TSTP Solution File: GEO217+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO217+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 20:35:46 EDT 2022
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO217+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 06:59:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(unorthogonal_lines_type, type, (
% 0.22/0.41 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.22/0.41 tff(tptp_fun_N_0_type, type, (
% 0.22/0.41 tptp_fun_N_0: $i)).
% 0.22/0.41 tff(tptp_fun_M_1_type, type, (
% 0.22/0.41 tptp_fun_M_1: $i)).
% 0.22/0.41 tff(tptp_fun_L_2_type, type, (
% 0.22/0.41 tptp_fun_L_2: $i)).
% 0.22/0.41 tff(convergent_lines_type, type, (
% 0.22/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 ((~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(3,axiom,(~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.41 tff(8,plain,
% 0.22/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.22/0.41 tff(11,plain,(
% 0.22/0.41 ~((~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[10])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 ((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0))),
% 0.22/0.41 inference(or_elim,[status(thm)],[11])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (~convergent_lines(L!2, M!1)),
% 0.22/0.41 inference(and_elim,[status(thm)],[12])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))) | convergent_lines(L!2, M!1)),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (~convergent_lines(L!2, N!0)),
% 0.22/0.41 inference(and_elim,[status(thm)],[12])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.41 tff(19,assumption,(unorthogonal_lines(M!1, N!0)), introduced(assumption)).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (convergent_lines(M!1, N!0)),
% 0.22/0.41 inference(or_elim,[status(thm)],[11])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (^[L: $i, M: $i, N: $i] : refl(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(22,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.42 tff(23,plain,
% 0.22/0.42 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) <=> (~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> (~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))))), rewrite((~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))) <=> ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))), rewrite(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(24,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(26,plain,
% 0.22/0.42 (^[L: $i, M: $i, N: $i] : rewrite(((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.42 tff(28,axiom,(![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','cotno1')).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.22/0.42 tff(31,plain,(
% 0.22/0.42 ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~unorthogonal_lines(M!1, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~unorthogonal_lines(M!1, N!0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))) <=> ((~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~unorthogonal_lines(M!1, N!0)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~unorthogonal_lines(M!1, N!0))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[35])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~unorthogonal_lines(M!1, N!0)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[36, 34])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~unorthogonal_lines(M!1, N!0))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[39, 33, 20, 19, 18, 15])).
% 0.22/0.42 tff(41,plain,(~unorthogonal_lines(M!1, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(42,assumption,(~convergent_lines(N!0, L!2)), introduced(assumption)).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 (![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)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (^[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))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (![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)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.22/0.42 tff(50,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.22/0.42 tff(53,plain,(
% 0.22/0.42 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[52])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, M!1) | unorthogonal_lines(M!1, N!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, M!1) | unorthogonal_lines(M!1, N!0))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1)) <=> ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, M!1) | unorthogonal_lines(M!1, N!0))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, M!1) | unorthogonal_lines(M!1, N!0)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[57])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, M!1) | unorthogonal_lines(M!1, N!0))),
% 0.22/0.43 inference(transitivity,[status(thm)],[58, 56])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, M!1))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (~convergent_lines(M!1, N!0)) | unorthogonal_lines(M!1, M!1) | unorthogonal_lines(M!1, N!0)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 (unorthogonal_lines(M!1, M!1) | unorthogonal_lines(M!1, N!0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[61, 55, 20])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (unorthogonal_lines(M!1, M!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[62, 41])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 (((~unorthogonal_lines(M!1, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))))) <=> ((~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[65])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[66, 64])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, M!1)) | (~convergent_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~convergent_lines(M!1, M!1)) | (~unorthogonal_lines(M!1, M!1)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (~convergent_lines(M!1, M!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[69, 33, 63, 15])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[71])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 (^[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)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.22/0.43 tff(76,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.22/0.43 tff(79,plain,(
% 0.22/0.43 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[78])).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.22/0.43 tff(81,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(82,plain,
% 0.22/0.43 ((~![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)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(83,plain,
% 0.22/0.43 ((~![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))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.22/0.43 tff(84,plain,
% 0.22/0.43 (~convergent_lines(M!1, L!2)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[83, 80, 13, 70])).
% 0.22/0.43 tff(85,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, M!1) | convergent_lines(N!0, M!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, M!1) | convergent_lines(N!0, M!1))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(86,plain,
% 0.22/0.43 ((convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, M!1) | convergent_lines(N!0, M!1))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(87,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, M!1) | convergent_lines(N!0, M!1)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[86])).
% 0.22/0.43 tff(88,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, M!1) | convergent_lines(N!0, M!1))),
% 0.22/0.43 inference(transitivity,[status(thm)],[87, 85])).
% 0.22/0.43 tff(89,plain,
% 0.22/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, N!0)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(90,plain,
% 0.22/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, M!1) | convergent_lines(N!0, M!1)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 (convergent_lines(M!1, M!1) | convergent_lines(N!0, M!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[90, 80, 20])).
% 0.22/0.43 tff(92,plain,
% 0.22/0.43 (convergent_lines(N!0, M!1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[91, 70])).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 (((~![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(N!0, 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(N!0, L!2) | (~convergent_lines(N!0, M!1)) | convergent_lines(M!1, L!2))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 ((convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(N!0, M!1))) <=> (convergent_lines(N!0, L!2) | (~convergent_lines(N!0, M!1)) | convergent_lines(M!1, L!2))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(95,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(N!0, M!1)))) <=> ((~![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(N!0, M!1)) | convergent_lines(M!1, L!2)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(N!0, M!1)))) <=> ((~![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(N!0, M!1)) | convergent_lines(M!1, L!2))),
% 0.22/0.43 inference(transitivity,[status(thm)],[95, 93])).
% 0.22/0.43 tff(97,plain,
% 0.22/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(N!0, M!1)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(N!0, L!2) | (~convergent_lines(N!0, M!1)) | convergent_lines(M!1, L!2)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[98, 80, 92, 84, 42])).
% 0.22/0.43 tff(100,plain,(convergent_lines(N!0, L!2)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(101,assumption,(~convergent_lines(N!0, N!0)), introduced(assumption)).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 ((convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2))) <=> (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[103])).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.22/0.43 inference(transitivity,[status(thm)],[104, 102])).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[107, 80, 16, 101, 100])).
% 0.22/0.43 tff(109,plain,(convergent_lines(N!0, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (unorthogonal_lines(M!1, N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(M!1, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(111,plain,
% 0.22/0.44 (((~convergent_lines(N!0, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0)) <=> (unorthogonal_lines(M!1, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(112,plain,
% 0.22/0.44 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (unorthogonal_lines(M!1, N!0) | (~convergent_lines(N!0, N!0))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[111])).
% 0.22/0.44 tff(113,plain,
% 0.22/0.44 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(M!1, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[112, 110])).
% 0.22/0.44 tff(114,plain,
% 0.22/0.44 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, N!0)) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(115,plain,
% 0.22/0.44 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(M!1, N!0) | (~convergent_lines(N!0, N!0))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.22/0.44 tff(116,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[115, 55, 109, 41])).
% 0.22/0.44 % SZS output end Proof
%------------------------------------------------------------------------------