%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO212+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:05:58 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO212+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 14:41:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(convergent_lines_type, type, (
% 0.19/0.43 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.43 tff(tptp_fun_N_0_type, type, (
% 0.19/0.43 tptp_fun_N_0: $i)).
% 0.19/0.43 tff(tptp_fun_L_2_type, type, (
% 0.19/0.43 tptp_fun_L_2: $i)).
% 0.19/0.43 tff(tptp_fun_M_1_type, type, (
% 0.19/0.43 tptp_fun_M_1: $i)).
% 0.19/0.43 tff(unorthogonal_lines_type, type, (
% 0.19/0.43 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.43 tff(distinct_lines_type, type, (
% 0.19/0.43 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.43 tff(apart_point_and_line_type, type, (
% 0.19/0.43 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.43 tff(intersection_point_type, type, (
% 0.19/0.43 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.43 tff(1,assumption,(convergent_lines(N!0, N!0)), introduced(assumption)).
% 0.19/0.43 tff(2,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(3,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)],[2])).
% 0.19/0.43 tff(4,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(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.43 tff(7,plain,(
% 0.19/0.43 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(skolemize,[status(sab)],[6])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(N!0, N!0))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.43 tff(11,plain,(~convergent_lines(N!0, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 ((~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))) <=> (~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (convergent_lines(L, N) | unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(15,axiom,(~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (convergent_lines(L, N) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.19/0.43 tff(20,plain,(
% 0.19/0.43 ~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[19])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (~convergent_lines(L!2, N!0)),
% 0.19/0.43 inference(or_elim,[status(thm)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (~unorthogonal_lines(M!1, N!0)),
% 0.19/0.43 inference(or_elim,[status(thm)],[21])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))) | unorthogonal_lines(M!1, N!0)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 ((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,assumption,(convergent_lines(L!2, M!1)), introduced(assumption)).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (unorthogonal_lines(L!2, M!1)),
% 0.19/0.43 inference(or_elim,[status(thm)],[21])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (^[L: $i, M: $i, N: $i] : refl(((~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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (^[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)) | (~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(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(33,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)))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.43 tff(34,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)))) <=> ![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(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.43 tff(37,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')).
% 0.19/0.43 tff(38,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)],[37, 36])).
% 0.19/0.43 tff(39,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)],[38, 34])).
% 0.19/0.43 tff(40,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)],[39])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))) <=> ((~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (((~![L: $i, M: $i, N: $i] : ((~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!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (((~![L: $i, M: $i, N: $i] : ((~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!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[45, 43])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 ((~![L: $i, M: $i, N: $i] : ((~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!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[48, 42, 29, 28, 27, 24])).
% 0.19/0.44 tff(50,plain,(~convergent_lines(L!2, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(51,assumption,(convergent_lines(M!1, M!1)), introduced(assumption)).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(M!1, M!1))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[52, 8, 51])).
% 0.19/0.44 tff(54,plain,(~convergent_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.44 tff(60,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')).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.44 tff(63,plain,(
% 0.19/0.44 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[62])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, M!1) | convergent_lines(L!2, 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(M!1, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 ((convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))) <=> (convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (((~![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(M!1, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(M!1, L!2))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (((~![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(M!1, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(M!1, L!2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (~convergent_lines(M!1, L!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[70, 64, 54, 50])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(75,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.44 tff(77,plain,(
% 0.19/0.44 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.44 inference(skolemize,[status(sab)],[76])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (convergent_lines(M!1, N!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[81, 78, 25])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (((~![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, L!2) | 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(M!1, N!0)) | convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 ((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(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (((~![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(N!0, L!2) | convergent_lines(M!1, L!2)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (((~![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(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.19/0.44 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 ((~![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, L!2) | convergent_lines(M!1, L!2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[88, 64, 82])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (convergent_lines(N!0, L!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[89, 71])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.44 tff(96,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.44 tff(99,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[98])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), L!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), L!2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), L!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), L!2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 ((~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), L!2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[103, 100])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (~apart_point_and_line(intersection_point(N!0, L!2), L!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[104, 90])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.44 tff(111,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.19/0.44 tff(114,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[113])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), N!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), N!0)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), N!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), N!0))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 ((~convergent_lines(N!0, L!2)) | (~apart_point_and_line(intersection_point(N!0, L!2), N!0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (~apart_point_and_line(intersection_point(N!0, L!2), N!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[119, 90])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.45 tff(126,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.45 tff(129,plain,(
% 0.19/0.45 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[128])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!2, N!0) | (~distinct_lines(L!2, N!0)) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | apart_point_and_line(intersection_point(N!0, L!2), N!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | convergent_lines(L!2, N!0) | (~distinct_lines(L!2, N!0)) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | apart_point_and_line(intersection_point(N!0, L!2), N!0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(132,plain,
% 0.19/0.45 ((convergent_lines(L!2, N!0) | apart_point_and_line(intersection_point(N!0, L!2), N!0) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | (~distinct_lines(L!2, N!0))) <=> (convergent_lines(L!2, N!0) | (~distinct_lines(L!2, N!0)) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | apart_point_and_line(intersection_point(N!0, L!2), N!0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!2, N!0) | apart_point_and_line(intersection_point(N!0, L!2), N!0) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | (~distinct_lines(L!2, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!2, N!0) | (~distinct_lines(L!2, N!0)) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | apart_point_and_line(intersection_point(N!0, L!2), N!0)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[132])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!2, N!0) | apart_point_and_line(intersection_point(N!0, L!2), N!0) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | (~distinct_lines(L!2, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | convergent_lines(L!2, N!0) | (~distinct_lines(L!2, N!0)) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | apart_point_and_line(intersection_point(N!0, L!2), N!0))),
% 0.19/0.45 inference(transitivity,[status(thm)],[133, 131])).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!2, N!0) | apart_point_and_line(intersection_point(N!0, L!2), N!0) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | (~distinct_lines(L!2, N!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | convergent_lines(L!2, N!0) | (~distinct_lines(L!2, N!0)) | apart_point_and_line(intersection_point(N!0, L!2), L!2) | apart_point_and_line(intersection_point(N!0, L!2), N!0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (~distinct_lines(L!2, N!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[136, 130, 22, 120, 105])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[141])).
% 0.19/0.45 tff(143,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.19/0.45 tff(146,plain,(
% 0.19/0.45 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[145])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((distinct_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2))) <=> (distinct_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.19/0.45 inference(transitivity,[status(thm)],[150, 148])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[153, 147, 137, 90, 11])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------