%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO217+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 05:05:59 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO217+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:42:02 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(convergent_lines_type, type, (
% 0.20/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_N_0_type, type, (
% 0.20/0.39 tptp_fun_N_0: $i)).
% 0.20/0.39 tff(unorthogonal_lines_type, type, (
% 0.20/0.39 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_M_1_type, type, (
% 0.20/0.39 tptp_fun_M_1: $i)).
% 0.20/0.39 tff(tptp_fun_L_2_type, type, (
% 0.20/0.39 tptp_fun_L_2: $i)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(3,axiom,(~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.39 tff(8,plain,(
% 0.20/0.39 ~((~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[7])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0))),
% 0.20/0.39 inference(or_elim,[status(thm)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~convergent_lines(L!2, N!0)),
% 0.20/0.39 inference(and_elim,[status(thm)],[9])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~convergent_lines(L!2, M!1)),
% 0.20/0.39 inference(and_elim,[status(thm)],[9])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))) | convergent_lines(L!2, M!1)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (convergent_lines(M!1, N!0)),
% 0.20/0.39 inference(or_elim,[status(thm)],[8])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (^[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))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (^[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)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![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))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (^[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)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (![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] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.39 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/sandbox2/benchmark/Axioms/GEO006+4.ax','cotno1')).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![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))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![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))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.39 tff(27,plain,(
% 0.20/0.39 ![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))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (((~![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)))))) | ((~convergent_lines(M!1, N!0)) | (~unorthogonal_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)))))) | (~convergent_lines(M!1, N!0)) | (~unorthogonal_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)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (((~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))))) <=> ((~convergent_lines(M!1, N!0)) | (~unorthogonal_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)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (((~![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)))))) | ((~convergent_lines(M!1, N!0)) | (~unorthogonal_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))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (((~![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)))))) | (~convergent_lines(M!1, N!0)) | (~unorthogonal_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)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~![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)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~![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)))))) | (~convergent_lines(M!1, N!0)) | (~unorthogonal_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))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (~unorthogonal_lines(M!1, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[35, 29, 16, 15, 12])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))) | unorthogonal_lines(M!1, N!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.40 tff(46,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.40 tff(49,plain,(
% 0.20/0.40 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[48])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (unorthogonal_lines(M!1, M!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[54, 51, 16, 36])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (((~![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)))))) | ((~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)))) <=> ((~![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)))))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (((~unorthogonal_lines(M!1, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))))) <=> ((~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (((~![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, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![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)))))) | ((~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (((~![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, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![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)))))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[58, 56])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~![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, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ((~![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)))))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (~convergent_lines(M!1, M!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[61, 29, 15, 55])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.40 tff(68,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/GEO006+0.ax','ax6')).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.40 tff(71,plain,(
% 0.20/0.40 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1))) <=> ((~![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(N!0, M!1) | convergent_lines(M!1, M!1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ((convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1))),
% 0.20/0.40 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[78, 72, 16])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (convergent_lines(N!0, M!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[79, 62])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (((~![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)))))) | ((~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~unorthogonal_lines(N!0, M!1)))) <=> ((~![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)))))) | (~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~unorthogonal_lines(N!0, M!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (((~unorthogonal_lines(N!0, M!1)) | (~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))))) <=> ((~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~unorthogonal_lines(N!0, M!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (((~![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(N!0, M!1)) | (~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![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)))))) | ((~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~unorthogonal_lines(N!0, M!1))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (((~![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(N!0, M!1)) | (~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![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)))))) | (~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~unorthogonal_lines(N!0, M!1)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 ((~![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(N!0, M!1)) | (~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ((~![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)))))) | (~convergent_lines(N!0, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~unorthogonal_lines(N!0, M!1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (~unorthogonal_lines(N!0, M!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[86, 29, 80, 15, 12])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, M!1)) | unorthogonal_lines(N!0, M!1) | unorthogonal_lines(N!0, N!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (~convergent_lines(N!0, M!1)) | unorthogonal_lines(N!0, M!1) | unorthogonal_lines(N!0, N!0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, M!1)) | unorthogonal_lines(N!0, M!1) | unorthogonal_lines(N!0, N!0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (~convergent_lines(N!0, M!1)) | unorthogonal_lines(N!0, M!1) | unorthogonal_lines(N!0, N!0)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (unorthogonal_lines(N!0, N!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[90, 51, 80, 87])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~![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)))))) | ((~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(N!0, N!0)) | (~unorthogonal_lines(N!0, 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)))))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(N!0, N!0)) | (~unorthogonal_lines(N!0, N!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (((~unorthogonal_lines(N!0, N!0)) | (~convergent_lines(N!0, N!0)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))))) <=> ((~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(N!0, N!0)) | (~unorthogonal_lines(N!0, N!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~![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(N!0, N!0)) | (~convergent_lines(N!0, N!0)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, 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)))))) | ((~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(N!0, N!0)) | (~unorthogonal_lines(N!0, N!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~![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(N!0, N!0)) | (~convergent_lines(N!0, N!0)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, 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)))))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(N!0, N!0)) | (~unorthogonal_lines(N!0, N!0)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~![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(N!0, N!0)) | (~convergent_lines(N!0, N!0)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~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(97,plain,
% 0.20/0.41 ((~![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)))))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(N!0, N!0)) | (~unorthogonal_lines(N!0, N!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (~convergent_lines(N!0, N!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 29, 91, 38])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~![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)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~![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))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (~convergent_lines(M!1, L!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 72, 13, 62])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 ((convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.20/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (convergent_lines(N!0, L!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 72, 16, 102])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[112, 72, 10, 109, 98])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------