TSTP Solution File: ITP383_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP383_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 Sep 17 04:18:54 EDT 2022
% Result : Theorem 0.54s 0.64s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP383_1 : TPTP v8.1.0. Released v8.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:19:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.54/0.64 % SZS status Theorem
% 0.54/0.64 % SZS output start Proof
% 0.54/0.64 tff(tptp_fun__fun_app_bd__type, type, (
% 0.54/0.64 tptp_fun__fun_app_bd_: ( 'A_update_a_update_fun$' * 'A_update$' ) > 'A_update$')).
% 0.54/0.64 tff(tptp_fun__fun_app_u__type, type, (
% 0.54/0.64 tptp_fun__fun_app_u_: ( 'C_update_a_update_fun$' * 'C_update$' ) > 'A_update$')).
% 0.54/0.64 tff(tptp_fun__g___type, type, (
% 0.54/0.64 tptp_fun__g__: 'C_update_a_update_fun$')).
% 0.54/0.64 tff(tptp_fun__comp_update___type, type, (
% 0.54/0.64 tptp_fun__comp_update__: 'A_update$' > 'A_update_a_update_fun$')).
% 0.54/0.64 tff(tptp_fun__fun_app_au__type, type, (
% 0.54/0.64 tptp_fun__fun_app_au_: ( 'D_update_a_update_fun$' * 'D_update$' ) > 'A_update$')).
% 0.54/0.64 tff(tptp_fun__h___type, type, (
% 0.54/0.64 tptp_fun__h__: 'D_update_a_update_fun$')).
% 0.54/0.64 tff(tptp_fun__fun_app_k__type, type, (
% 0.54/0.64 tptp_fun__fun_app_k_: ( 'C_update_a_update_fun_bool_fun$' * 'C_update_a_update_fun$' ) > $o)).
% 0.54/0.64 tff(tptp_fun__register___type, type, (
% 0.54/0.64 tptp_fun__register__: 'C_update_a_update_fun_bool_fun$')).
% 0.54/0.64 tff(tptp_fun__fun_app_j__type, type, (
% 0.54/0.64 tptp_fun__fun_app_j_: ( 'D_update_a_update_fun_bool_fun$' * 'D_update_a_update_fun$' ) > $o)).
% 0.54/0.64 tff(tptp_fun__register_e__type, type, (
% 0.54/0.64 tptp_fun__register_e_: 'D_update_a_update_fun_bool_fun$')).
% 0.54/0.64 tff(tptp_fun__compatible___type, type, (
% 0.54/0.64 tptp_fun__compatible__: 'C_update_a_update_fun$' > 'D_update_a_update_fun_bool_fun$')).
% 0.54/0.64 tff(tptp_fun_A__questionmark_v2_19_type, type, (
% 0.54/0.64 tptp_fun_A__questionmark_v2_19: ( 'D_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_update$')).
% 0.54/0.64 tff(tptp_fun_A__questionmark_v3_18_type, type, (
% 0.54/0.64 tptp_fun_A__questionmark_v3_18: ( 'D_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'D_update$')).
% 0.54/0.64 tff(1,plain,
% 0.54/0.64 ((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) <=> (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|))),
% 0.54/0.64 inference(rewrite,[status(thm)],[])).
% 0.54/0.64 tff(2,axiom,(~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture59')).
% 0.54/0.64 tff(3,plain,
% 0.54/0.64 (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)),
% 0.54/0.64 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.54/0.64 tff(4,plain,
% 0.54/0.64 (((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))) | tptp_fun__fun_app_k_(|'register$'|, |'g$'|)),
% 0.54/0.64 inference(tautology,[status(thm)],[])).
% 0.54/0.64 tff(5,plain,
% 0.54/0.64 ((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))),
% 0.54/0.64 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.54/0.64 tff(6,plain,
% 0.54/0.64 (tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) <=> tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)),
% 0.54/0.64 inference(rewrite,[status(thm)],[])).
% 0.54/0.64 tff(7,axiom,(tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom60')).
% 0.54/0.64 tff(8,plain,
% 0.54/0.64 (tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)),
% 0.54/0.64 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.54/0.64 tff(9,plain,
% 0.54/0.64 ((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)))))))) | (~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))),
% 0.54/0.64 inference(tautology,[status(thm)],[])).
% 0.54/0.64 tff(10,plain,
% 0.54/0.64 (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)))))))),
% 0.54/0.64 inference(unit_resolution,[status(thm)],[9, 8, 5])).
% 0.54/0.64 tff(11,plain,
% 0.54/0.64 (((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))) | ((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)))))))),
% 0.54/0.64 inference(tautology,[status(thm)],[])).
% 0.54/0.64 tff(12,plain,
% 0.54/0.64 ((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))),
% 0.54/0.64 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.54/0.64 tff(13,plain,
% 0.54/0.64 (^[A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : rewrite((~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))) <=> (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))))))),
% 0.54/0.64 inference(bind,[status(th)],[])).
% 0.54/0.64 tff(14,plain,
% 0.54/0.64 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))),
% 0.54/0.64 inference(quant_intro,[status(thm)],[13])).
% 0.54/0.64 tff(15,plain,
% 0.54/0.64 (^[A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : refl((~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))) <=> (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))))),
% 0.54/0.64 inference(bind,[status(th)],[])).
% 0.54/0.64 tff(16,plain,
% 0.54/0.64 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))),
% 0.54/0.64 inference(quant_intro,[status(thm)],[15])).
% 0.54/0.64 tff(17,plain,
% 0.54/0.64 (^[A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : rewrite((~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))) <=> (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))))),
% 0.54/0.64 inference(bind,[status(th)],[])).
% 0.54/0.64 tff(18,plain,
% 0.54/0.64 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))),
% 0.54/0.64 inference(quant_intro,[status(thm)],[17])).
% 0.54/0.64 tff(19,plain,
% 0.54/0.64 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))),
% 0.54/0.64 inference(transitivity,[status(thm)],[18, 16])).
% 0.54/0.64 tff(20,plain,
% 0.54/0.64 (^[A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : trans(monotonicity(rewrite(((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) <=> ((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))), rewrite((tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))) <=> (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))), ((((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) <=> (((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))), rewrite((((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) <=> (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))), ((((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) <=> (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))))),
% 0.54/0.65 inference(bind,[status(th)],[])).
% 0.54/0.65 tff(21,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))),
% 0.54/0.65 inference(quant_intro,[status(thm)],[20])).
% 0.54/0.65 tff(22,plain,
% 0.54/0.65 (^[A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : rewrite((((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | ((~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))) <=> (((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))),
% 0.54/0.65 inference(bind,[status(th)],[])).
% 0.54/0.65 tff(23,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | ((~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))),
% 0.54/0.65 inference(quant_intro,[status(thm)],[22])).
% 0.54/0.65 tff(24,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))),
% 0.54/0.65 inference(rewrite,[status(thm)],[])).
% 0.54/0.65 tff(25,plain,
% 0.54/0.65 (^[A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : rewrite((tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> ((tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) <=> (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))),
% 0.54/0.65 inference(bind,[status(th)],[])).
% 0.54/0.65 tff(26,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> ((tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) <=> ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))),
% 0.54/0.65 inference(quant_intro,[status(thm)],[25])).
% 0.54/0.65 tff(27,axiom,(![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> ((tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom115')).
% 0.54/0.65 tff(28,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))),
% 0.54/0.65 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.54/0.65 tff(29,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) <=> (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))),
% 0.54/0.65 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.54/0.65 tff(30,plain,(
% 0.54/0.65 ![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | ((~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))))),
% 0.54/0.65 inference(skolemize,[status(sab)],[29])).
% 0.54/0.65 tff(31,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0) & tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1) & ![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))) & (tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))),
% 0.54/0.65 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.54/0.65 tff(32,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))),
% 0.54/0.65 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.54/0.65 tff(33,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)))))))) | (~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0)))))))))),
% 0.54/0.65 inference(modus_ponens,[status(thm)],[32, 19])).
% 0.54/0.65 tff(34,plain,
% 0.54/0.65 (![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))),
% 0.54/0.65 inference(modus_ponens,[status(thm)],[33, 14])).
% 0.54/0.65 tff(35,plain,
% 0.54/0.65 (((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))))) <=> ((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)))))))))))),
% 0.54/0.65 inference(rewrite,[status(thm)],[])).
% 0.54/0.65 tff(36,plain,
% 0.54/0.65 ((~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)))))))))) <=> (~((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))))),
% 0.54/0.65 inference(rewrite,[status(thm)],[])).
% 0.54/0.65 tff(37,plain,
% 0.54/0.65 (((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))))) <=> ((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)))))))))))),
% 0.54/0.65 inference(monotonicity,[status(thm)],[36])).
% 0.54/0.65 tff(38,plain,
% 0.54/0.65 (((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))))) <=> ((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)))))))))))),
% 0.54/0.65 inference(transitivity,[status(thm)],[37, 35])).
% 0.54/0.65 tff(39,plain,
% 0.54/0.65 ((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))))),
% 0.56/0.71 inference(quant_inst,[status(thm)],[])).
% 0.56/0.71 tff(40,plain,
% 0.56/0.71 ((~![A__questionmark_v0: 'C_update_a_update_fun$', A__questionmark_v1: 'D_update_a_update_fun$'] : (~((~(tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1) | (~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, tptp_fun_A__questionmark_v3_18(A__questionmark_v1, A__questionmark_v0))), tptp_fun__fun_app_u_(A__questionmark_v0, tptp_fun_A__questionmark_v2_19(A__questionmark_v1, A__questionmark_v0))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(A__questionmark_v0), A__questionmark_v1)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, A__questionmark_v1)) | (~tptp_fun__fun_app_k_(|'register$'|, A__questionmark_v0)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2)), tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(A__questionmark_v1, A__questionmark_v3)), tptp_fun__fun_app_u_(A__questionmark_v0, A__questionmark_v2))))))))))) | (~((~((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) | (~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~(tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))), tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, tptp_fun_A__questionmark_v3_18(|'h$'|, |'g$'|))), tptp_fun__fun_app_u_(|'g$'|, tptp_fun_A__questionmark_v2_19(|'h$'|, |'g$'|))))))) | (~((~tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)) | (~((~tptp_fun__fun_app_j_(|'register$e'|, |'h$'|)) | (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) | (~![A__questionmark_v2: 'C_update$', A__questionmark_v3: 'D_update$'] : (tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2)), tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)) = tptp_fun__fun_app_bd_(tptp_fun__comp_update__(tptp_fun__fun_app_au_(|'h$'|, A__questionmark_v3)), tptp_fun__fun_app_u_(|'g$'|, A__questionmark_v2))))))))))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.56/0.71 tff(41,plain,
% 0.56/0.71 ($false),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[40, 34, 12])).
% 0.56/0.71 % SZS output end Proof
%------------------------------------------------------------------------------