TSTP Solution File: GEO214+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO214+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Fri Sep 16 20:35:45 EDT 2022
% Result : Theorem 0.14s 0.35s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO214+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n012.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 31 06:57:35 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.35 % SZS status Theorem
% 0.14/0.35 % SZS output start Proof
% 0.14/0.35 tff(convergent_lines_type, type, (
% 0.14/0.35 convergent_lines: ( $i * $i ) > $o)).
% 0.14/0.35 tff(tptp_fun_M_0_type, type, (
% 0.14/0.35 tptp_fun_M_0: $i)).
% 0.14/0.35 tff(tptp_fun_L_1_type, type, (
% 0.14/0.35 tptp_fun_L_1: $i)).
% 0.14/0.35 tff(unorthogonal_lines_type, type, (
% 0.14/0.35 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.14/0.35 tff(1,assumption,(convergent_lines(L!1, L!1)), introduced(assumption)).
% 0.14/0.35 tff(2,plain,
% 0.14/0.35 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(3,plain,
% 0.14/0.35 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.35 tff(4,plain,
% 0.14/0.35 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.14/0.35 tff(6,plain,
% 0.14/0.35 (![X: $i] : (~convergent_lines(X, X))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.35 tff(7,plain,(
% 0.14/0.35 ![X: $i] : (~convergent_lines(X, X))),
% 0.14/0.35 inference(skolemize,[status(sab)],[6])).
% 0.14/0.35 tff(8,plain,
% 0.14/0.35 (![X: $i] : (~convergent_lines(X, X))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.35 tff(9,plain,
% 0.14/0.35 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!1, L!1))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(10,plain,
% 0.14/0.35 ($false),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.14/0.35 tff(11,plain,(~convergent_lines(L!1, L!1)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.35 tff(12,plain,
% 0.14/0.35 (((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))) | convergent_lines(L!1, L!1)),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(13,plain,
% 0.14/0.35 ((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.14/0.35 tff(14,plain,
% 0.14/0.35 ((~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))) <=> (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(15,plain,
% 0.14/0.35 ((~![L: $i, M: $i] : (unorthogonal_lines(L, M) => unorthogonal_lines(M, L))) <=> (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(16,axiom,(~![L: $i, M: $i] : (unorthogonal_lines(L, M) => unorthogonal_lines(M, L))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.14/0.35 tff(17,plain,
% 0.14/0.35 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.14/0.35 tff(18,plain,
% 0.14/0.35 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.14/0.35 tff(19,plain,
% 0.14/0.35 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.14/0.35 tff(20,plain,
% 0.14/0.35 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.14/0.35 tff(21,plain,
% 0.14/0.35 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.14/0.35 tff(22,plain,
% 0.14/0.35 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.14/0.35 tff(23,plain,
% 0.14/0.35 (~![L: $i, M: $i] : ((~unorthogonal_lines(L, M)) | unorthogonal_lines(M, L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.14/0.35 tff(24,plain,(
% 0.14/0.35 ~((~unorthogonal_lines(L!1, M!0)) | unorthogonal_lines(M!0, L!1))),
% 0.14/0.35 inference(skolemize,[status(sab)],[23])).
% 0.14/0.35 tff(25,plain,
% 0.14/0.35 (~unorthogonal_lines(M!0, L!1)),
% 0.14/0.35 inference(or_elim,[status(thm)],[24])).
% 0.14/0.35 tff(26,plain,
% 0.14/0.35 (((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1))) | unorthogonal_lines(M!0, L!1)),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(27,plain,
% 0.14/0.35 ((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.14/0.35 tff(28,assumption,(convergent_lines(L!1, M!0)), introduced(assumption)).
% 0.14/0.35 tff(29,plain,
% 0.14/0.35 (unorthogonal_lines(L!1, M!0)),
% 0.14/0.35 inference(or_elim,[status(thm)],[24])).
% 0.14/0.35 tff(30,plain,
% 0.14/0.35 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(31,plain,
% 0.14/0.35 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.35 tff(32,plain,
% 0.14/0.35 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((convergent_lines(M, N) & unorthogonal_lines(M, N)) <=> (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), rewrite((convergent_lines(L, N) & unorthogonal_lines(L, N)) <=> (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))), trans(monotonicity(rewrite((convergent_lines(L, M) & unorthogonal_lines(L, M)) <=> (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> (~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), rewrite((~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), rewrite(((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(33,plain,
% 0.14/0.35 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.35 tff(34,plain,
% 0.14/0.35 (![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))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(35,plain,
% 0.14/0.35 (^[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))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(36,plain,
% 0.14/0.35 (![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))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.35 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')).
% 0.14/0.35 tff(38,plain,
% 0.14/0.35 (![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))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.35 tff(39,plain,
% 0.14/0.35 (![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))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.14/0.35 tff(40,plain,(
% 0.14/0.35 ![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))))),
% 0.14/0.35 inference(skolemize,[status(sab)],[39])).
% 0.14/0.35 tff(41,plain,
% 0.14/0.35 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.14/0.35 tff(42,plain,
% 0.14/0.35 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.14/0.35 tff(43,plain,
% 0.14/0.35 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_lines(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(44,plain,
% 0.14/0.35 (((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0))) <=> ((~unorthogonal_lines(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(45,plain,
% 0.14/0.35 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_lines(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))))))),
% 0.14/0.35 inference(monotonicity,[status(thm)],[44])).
% 0.14/0.35 tff(46,plain,
% 0.14/0.35 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))))),
% 0.14/0.35 inference(transitivity,[status(thm)],[45, 43])).
% 0.14/0.35 tff(47,plain,
% 0.14/0.35 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1)))) | (~unorthogonal_lines(L!1, M!0)))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(48,plain,
% 0.14/0.35 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~((~convergent_lines(M!0, L!1)) | (~unorthogonal_lines(M!0, L!1)))) | (~((~convergent_lines(L!1, L!1)) | (~unorthogonal_lines(L!1, L!1))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.14/0.35 tff(49,plain,
% 0.14/0.35 ($false),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[48, 42, 29, 28, 27, 13])).
% 0.14/0.35 tff(50,plain,(~convergent_lines(L!1, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.35 tff(51,plain,
% 0.14/0.35 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(52,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[51])).
% 0.14/0.35 tff(53,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(54,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.14/0.35 tff(55,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.14/0.35 tff(56,plain,(
% 0.14/0.35 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(skolemize,[status(sab)],[55])).
% 0.14/0.35 tff(57,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.14/0.35 tff(58,plain,
% 0.14/0.35 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(59,plain,
% 0.14/0.35 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(60,plain,
% 0.14/0.35 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!0, L!1) | unorthogonal_lines(M!0, L!1)),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.14/0.35 tff(61,plain,
% 0.14/0.35 (convergent_lines(M!0, L!1)),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[60, 57, 25])).
% 0.14/0.35 tff(62,plain,
% 0.14/0.35 (^[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))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(63,plain,
% 0.14/0.35 (![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)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[62])).
% 0.14/0.35 tff(64,plain,
% 0.14/0.35 (![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)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(65,plain,
% 0.14/0.35 (^[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)))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(66,plain,
% 0.14/0.35 (![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)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[65])).
% 0.14/0.35 tff(67,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.14/0.35 tff(68,plain,
% 0.14/0.35 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.14/0.35 tff(69,plain,
% 0.14/0.35 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.14/0.35 tff(70,plain,(
% 0.14/0.35 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.35 inference(skolemize,[status(sab)],[69])).
% 0.14/0.35 tff(71,plain,
% 0.14/0.35 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.14/0.36 tff(72,plain,
% 0.14/0.36 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!0, L!1)) | convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!0, L!1)) | convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(73,plain,
% 0.14/0.36 ((convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1))) <=> ((~convergent_lines(M!0, L!1)) | convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(74,plain,
% 0.14/0.36 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!0, L!1)) | convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0)))),
% 0.14/0.36 inference(monotonicity,[status(thm)],[73])).
% 0.14/0.36 tff(75,plain,
% 0.14/0.36 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!0, L!1)) | convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0))),
% 0.14/0.36 inference(transitivity,[status(thm)],[74, 72])).
% 0.14/0.36 tff(76,plain,
% 0.14/0.36 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0) | (~convergent_lines(M!0, L!1)))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(77,plain,
% 0.14/0.36 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!0, L!1)) | convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0)),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.14/0.36 tff(78,plain,
% 0.14/0.36 (convergent_lines(L!1, M!0) | convergent_lines(M!0, M!0)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[77, 71, 61])).
% 0.14/0.36 tff(79,plain,
% 0.14/0.36 (convergent_lines(M!0, M!0)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[78, 50])).
% 0.14/0.36 tff(80,plain,
% 0.14/0.36 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(M!0, M!0))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(81,plain,
% 0.14/0.36 ($false),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[80, 8, 79])).
% 0.14/0.36 % SZS output end Proof
%------------------------------------------------------------------------------