: $i)).
% 0.19/0.42 tff(unorthogonal_lines_type, type, (
% 0.19/0.42 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.42 tff(distinct_lines_type, type, (
% 0.19/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 ((~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))) <=> (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 ((~![L: $i, M: $i] : (unorthogonal_lines(L, M) => unorthogonal_lines(M, L))) <=> (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(3,axiom,(~![L: $i, M: $i] : (unorthogonal_lines(L, M) => unorthogonal_lines(M, L))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.42 tff(8,plain,(
% 0.19/0.42 ~((~unorthogonal_lines(L!1, M!0)) | unorthogonal_lines(M!0, L!1))),
% 0.19/0.42 inference(skolemize,[status(sab)],[7])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (~unorthogonal_lines(M!0, L!1)),
% 0.19/0.42 inference(or_elim,[status(thm)],[8])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1))) | unorthogonal_lines(M!0, L!1)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 ((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.42 tff(12,assumption,(convergent_lines(L!1, M!0)), introduced(assumption)).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(16,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.42 tff(18,plain,(
% 0.19/0.42 ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[17])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(L!1, L!1))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (~distinct_lines(L!1, L!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.42 tff(27,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.42 tff(30,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.42 inference(skolemize,[status(sab)],[29])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!1, L!1)) | distinct_lines(L!1, L!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!1, L!1)) | distinct_lines(L!1, L!1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!1, L!1)) | distinct_lines(L!1, L!1))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!1, L!1)) | distinct_lines(L!1, L!1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (~convergent_lines(L!1, L!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))) | convergent_lines(L!1, L!1)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (unorthogonal_lines(L!1, M!0)),
% 0.19/0.42 inference(or_elim,[status(thm)],[8])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (^[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)) | (~((~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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (![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)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.42 tff(46,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/sandbox2/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.43 tff(49,plain,(
% 0.19/0.43 ![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))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[48])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (((~![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(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_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(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (((~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(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (((~![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(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (((~![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(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(L!1, M!0)) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~convergent_lines(L!1, M!0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[57, 51, 38, 37, 12, 11])).
% 0.19/0.43 tff(59,plain,(~convergent_lines(L!1, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(63,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.43 tff(65,plain,(
% 0.19/0.43 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(skolemize,[status(sab)],[64])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(M!0, M!0))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (~convergent_lines(M!0, M!0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(72,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.43 tff(74,plain,(
% 0.19/0.43 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.43 inference(skolemize,[status(sab)],[73])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (((~![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (convergent_lines(M!0, L!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[78, 75, 9])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.43 tff(85,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')).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.43 tff(88,plain,(
% 0.19/0.43 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[87])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (((~![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 ((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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (((~![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)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (((~![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))),
% 0.19/0.43 inference(transitivity,[status(thm)],[92, 90])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!0, L!1)) | convergent_lines(M!0, M!0) | convergent_lines(L!1, M!0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[95, 89, 79, 68, 59])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------