%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO219+2 : 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 05:06:00 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO219+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % 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 14:42:17 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(convergent_lines_type, type, (
% 0.19/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_N_0_type, type, (
% 0.19/0.38 tptp_fun_N_0: $i)).
% 0.19/0.38 tff(tptp_fun_M_1_type, type, (
% 0.19/0.38 tptp_fun_M_1: $i)).
% 0.19/0.38 tff(unorthogonal_lines_type, type, (
% 0.19/0.38 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_L_2_type, type, (
% 0.19/0.38 tptp_fun_L_2: $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))) => (~unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(3,axiom,(~![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N))) => (~unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.38 tff(8,plain,(
% 0.19/0.38 ~((~unorthogonal_lines(M!1, N!0)) | (~((~unorthogonal_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[7])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ((~unorthogonal_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0))),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~convergent_lines(L!2, N!0)),
% 0.19/0.38 inference(and_elim,[status(thm)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (~unorthogonal_lines(L!2, M!1)),
% 0.19/0.38 inference(and_elim,[status(thm)],[9])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))) | unorthogonal_lines(L!2, M!1)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (unorthogonal_lines(M!1, N!0)),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (^[L: $i, M: $i, N: $i] : refl(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~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(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> (~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))))), rewrite((~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~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(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))), rewrite(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (^[L: $i, M: $i, N: $i] : rewrite(((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (![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] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.38 tff(24,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+4.ax','cotno1')).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.38 tff(27,plain,(
% 0.19/0.38 ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[26])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (~convergent_lines(M!1, N!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[32, 29, 16, 15, 12])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (^[L: $i, M: $i] : 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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(39,axiom,(![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','coipo1')).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.38 tff(41,plain,(
% 0.19/0.38 ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[40])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (convergent_lines(L!2, M!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 43, 13])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.38 tff(53,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.38 tff(56,plain,(
% 0.19/0.38 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[55])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 ((convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1))) <=> (convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 57, 10, 47, 33])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------