%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO220+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:06:01 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : GEO220+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.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 14:42:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(unorthogonal_lines_type, type, (
% 0.20/0.38 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_N_0_type, type, (
% 0.20/0.38 tptp_fun_N_0: $i)).
% 0.20/0.38 tff(tptp_fun_L_2_type, type, (
% 0.20/0.38 tptp_fun_L_2: $i)).
% 0.20/0.38 tff(orthogonal_lines_type, type, (
% 0.20/0.38 orthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_M_1_type, type, (
% 0.20/0.38 tptp_fun_M_1: $i)).
% 0.20/0.38 tff(parallel_lines_type, type, (
% 0.20/0.38 parallel_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(convergent_lines_type, type, (
% 0.20/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : refl((~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : trans(rewrite((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))), rewrite((~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))), ((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.38 tff(6,axiom,(![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a5')).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,(
% 0.20/0.38 ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[8])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))) | (~(unorthogonal_lines(L!2, N!0) <=> orthogonal_lines(L!2, N!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (~(unorthogonal_lines(L!2, N!0) <=> orthogonal_lines(L!2, N!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 ((~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & orthogonal_lines(L, N))) | parallel_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & orthogonal_lines(L, N))) | parallel_lines(M, N)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((~![L: $i, M: $i, N: $i] : ((orthogonal_lines(L, M) & orthogonal_lines(L, N)) => parallel_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & orthogonal_lines(L, N))) | parallel_lines(M, N)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,axiom,(~![L: $i, M: $i, N: $i] : ((orthogonal_lines(L, M) & orthogonal_lines(L, N)) => parallel_lines(M, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & orthogonal_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & orthogonal_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & orthogonal_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & orthogonal_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.39 tff(20,plain,(
% 0.20/0.39 ~((~(orthogonal_lines(L!2, M!1) & orthogonal_lines(L!2, N!0))) | parallel_lines(M!1, N!0))),
% 0.20/0.39 inference(skolemize,[status(sab)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (orthogonal_lines(L!2, M!1) & orthogonal_lines(L!2, N!0)),
% 0.20/0.39 inference(or_elim,[status(thm)],[20])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (orthogonal_lines(L!2, N!0)),
% 0.20/0.39 inference(and_elim,[status(thm)],[21])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((unorthogonal_lines(L!2, N!0) <=> orthogonal_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)) | (~orthogonal_lines(L!2, N!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((unorthogonal_lines(L!2, N!0) <=> orthogonal_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (~unorthogonal_lines(L!2, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[24, 12])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))) | (~(unorthogonal_lines(L!2, M!1) <=> orthogonal_lines(L!2, M!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~(unorthogonal_lines(L!2, M!1) <=> orthogonal_lines(L!2, M!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 10])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (orthogonal_lines(L!2, M!1)),
% 0.20/0.39 inference(and_elim,[status(thm)],[21])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((unorthogonal_lines(L!2, M!1) <=> orthogonal_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~orthogonal_lines(L!2, M!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((unorthogonal_lines(L!2, M!1) <=> orthogonal_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (~unorthogonal_lines(L!2, M!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : refl((~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : trans(rewrite((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))), rewrite((~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))), ((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.39 tff(37,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.39 tff(40,plain,(
% 0.20/0.39 ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))) | (~(convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (~(convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (~parallel_lines(M!1, N!0)),
% 0.20/0.39 inference(or_elim,[status(thm)],[20])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0)) | convergent_lines(M!1, N!0) | parallel_lines(M!1, N!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((convergent_lines(M!1, N!0) <=> parallel_lines(M!1, N!0)) | convergent_lines(M!1, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (convergent_lines(M!1, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.39 tff(50,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))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(51,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] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.39 tff(52,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, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (^[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))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.39 tff(55,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')).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.39 tff(58,plain,(
% 0.20/0.39 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(L!2, N!0))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(L!2, N!0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0))) <=> (unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(L!2, N!0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(L!2, N!0)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(L!2, N!0))),
% 0.20/0.39 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!2, M!1) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(L!2, N!0)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[66, 60, 47, 31, 25])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------