%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT152+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:37:01 PM UTC 2026
% Result : Theorem 9.24s 2.16s
% Output : Refutation 9.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 18
% Syntax : Number of formulae : 176 ( 36 unt; 10 def)
% Number of atoms : 832 ( 204 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1023 ( 367 ~; 630 |; 6 &)
% ( 9 <=>; 8 =>; 0 <=; 3 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 18 con; 0-6 aty)
% Number of variables : 292 ( 0 sgn 289 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I1_J) ).
fof(f5,axiom,
v_b____ != v_c____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I2_J) ).
fof(f8,axiom,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I5_J) ).
fof(f10,axiom,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),c_Arrow__Order__Mirabelle_OProf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cP) ).
fof(f11,axiom,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),X0))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062_Iconverse_Ao_AP_J_Ai_092_060_094esub_062_Aa_J_A_061_A_Ib_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ac_J_096) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4,X5] :
( X5 != X4
=> ( X3 != X2
=> ( X5 != X2
=> ( X4 != X3
=> ( c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
=> ( c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
=> ( ! [X6] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,X6))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,X6)) )
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
fof(f106,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Fun_Ocomp(X6,X5,X4,X3,X2) = X1
=> hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(f519,conjecture,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(v_F,c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____)))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_F,v_P_H____)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f520,negated_conjecture,
~ ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(v_F,c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____)))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_F,v_P_H____)) ),
inference(negated_conjecture,[status(cth)],[f519]) ).
fof(f549,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0)) )
| ? [X6] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,X6))
<~> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,X6)) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| X3 = X4
| X2 = X5
| X2 = X3
| X4 = X5 ),
inference(ennf_transformation,[],[f12]) ).
fof(f550,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1))
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0)) )
| ? [X6] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,X6))
<~> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,X6)) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| X3 = X4
| X2 = X5
| X2 = X3
| X4 = X5 ),
inference(flattening,[],[f549]) ).
fof(f646,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0)
| c_Fun_Ocomp(X6,X5,X4,X3,X2) != X1 ),
inference(ennf_transformation,[],[f106]) ).
fof(f1006,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(v_F,c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____)))
<~> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_F,v_P_H____)) ),
inference(ennf_transformation,[],[f520]) ).
fof(f1013,plain,
! [X0] :
( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),X0)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f1014,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1)) ) )
| ? [X6] :
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,X6))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,X6)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,X6))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,X6)) ) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| X3 = X4
| X2 = X5
| X2 = X3
| X4 = X5 ),
inference(nnf_transformation,[],[f550]) ).
fof(f1015,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0)) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1)) ) )
| ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,sK3(X0,X1,X2,X3,X4,X5)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,sK3(X0,X1,X2,X3,X4,X5))) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,sK3(X0,X1,X2,X3,X4,X5)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,sK3(X0,X1,X2,X3,X4,X5))) ) )
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| X3 = X4
| X2 = X5
| X2 = X3
| X4 = X5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X6,sK3(X0,X1,X2,X3,X4,X5))],[f1014]) ).
fof(f1213,plain,
( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_F,v_P_H____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(v_F,c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____))) )
& ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_F,v_P_H____))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(v_F,c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____))) ) ),
inference(nnf_transformation,[],[f1006]) ).
fof(f1217,plain,
v_a____ != v_b____,
inference(cnf_transformation,[],[f4]) ).
fof(f1218,plain,
v_b____ != v_c____,
inference(cnf_transformation,[],[f5]) ).
fof(f1221,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf),
inference(cnf_transformation,[],[f8]) ).
fof(f1224,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),c_Arrow__Order__Mirabelle_OProf),
inference(cnf_transformation,[],[f10]) ).
fof(f1225,plain,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),X0)) ),
inference(cnf_transformation,[],[f1013]) ).
fof(f1226,plain,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(cnf_transformation,[],[f1013]) ).
fof(f1227,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,sK3(X0,X1,X2,X3,X4,X5)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,sK3(X0,X1,X2,X3,X4,X5)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| X3 = X4
| X2 = X5
| X2 = X3
| X4 = X5 ),
inference(cnf_transformation,[],[f1015]) ).
fof(f1228,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(X1,sK3(X0,X1,X2,X3,X4,X5)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),hAPP(v_F,X1))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X0,sK3(X0,X1,X2,X3,X4,X5)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| X3 = X4
| X2 = X5
| X2 = X3
| X4 = X5 ),
inference(cnf_transformation,[],[f1015]) ).
fof(f1426,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(X1,X0) = hAPP(X3,hAPP(X2,X0))
| c_Fun_Ocomp(X6,X5,X4,X3,X2) != X1 ),
inference(cnf_transformation,[],[f646]) ).
fof(f1949,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_F,v_P_H____))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(v_F,c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____))) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1950,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_F,v_P_H____))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(v_F,c_Fun_Ocomp(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____))) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f2074,plain,
! [X2,X3,X0,X6,X4,X5] : hAPP(X3,hAPP(X2,X0)) = hAPP(c_Fun_Ocomp(X6,X5,X4,X3,X2),X0),
inference(equality_resolution,[],[f1426]) ).
fof(f2142,definition,
sF81 = tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
introduced(definition,[new_symbols(definition,[sF81])],[function_definition]) ).
fof(f2143,plain,
tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = sF81,
inference(reorient_equations,[],[f2142]) ).
fof(f2144,definition,
sF82 = c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),
introduced(definition,[new_symbols(definition,[sF82])],[function_definition]) ).
fof(f2145,plain,
c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____) = sF82,
inference(reorient_equations,[],[f2144]) ).
fof(f2146,definition,
sF83 = hAPP(v_F,v_P_H____),
introduced(definition,[new_symbols(definition,[sF83])],[function_definition]) ).
fof(f2147,plain,
hAPP(v_F,v_P_H____) = sF83,
inference(reorient_equations,[],[f2146]) ).
fof(f2148,definition,
sF84 = c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),
introduced(definition,[new_symbols(definition,[sF84])],[function_definition]) ).
fof(f2149,plain,
c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____) = sF84,
inference(reorient_equations,[],[f2148]) ).
fof(f2150,definition,
sF85 = tc_fun(sF81,tc_HOL_Obool),
introduced(definition,[new_symbols(definition,[sF85])],[function_definition]) ).
fof(f2151,plain,
tc_fun(sF81,tc_HOL_Obool) = sF85,
inference(reorient_equations,[],[f2150]) ).
fof(f2152,definition,
sF86 = c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
introduced(definition,[new_symbols(definition,[sF86])],[function_definition]) ).
fof(f2153,plain,
c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = sF86,
inference(reorient_equations,[],[f2152]) ).
fof(f2154,definition,
sF87 = c_Fun_Ocomp(sF85,sF85,tc_Arrow__Order__Mirabelle_Oindi,sF86,v_P____),
introduced(definition,[new_symbols(definition,[sF87])],[function_definition]) ).
fof(f2155,plain,
c_Fun_Ocomp(sF85,sF85,tc_Arrow__Order__Mirabelle_Oindi,sF86,v_P____) = sF87,
inference(reorient_equations,[],[f2154]) ).
fof(f2156,definition,
sF88 = hAPP(v_F,sF87),
introduced(definition,[new_symbols(definition,[sF88])],[function_definition]) ).
fof(f2157,plain,
hAPP(v_F,sF87) = sF88,
inference(reorient_equations,[],[f2156]) ).
fof(f2158,plain,
( ~ c_member(sF81,sF82,sF83)
| ~ c_member(sF81,sF84,sF88) ),
inference(definition_folding,[],[f1950,f2157,f2155,f2153,f2151,f2143,f2151,f2143,f2149,f2143,f2147,f2145,f2143]) ).
fof(f2159,plain,
( c_member(sF81,sF82,sF83)
| c_member(sF81,sF84,sF88) ),
inference(definition_folding,[],[f1949,f2157,f2155,f2153,f2151,f2143,f2151,f2143,f2149,f2143,f2147,f2145,f2143]) ).
fof(f2168,definition,
( spl89_1
<=> c_member(sF81,sF84,sF88) ),
introduced(definition,[new_symbols(definition,[spl89_1])],[avatar_definition]) ).
fof(f2169,plain,
( ~ c_member(sF81,sF84,sF88)
| spl89_1 ),
inference(avatar_component_clause,[],[f2168]) ).
fof(f2170,plain,
( c_member(sF81,sF84,sF88)
| ~ spl89_1 ),
inference(avatar_component_clause,[],[f2168]) ).
fof(f2172,definition,
( spl89_2
<=> c_member(sF81,sF82,sF83) ),
introduced(definition,[new_symbols(definition,[spl89_2])],[avatar_definition]) ).
fof(f2173,plain,
( ~ c_member(sF81,sF82,sF83)
| spl89_2 ),
inference(avatar_component_clause,[],[f2172]) ).
fof(f2174,plain,
( c_member(sF81,sF82,sF83)
| ~ spl89_2 ),
inference(avatar_component_clause,[],[f2172]) ).
fof(f2175,plain,
( spl89_1
| spl89_2 ),
inference(avatar_split_clause,[],[f2159,f2172,f2168]) ).
fof(f2176,plain,
( ~ spl89_1
| ~ spl89_2 ),
inference(avatar_split_clause,[],[f2158,f2172,f2168]) ).
fof(f2183,plain,
! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f1225,f2074]) ).
fof(f2184,plain,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f1226,f2074]) ).
fof(f2189,plain,
! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(sF86,hAPP(v_P____,X0)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2183,f2153]) ).
fof(f2190,plain,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_a____),hAPP(sF86,hAPP(v_P____,X0)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2184,f2153]) ).
fof(f2191,plain,
! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(sF86,hAPP(v_P____,X0)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2189,f2149]) ).
fof(f2192,plain,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(sF86,hAPP(v_P____,X0)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2190,f2149]) ).
fof(f2193,plain,
! [X0] :
( ~ c_member(sF81,sF84,hAPP(sF86,hAPP(v_P____,X0)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2191,f2143]) ).
fof(f2194,plain,
! [X0] :
( c_member(sF81,sF84,hAPP(sF86,hAPP(v_P____,X0)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b____,v_c____),hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2192,f2143]) ).
fof(f2195,plain,
! [X0] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_P_H____,X0))
| ~ c_member(sF81,sF84,hAPP(sF86,hAPP(v_P____,X0))) ),
inference(forward_demodulation,[],[f2193,f2145]) ).
fof(f2196,plain,
! [X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_P_H____,X0))
| c_member(sF81,sF84,hAPP(sF86,hAPP(v_P____,X0))) ),
inference(forward_demodulation,[],[f2194,f2145]) ).
fof(f2197,plain,
! [X0] :
( ~ c_member(sF81,sF84,hAPP(sF86,hAPP(v_P____,X0)))
| c_member(sF81,sF82,hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2195,f2143]) ).
fof(f2198,plain,
! [X0] :
( c_member(sF81,sF84,hAPP(sF86,hAPP(v_P____,X0)))
| ~ c_member(sF81,sF82,hAPP(v_P_H____,X0)) ),
inference(forward_demodulation,[],[f2196,f2143]) ).
fof(f2278,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),c_Fun_Ocomp(tc_fun(sF81,tc_HOL_Obool),tc_fun(sF81,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____),c_Arrow__Order__Mirabelle_OProf),
inference(superposition,[],[f1224,f2143]) ).
fof(f2279,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),c_Fun_Ocomp(tc_fun(sF81,tc_HOL_Obool),tc_fun(sF81,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,sF86,v_P____),c_Arrow__Order__Mirabelle_OProf),
inference(forward_demodulation,[],[f2278,f2153]) ).
fof(f2280,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),c_Fun_Ocomp(sF85,sF85,tc_Arrow__Order__Mirabelle_Oindi,sF86,v_P____),c_Arrow__Order__Mirabelle_OProf),
inference(forward_demodulation,[],[f2279,f2151]) ).
fof(f2281,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),sF87,c_Arrow__Order__Mirabelle_OProf),
inference(forward_demodulation,[],[f2280,f2155]) ).
fof(f2283,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3
| v_a____ = v_b____ ),
inference(superposition,[],[f1227,f2149]) ).
fof(f2292,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_subsumption_resolution,[],[f2283,f1217]) ).
fof(f2298,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2292,f2143]) ).
fof(f2304,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2298,f2143]) ).
fof(f2310,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,sF84,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2304,f2143]) ).
fof(f2316,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2310,f2143]) ).
fof(f2322,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2316,f2143]) ).
fof(f2328,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2322,f2151]) ).
fof(f2334,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2328,f2143]) ).
fof(f2340,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2334,f2151]) ).
fof(f2343,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3
| v_b____ = v_c____ ),
inference(superposition,[],[f1227,f2145]) ).
fof(f2352,plain,
! [X2,X3,X0,X1] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_subsumption_resolution,[],[f2343,f1218]) ).
fof(f2358,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2352,f2143]) ).
fof(f2364,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_F,X0))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2358,f2143]) ).
fof(f2370,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,sF82,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2364,f2143]) ).
fof(f2376,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2370,f2143]) ).
fof(f2382,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2376,f2143]) ).
fof(f2388,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2382,f2151]) ).
fof(f2394,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2388,f2143]) ).
fof(f2400,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2394,f2151]) ).
fof(f2411,plain,
! [X0,X1] :
( c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| v_b____ = v_c____
| v_a____ = v_b____
| v_a____ = v_b____ ),
inference(superposition,[],[f2400,f2149]) ).
fof(f2416,plain,
! [X0,X1] :
( c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| v_b____ = v_c____
| v_a____ = v_b____ ),
inference(duplicate_literal_removal,[],[f2411]) ).
fof(f2418,plain,
! [X0,X1] :
( c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = v_b____ ),
inference(forward_subsumption_resolution,[],[f2416,f1218]) ).
fof(f2419,plain,
! [X0,X1] :
( c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf) ),
inference(forward_subsumption_resolution,[],[f2418,f1217]) ).
fof(f2534,plain,
! [X0,X1] :
( c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = v_b____
| v_b____ = v_c____
| v_b____ = v_c____ ),
inference(superposition,[],[f2340,f2145]) ).
fof(f2537,plain,
! [X0,X1] :
( c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = v_b____
| v_b____ = v_c____ ),
inference(duplicate_literal_removal,[],[f2534]) ).
fof(f2539,plain,
! [X0,X1] :
( c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| v_b____ = v_c____ ),
inference(forward_subsumption_resolution,[],[f2537,f1217]) ).
fof(f2541,plain,
! [X0,X1] :
( c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf) ),
inference(forward_subsumption_resolution,[],[f2539,f1218]) ).
fof(f2843,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3
| v_a____ = v_b____ ),
inference(superposition,[],[f1228,f2149]) ).
fof(f2844,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3
| v_b____ = v_c____ ),
inference(superposition,[],[f1228,f2145]) ).
fof(f2849,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_subsumption_resolution,[],[f2844,f1218]) ).
fof(f2850,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_subsumption_resolution,[],[f2843,f1217]) ).
fof(f2853,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF82,hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2849,f2143]) ).
fof(f2854,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sF84,hAPP(v_F,X0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2850,f2143]) ).
fof(f2857,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2853,f2143]) ).
fof(f2858,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2854,f2143]) ).
fof(f2860,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2857,f2143]) ).
fof(f2861,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2858,f2143]) ).
fof(f2863,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2860,f2143]) ).
fof(f2864,plain,
! [X2,X3,X0,X1] :
( c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2861,f2143]) ).
fof(f2866,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2863,f2143]) ).
fof(f2867,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2864,f2143]) ).
fof(f2869,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2866,f2151]) ).
fof(f2870,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2867,f2151]) ).
fof(f2872,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2869,f2143]) ).
fof(f2873,plain,
! [X2,X3,X0,X1] :
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2870,f2143]) ).
fof(f2874,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X1,X0,X2,X3,v_c____,v_b____)))
| v_c____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2872,f2151]) ).
fof(f2875,plain,
! [X2,X3,X0,X1] :
( ~ c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(X1,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X2),hAPP(v_F,X1))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(X0,sK3(X1,X0,X2,X3,v_a____,v_b____)))
| v_a____ = X3
| v_b____ = X2
| X2 = X3 ),
inference(forward_demodulation,[],[f2873,f2151]) ).
fof(f2878,plain,
! [X0,X1] :
( ~ c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| v_b____ = v_c____
| v_a____ = v_b____
| v_a____ = v_b____ ),
inference(superposition,[],[f2874,f2149]) ).
fof(f2882,plain,
! [X0,X1] :
( ~ c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| v_b____ = v_c____
| v_a____ = v_b____ ),
inference(duplicate_literal_removal,[],[f2878]) ).
fof(f2886,plain,
! [X0,X1] :
( ~ c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| v_a____ = v_b____ ),
inference(forward_subsumption_resolution,[],[f2882,f1218]) ).
fof(f2887,plain,
! [X0,X1] :
( ~ c_member(sF81,sF84,hAPP(X0,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF84,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(X1,sK3(X0,X1,v_a____,v_b____,v_c____,v_b____))) ),
inference(forward_subsumption_resolution,[],[f2886,f1217]) ).
fof(f2891,plain,
! [X0,X1] :
( ~ c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| v_a____ = v_b____
| v_b____ = v_c____
| v_b____ = v_c____ ),
inference(superposition,[],[f2875,f2145]) ).
fof(f2893,plain,
! [X0,X1] :
( ~ c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| v_a____ = v_b____
| v_b____ = v_c____ ),
inference(duplicate_literal_removal,[],[f2891]) ).
fof(f2897,plain,
! [X0,X1] :
( ~ c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| v_b____ = v_c____ ),
inference(forward_subsumption_resolution,[],[f2893,f1217]) ).
fof(f2899,plain,
! [X0,X1] :
( ~ c_member(sF81,sF84,hAPP(X1,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X1,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF84,hAPP(v_F,X1))
| ~ c_member(sF81,sF82,hAPP(X0,sK3(X0,X1,v_c____,v_b____,v_a____,v_b____))) ),
inference(forward_subsumption_resolution,[],[f2897,f1218]) ).
fof(f2969,plain,
! [X0] : hAPP(sF86,hAPP(v_P____,X0)) = hAPP(sF87,X0),
inference(superposition,[],[f2074,f2155]) ).
fof(f3135,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(sF81,tc_HOL_Obool)),v_P_H____,c_Arrow__Order__Mirabelle_OProf),
inference(superposition,[],[f1221,f2143]) ).
fof(f3136,plain,
c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),v_P_H____,c_Arrow__Order__Mirabelle_OProf),
inference(forward_demodulation,[],[f3135,f2151]) ).
fof(f3198,plain,
! [X0] :
( ~ c_member(sF81,sF84,hAPP(sF87,X0))
| c_member(sF81,sF82,hAPP(v_P_H____,X0)) ),
inference(superposition,[],[f2197,f2969]) ).
fof(f3199,plain,
! [X0] :
( ~ c_member(sF81,sF82,hAPP(v_P_H____,X0))
| c_member(sF81,sF84,hAPP(sF87,X0)) ),
inference(superposition,[],[f2198,f2969]) ).
fof(f3222,plain,
! [X0] :
( c_member(sF81,sF82,hAPP(X0,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),sF87,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____))) ),
inference(resolution,[],[f2541,f3198]) ).
fof(f3227,plain,
! [X0] :
( c_member(sF81,sF82,hAPP(X0,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____))) ),
inference(forward_subsumption_resolution,[],[f3222,f2281]) ).
fof(f3232,plain,
! [X0] :
( c_member(sF81,sF82,hAPP(X0,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),sF87,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____))) ),
inference(resolution,[],[f2419,f3198]) ).
fof(f3237,plain,
! [X0] :
( c_member(sF81,sF82,hAPP(X0,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____))) ),
inference(forward_subsumption_resolution,[],[f3232,f2281]) ).
fof(f3238,plain,
! [X0] :
( c_member(sF81,sF84,sF88)
| c_member(sF81,sF82,hAPP(X0,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____))) ),
inference(forward_demodulation,[],[f3237,f2157]) ).
fof(f3239,plain,
( ! [X0] :
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(sF87,X0,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,X0)) )
| spl89_1 ),
inference(forward_subsumption_resolution,[],[f3238,f2169]) ).
fof(f3241,plain,
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| spl89_1 ),
inference(factoring,[],[f3239]) ).
fof(f3243,plain,
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| spl89_1 ),
inference(forward_subsumption_resolution,[],[f3241,f3136]) ).
fof(f3244,plain,
( ~ c_member(sF81,sF82,sF83)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| spl89_1 ),
inference(forward_demodulation,[],[f3243,f2147]) ).
fof(f3245,plain,
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| spl89_1
| ~ spl89_2 ),
inference(forward_subsumption_resolution,[],[f3244,f2174]) ).
fof(f3246,plain,
( c_member(sF81,sF84,hAPP(sF87,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| spl89_1
| ~ spl89_2 ),
inference(resolution,[],[f3245,f3199]) ).
fof(f3249,plain,
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),sF87,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| spl89_1
| ~ spl89_2 ),
inference(resolution,[],[f3246,f2887]) ).
fof(f3250,plain,
( c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| spl89_1
| ~ spl89_2 ),
inference(forward_subsumption_resolution,[],[f3249,f2281]) ).
fof(f3252,plain,
( c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ c_member(sF81,sF82,hAPP(v_P_H____,sK3(sF87,v_P_H____,v_a____,v_b____,v_c____,v_b____)))
| spl89_1
| ~ spl89_2 ),
inference(forward_subsumption_resolution,[],[f3250,f3136]) ).
fof(f3254,plain,
( c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| spl89_1
| ~ spl89_2 ),
inference(forward_subsumption_resolution,[],[f3252,f3245]) ).
fof(f3256,plain,
( c_member(sF81,sF84,sF88)
| ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| spl89_1
| ~ spl89_2 ),
inference(forward_demodulation,[],[f3254,f2157]) ).
fof(f3258,plain,
( ~ c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| spl89_1
| ~ spl89_2 ),
inference(forward_subsumption_resolution,[],[f3256,f2169]) ).
fof(f3259,plain,
( ~ c_member(sF81,sF82,sF83)
| spl89_1
| ~ spl89_2 ),
inference(forward_demodulation,[],[f3258,f2147]) ).
fof(f3260,plain,
( $false
| spl89_1
| ~ spl89_2 ),
inference(forward_subsumption_resolution,[],[f3259,f2174]) ).
fof(f3261,plain,
( spl89_1
| ~ spl89_2 ),
inference(avatar_contradiction_clause,[],[f3260]) ).
fof(f3266,plain,
! [X0] :
( ~ c_member(sF81,sF84,sF88)
| c_member(sF81,sF82,hAPP(X0,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,X0))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____))) ),
inference(forward_demodulation,[],[f3227,f2157]) ).
fof(f3270,plain,
( ! [X0] :
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(X0,sK3(X0,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),X0,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_F,X0)) )
| ~ spl89_1 ),
inference(forward_subsumption_resolution,[],[f3266,f2170]) ).
fof(f3317,plain,
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ spl89_1 ),
inference(factoring,[],[f3270]) ).
fof(f3319,plain,
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ spl89_1 ),
inference(forward_subsumption_resolution,[],[f3317,f3136]) ).
fof(f3320,plain,
( c_member(sF81,sF82,sF83)
| c_member(sF81,sF82,hAPP(v_P_H____,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ spl89_1 ),
inference(forward_demodulation,[],[f3319,f2147]) ).
fof(f3321,plain,
( c_member(sF81,sF82,hAPP(v_P_H____,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ spl89_1
| spl89_2 ),
inference(forward_subsumption_resolution,[],[f3320,f2173]) ).
fof(f3322,plain,
( c_member(sF81,sF84,hAPP(sF87,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ spl89_1
| spl89_2 ),
inference(resolution,[],[f3321,f3199]) ).
fof(f3324,plain,
( ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),v_P_H____,c_Arrow__Order__Mirabelle_OProf)
| c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),sF87,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(sF81,sF82,hAPP(v_P_H____,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ spl89_1
| spl89_2 ),
inference(resolution,[],[f3322,f2899]) ).
fof(f3327,plain,
( c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,sF85),sF87,c_Arrow__Order__Mirabelle_OProf)
| ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(sF81,sF82,hAPP(v_P_H____,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ spl89_1
| spl89_2 ),
inference(forward_subsumption_resolution,[],[f3324,f3136]) ).
fof(f3329,plain,
( c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ c_member(sF81,sF82,hAPP(v_P_H____,sK3(v_P_H____,sF87,v_c____,v_b____,v_a____,v_b____)))
| ~ spl89_1
| spl89_2 ),
inference(forward_subsumption_resolution,[],[f3327,f2281]) ).
fof(f3331,plain,
( c_member(sF81,sF82,hAPP(v_F,v_P_H____))
| ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ spl89_1
| spl89_2 ),
inference(forward_subsumption_resolution,[],[f3329,f3321]) ).
fof(f3333,plain,
( c_member(sF81,sF82,sF83)
| ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ spl89_1
| spl89_2 ),
inference(forward_demodulation,[],[f3331,f2147]) ).
fof(f3334,plain,
( ~ c_member(sF81,sF84,hAPP(v_F,sF87))
| ~ spl89_1
| spl89_2 ),
inference(forward_subsumption_resolution,[],[f3333,f2173]) ).
fof(f3335,plain,
( ~ c_member(sF81,sF84,sF88)
| ~ spl89_1
| spl89_2 ),
inference(forward_demodulation,[],[f3334,f2157]) ).
fof(f3336,plain,
( $false
| ~ spl89_1
| spl89_2 ),
inference(forward_subsumption_resolution,[],[f3335,f2170]) ).
fof(f3337,plain,
( ~ spl89_1
| spl89_2 ),
inference(avatar_contradiction_clause,[],[f3336]) ).
cnf(s1,plain,
( spl89_1
| spl89_2 ),
inference(sat_conversion,[],[f2175]) ).
cnf(s2,plain,
( ~ spl89_1
| ~ spl89_2 ),
inference(sat_conversion,[],[f2176]) ).
cnf(s9,plain,
( spl89_1
| ~ spl89_2 ),
inference(sat_conversion,[],[f3261]) ).
cnf(s10,plain,
( ~ spl89_1
| spl89_2 ),
inference(sat_conversion,[],[f3337]) ).
cnf(s11,plain,
spl89_1,
inference(rat,[],[s1,s9]) ).
cnf(s12,plain,
spl89_2,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s12,s11]) ).
fof(f3338,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT152+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:46:10 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.24/2.16 % (3076439)Detected formulas, will run a generic FOF schedule.
% 9.24/2.16 % (3076447)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2440522182:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.24/2.16 % (3076447)Refutation not found, incomplete strategy
% 9.24/2.16 % (3076447)------------------------------
% 9.24/2.16 % (3076447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076447)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076447)Termination reason: Refutation not found, incomplete strategy
% 9.24/2.16 % (3076447)Time elapsed: 0.004 s
% 9.24/2.16 % (3076447)Peak memory usage: 89 MB
% 9.24/2.16 % (3076447)Instructions burned: 12 (million)
% 9.24/2.16 % (3076450)dis-21_1_sil=8000:lcm=predicate:random_seed=3516397415:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 9.24/2.16 % (3076448)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=907720760:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.24/2.16 % (3076445)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1730652789:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.24/2.16 % (3076444)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2558217834:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.24/2.16 % (3076446)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3369591480:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.24/2.16 % (3076449)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=309162849:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.24/2.16 % (3076450)Instruction limit reached!
% 9.24/2.16 % (3076450)------------------------------
% 9.24/2.16 % (3076450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076450)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076450)Termination reason: Instruction limit
% 9.24/2.16 % (3076450)Termination phase: Saturation
% 9.24/2.16 % (3076450)Time elapsed: 0.067 s
% 9.24/2.16 % (3076450)Peak memory usage: 90 MB
% 9.24/2.16 % (3076450)Instructions burned: 129 (million)
% 9.24/2.16 % (3076448)Instruction limit reached!
% 9.24/2.16 % (3076448)------------------------------
% 9.24/2.16 % (3076448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076448)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076448)Termination reason: Instruction limit
% 9.24/2.16 % (3076448)Termination phase: Saturation
% 9.24/2.16 % (3076448)Time elapsed: 0.077 s
% 9.24/2.16 % (3076448)Peak memory usage: 89 MB
% 9.24/2.16 % (3076448)Instructions burned: 119 (million)
% 9.24/2.16 % (3076449)Instruction limit reached!
% 9.24/2.16 % (3076449)------------------------------
% 9.24/2.16 % (3076449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076449)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076449)Termination reason: Instruction limit
% 9.24/2.16 % (3076449)Termination phase: Saturation
% 9.24/2.16 % (3076449)Time elapsed: 0.086 s
% 9.24/2.16 % (3076449)Peak memory usage: 90 MB
% 9.24/2.16 % (3076449)Instructions burned: 141 (million)
% 9.24/2.16 % (3076447)------------------------------
% 9.24/2.16 % (3076447)------------------------------
% 9.24/2.16 % (3076458)lrs+10_1_sil=8000:sp=occurrence:random_seed=324710546:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.24/2.16 % (3076460)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3562162469:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.24/2.16 % (3076459)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1847267376:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.24/2.16 % (3076461)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1859148003:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.24/2.16 % (3076459)Instruction limit reached!
% 9.24/2.16 % (3076459)------------------------------
% 9.24/2.16 % (3076459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076459)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076459)Termination reason: Instruction limit
% 9.24/2.16 % (3076459)Termination phase: Saturation
% 9.24/2.16 % (3076459)Time elapsed: 0.085 s
% 9.24/2.16 % (3076459)Peak memory usage: 90 MB
% 9.24/2.16 % (3076459)Instructions burned: 158 (million)
% 9.24/2.16 % (3076461)Instruction limit reached!
% 9.24/2.16 % (3076461)------------------------------
% 9.24/2.16 % (3076461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076461)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076461)Termination reason: Instruction limit
% 9.24/2.16 % (3076461)Termination phase: Saturation
% 9.24/2.16 % (3076461)Time elapsed: 0.073 s
% 9.24/2.16 % (3076461)Peak memory usage: 91 MB
% 9.24/2.16 % (3076461)Instructions burned: 249 (million)
% 9.24/2.16 % (3076458)Instruction limit reached!
% 9.24/2.16 % (3076458)------------------------------
% 9.24/2.16 % (3076458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076458)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076458)Termination reason: Instruction limit
% 9.24/2.16 % (3076458)Termination phase: Saturation
% 9.24/2.16 % (3076458)Time elapsed: 0.182 s
% 9.24/2.16 % (3076458)Peak memory usage: 91 MB
% 9.24/2.16 % (3076458)Instructions burned: 286 (million)
% 9.24/2.16 % (3076467)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3821326240:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 9.24/2.16 % (3076460)Instruction limit reached!
% 9.24/2.16 % (3076460)------------------------------
% 9.24/2.16 % (3076460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076460)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076460)Termination reason: Instruction limit
% 9.24/2.16 % (3076460)Termination phase: Saturation
% 9.24/2.16 % (3076460)Time elapsed: 0.201 s
% 9.24/2.16 % (3076460)Peak memory usage: 93 MB
% 9.24/2.16 % (3076460)Instructions burned: 326 (million)
% 9.24/2.16 % (3076466)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=861797598:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.24/2.16 % (3076466)Refutation not found, incomplete strategy
% 9.24/2.16 % (3076466)------------------------------
% 9.24/2.16 % (3076466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076466)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076466)Termination reason: Refutation not found, incomplete strategy
% 9.24/2.16 % (3076466)Time elapsed: 0.025 s
% 9.24/2.16 % (3076466)Peak memory usage: 90 MB
% 9.24/2.16 % (3076466)Instructions burned: 44 (million)
% 9.24/2.16 % (3076468)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2233437041:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.24/2.16 % (3076470)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=301873171:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 9.24/2.16 % (3076468)Instruction limit reached!
% 9.24/2.16 % (3076468)------------------------------
% 9.24/2.16 % (3076468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076468)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076468)Termination reason: Instruction limit
% 9.24/2.16 % (3076468)Termination phase: Saturation
% 9.24/2.16 % (3076468)Time elapsed: 0.061 s
% 9.24/2.16 % (3076468)Peak memory usage: 90 MB
% 9.24/2.16 % (3076468)Instructions burned: 114 (million)
% 9.24/2.16 % (3076470)Instruction limit reached!
% 9.24/2.16 % (3076470)------------------------------
% 9.24/2.16 % (3076470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076470)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076470)Termination reason: Instruction limit
% 9.24/2.16 % (3076470)Termination phase: Saturation
% 9.24/2.16 % (3076470)Time elapsed: 0.061 s
% 9.24/2.16 % (3076470)Peak memory usage: 90 MB
% 9.24/2.16 % (3076470)Instructions burned: 128 (million)
% 9.24/2.16 % (3076474)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4119851285:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.24/2.16 % (3076466)------------------------------
% 9.24/2.16 % (3076466)------------------------------
% 9.24/2.16 % (3076475)lrs+10_1_sil=8000:sp=occurrence:random_seed=1895335484:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.24/2.16 % (3076474)Instruction limit reached!
% 9.24/2.16 % (3076474)------------------------------
% 9.24/2.16 % (3076474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076474)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076474)Termination reason: Instruction limit
% 9.24/2.16 % (3076474)Termination phase: Saturation
% 9.24/2.16 % (3076474)Time elapsed: 0.057 s
% 9.24/2.16 % (3076474)Peak memory usage: 89 MB
% 9.24/2.16 % (3076474)Instructions burned: 115 (million)
% 9.24/2.16 % (3076477)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4172551025:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 9.24/2.16 % (3076479)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1103673603:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 9.24/2.16 % (3076467)First to succeed.
% 9.24/2.16 % (3076467)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3076439"
% 9.24/2.16 % (3076444)Also succeeded, but the first one will report.
% 9.24/2.16 % (3076477)Instruction limit reached!
% 9.24/2.16 % (3076477)------------------------------
% 9.24/2.16 % (3076477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/2.16 % (3076477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/2.16 % (3076477)CaDiCaL version: 2.1.3
% 9.24/2.16 % (3076477)Termination reason: Instruction limit
% 9.24/2.16 % (3076477)Termination phase: Saturation
% 9.24/2.16 % (3076477)Time elapsed: 0.244 s
% 9.24/2.16 % (3076477)Peak memory usage: 94 MB
% 9.24/2.16 % (3076477)Instructions burned: 437 (million)
% 9.24/2.16 % (3076467)Refutation found. Thanks to Tanya!
% 9.24/2.16 % SZS status Theorem for theBenchmark
% 9.24/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 9.63/2.36 % (3076467)------------------------------
% 9.63/2.36 % (3076467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.63/2.36 % (3076467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.63/2.36 % (3076467)CaDiCaL version: 2.1.3
% 9.63/2.36 % (3076467)Termination reason: Refutation
% 9.63/2.36 % (3076467)Time elapsed: 0.572 s
% 9.63/2.36 % (3076467)Peak memory usage: 141 MB
% 9.63/2.36 % (3076467)Instructions burned: 1564 (million)
% 9.63/2.36 % (3076467)------------------------------
% 9.63/2.36 % (3076467)------------------------------
% 9.63/2.36 % (3076439)Success in time 1.3 s
% 9.63/2.36 % Vampire exiting
%------------------------------------------------------------------------------