Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : ITP383_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% 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 Jun 21 05:12:46 AM UTC 2025

% Result   : Theorem 0.43s 0.62s
% Output   : Proof 0.47s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : ITP383_1 : TPTP v9.0.0. Released v8.0.0.
% 0.11/0.12  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Jun 19 18:49:04 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 0.43/0.62  % SZS status Theorem
% 0.43/0.62  % SZS output start Proof
% 0.43/0.62  tff(tptp_fun__fun_app_bd__type, type, (
% 0.43/0.62     tptp_fun__fun_app_bd_: ( |'A_update_a_update_fun$'| * |'A_update$'| ) > |'A_update$'|)).
% 0.43/0.62  tff(tptp_fun__fun_app_u__type, type, (
% 0.43/0.62     tptp_fun__fun_app_u_: ( |'C_update_a_update_fun$'| * |'C_update$'| ) > |'A_update$'|)).
% 0.43/0.62  tff(tptp_fun__g___type, type, (
% 0.43/0.62     tptp_fun__g__: |'C_update_a_update_fun$'|)).
% 0.43/0.62  tff(tptp_fun__comp_update___type, type, (
% 0.43/0.62     tptp_fun__comp_update__: |'A_update$'| > |'A_update_a_update_fun$'|)).
% 0.43/0.62  tff(tptp_fun__fun_app_au__type, type, (
% 0.43/0.62     tptp_fun__fun_app_au_: ( |'D_update_a_update_fun$'| * |'D_update$'| ) > |'A_update$'|)).
% 0.43/0.62  tff(tptp_fun__h___type, type, (
% 0.43/0.62     tptp_fun__h__: |'D_update_a_update_fun$'|)).
% 0.43/0.62  tff(tptp_fun__fun_app_k__type, type, (
% 0.43/0.62     tptp_fun__fun_app_k_: ( |'C_update_a_update_fun_bool_fun$'| * |'C_update_a_update_fun$'| ) > $o)).
% 0.43/0.62  tff(tptp_fun__register___type, type, (
% 0.43/0.62     tptp_fun__register__: |'C_update_a_update_fun_bool_fun$'|)).
% 0.43/0.62  tff(tptp_fun__fun_app_j__type, type, (
% 0.43/0.62     tptp_fun__fun_app_j_: ( |'D_update_a_update_fun_bool_fun$'| * |'D_update_a_update_fun$'| ) > $o)).
% 0.43/0.62  tff(tptp_fun__register_e__type, type, (
% 0.43/0.62     tptp_fun__register_e_: |'D_update_a_update_fun_bool_fun$'|)).
% 0.43/0.62  tff(tptp_fun__compatible___type, type, (
% 0.43/0.62     tptp_fun__compatible__: |'C_update_a_update_fun$'| > |'D_update_a_update_fun_bool_fun$'|)).
% 0.43/0.62  tff(tptp_fun_A__questionmark_v2_19_type, type, (
% 0.43/0.62     tptp_fun_A__questionmark_v2_19: ( |'D_update_a_update_fun$'| * |'C_update_a_update_fun$'| ) > |'C_update$'|)).
% 0.43/0.62  tff(tptp_fun_A__questionmark_v3_18_type, type, (
% 0.43/0.62     tptp_fun_A__questionmark_v3_18: ( |'D_update_a_update_fun$'| * |'C_update_a_update_fun$'| ) > |'D_update$'|)).
% 0.43/0.62  tff(1,plain,
% 0.43/0.62      ((~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)) <=> (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|))),
% 0.43/0.62      inference(rewrite,[status(thm)],[])).
% 0.43/0.62  tff(2,axiom,(~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture59')).
% 0.43/0.62  tff(3,plain,
% 0.43/0.62      (~tptp_fun__fun_app_k_(|'register$'|, |'g$'|)),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[2, 1])).
% 0.43/0.62  tff(4,plain,
% 0.43/0.62      (((~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$'|, |'g$'|)),
% 0.43/0.62      inference(tautology,[status(thm)],[])).
% 0.43/0.62  tff(5,plain,
% 0.43/0.62      ((~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))))),
% 0.43/0.62      inference(unit_resolution,[status(thm)],[4, 3])).
% 0.43/0.62  tff(6,plain,
% 0.43/0.62      (tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|) <=> tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)),
% 0.43/0.62      inference(rewrite,[status(thm)],[])).
% 0.43/0.62  tff(7,axiom,(tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom60')).
% 0.43/0.62  tff(8,plain,
% 0.43/0.62      (tptp_fun__fun_app_j_(tptp_fun__compatible__(|'g$'|), |'h$'|)),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[7, 6])).
% 0.43/0.62  tff(9,plain,
% 0.43/0.62      ((~((~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))))))),
% 0.43/0.62      inference(tautology,[status(thm)],[])).
% 0.43/0.62  tff(10,plain,
% 0.43/0.62      (~((~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)))))))),
% 0.43/0.62      inference(unit_resolution,[status(thm)],[9, 8, 5])).
% 0.43/0.62  tff(11,plain,
% 0.43/0.62      (((~((~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)))))))),
% 0.43/0.62      inference(tautology,[status(thm)],[])).
% 0.43/0.62  tff(12,plain,
% 0.43/0.62      ((~((~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))))))))),
% 0.43/0.62      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.43/0.62  tff(13,plain,
% 0.43/0.62      (^[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)))))))))))),
% 0.43/0.62      inference(bind,[status(th)],[])).
% 0.43/0.62  tff(14,plain,
% 0.43/0.62      (![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))))))))))),
% 0.43/0.62      inference(quant_intro,[status(thm)],[13])).
% 0.43/0.62  tff(15,plain,
% 0.43/0.62      (^[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))))))))))),
% 0.43/0.62      inference(bind,[status(th)],[])).
% 0.43/0.62  tff(16,plain,
% 0.43/0.62      (![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)))))))))),
% 0.43/0.62      inference(quant_intro,[status(thm)],[15])).
% 0.43/0.62  tff(17,plain,
% 0.43/0.62      (^[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))))))))))),
% 0.43/0.62      inference(bind,[status(th)],[])).
% 0.43/0.62  tff(18,plain,
% 0.43/0.62      (![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)))))))))),
% 0.43/0.62      inference(quant_intro,[status(thm)],[17])).
% 0.43/0.62  tff(19,plain,
% 0.43/0.62      (![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)))))))))),
% 0.43/0.62      inference(transitivity,[status(thm)],[18, 16])).
% 0.43/0.62  tff(20,plain,
% 0.43/0.62      (^[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)))))))))))),
% 0.43/0.62      inference(bind,[status(th)],[])).
% 0.43/0.62  tff(21,plain,
% 0.43/0.62      (![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)))))))))),
% 0.43/0.62      inference(quant_intro,[status(thm)],[20])).
% 0.43/0.62  tff(22,plain,
% 0.43/0.62      (^[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))))))))),
% 0.43/0.62      inference(bind,[status(th)],[])).
% 0.43/0.62  tff(23,plain,
% 0.43/0.62      (![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)))))))),
% 0.43/0.62      inference(quant_intro,[status(thm)],[22])).
% 0.43/0.62  tff(24,plain,
% 0.43/0.62      (![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)))))),
% 0.43/0.62      inference(rewrite,[status(thm)],[])).
% 0.43/0.62  tff(25,plain,
% 0.43/0.62      (^[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))))))),
% 0.43/0.62      inference(bind,[status(th)],[])).
% 0.43/0.62  tff(26,plain,
% 0.43/0.62      (![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)))))),
% 0.43/0.62      inference(quant_intro,[status(thm)],[25])).
% 0.43/0.62  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/sandbox/benchmark/theBenchmark.p','axiom115')).
% 0.43/0.62  tff(28,plain,
% 0.43/0.62      (![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)))))),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[27, 26])).
% 0.43/0.62  tff(29,plain,
% 0.43/0.62      (![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)))))),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[28, 24])).
% 0.43/0.62  tff(30,plain,(
% 0.43/0.62      ![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))))))))),
% 0.43/0.62      inference(skolemize,[status(sab)],[29])).
% 0.43/0.62  tff(31,plain,
% 0.43/0.62      (![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)))))))),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[30, 23])).
% 0.43/0.62  tff(32,plain,
% 0.43/0.62      (![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)))))))))),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[31, 21])).
% 0.43/0.62  tff(33,plain,
% 0.43/0.62      (![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)))))))))),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[32, 19])).
% 0.43/0.62  tff(34,plain,
% 0.43/0.62      (![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))))))))))),
% 0.43/0.62      inference(modus_ponens,[status(thm)],[33, 14])).
% 0.43/0.62  tff(35,plain,
% 0.43/0.62      (((~![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)))))))))))),
% 0.43/0.63      inference(rewrite,[status(thm)],[])).
% 0.43/0.63  tff(36,plain,
% 0.43/0.63      ((~((~(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))))))))))),
% 0.43/0.63      inference(rewrite,[status(thm)],[])).
% 0.43/0.63  tff(37,plain,
% 0.43/0.63      (((~![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)))))))))))),
% 0.43/0.63      inference(monotonicity,[status(thm)],[36])).
% 0.43/0.63  tff(38,plain,
% 0.43/0.63      (((~![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)))))))))))),
% 0.46/0.63      inference(transitivity,[status(thm)],[37, 35])).
% 0.46/0.63  tff(39,plain,
% 0.46/0.63      ((~![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))))))))))),
% 0.47/0.69      inference(quant_inst,[status(thm)],[])).
% 0.47/0.69  tff(40,plain,
% 0.47/0.69      ((~![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))))))))))),
% 0.47/0.69      inference(modus_ponens,[status(thm)],[39, 38])).
% 0.47/0.69  tff(41,plain,
% 0.47/0.69      ($false),
% 0.47/0.69      inference(unit_resolution,[status(thm)],[40, 34, 12])).
% 0.47/0.69  % SZS output end Proof
% 0.47/0.69  % E exiting
%------------------------------------------------------------------------------