%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP002_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 11:27:40 AM UTC 2026
% Result : Theorem 28.86s 5.33s
% Output : Refutation 32.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 35
% Syntax : Number of formulae : 249 ( 64 unt; 0 typ; 16 def)
% Number of atoms : 1743 ( 116 equ)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 625 ( 270 ~; 285 |; 25 &)
% ( 21 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1139 (1139 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 28 ( 25 usr; 24 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 182 ( 0 sgn 176 !; 6 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
inj__o: tp__o > $i ).
tff(func_def_7,type,
surj__o: $i > tp__o ).
tff(func_def_9,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_11,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_12,type,
ty_2Eoption_2Eoption: del > del ).
tff(func_def_13,type,
c_2Eoption_2ENONE: del > $i ).
tff(func_def_14,type,
c_2Eoption_2ETHE: del > $i ).
tff(func_def_15,type,
c_2Eoption_2ESOME: del > $i ).
tff(func_def_16,type,
c_2Eoption_2EIS__SOME: del > $i ).
tff(func_def_18,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_19,type,
c_2Ebool_2ECOND: del > $i ).
tff(func_def_20,type,
c_2Eoption_2EOPTION__MAP2: ( del * del * del ) > $i ).
tff(func_def_21,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_22,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_23,type,
sK0: del ).
tff(func_def_24,type,
sK1: del ).
tff(func_def_25,type,
sK2: del ).
tff(func_def_29,type,
sK6: ( del * $i * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(f1,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
tff(f2,axiom,
! [X0: $i] :
( mem(X0,bool)
=> ! [X1: $i] :
( mem(X1,bool)
=> ( ( p(X0)
<=> p(X1) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolext) ).
tff(f9,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
tff(f10,axiom,
inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2EF) ).
tff(f11,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
tff(f12,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
tff(f13,axiom,
inj__o(fo__c_2Ebool_2ET) = c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2ET) ).
tff(f14,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
tff(f15,axiom,
! [X0: del] : mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ENONE) ).
tff(f16,axiom,
! [X0: del] : mem(c_2Eoption_2ETHE(X0),arr(ty_2Eoption_2Eoption(X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ETHE) ).
tff(f17,axiom,
! [X0: del] : mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ESOME) ).
tff(f18,axiom,
! [X0: del] : mem(c_2Eoption_2EIS__SOME(X0),arr(ty_2Eoption_2Eoption(X0),bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EIS__SOME) ).
tff(f19,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
tff(f21,axiom,
! [X0: $i] :
( mem(X0,bool)
=> ! [X1: $i] :
( mem(X1,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
<=> ( p(X0)
& p(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
tff(f31,axiom,
! [X0: del,X1: $i] :
( mem(X1,X0)
=> ! [X2: $i] :
( mem(X2,X0)
=> ( ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2ET)),X1),X2) = X1 )
& ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2EF)),X1),X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
tff(f33,axiom,
! [X0: del] :
( ! [X1: $i] :
( mem(X1,X0)
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
<=> $true ) )
& ( p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EIS__SOME__DEF) ).
tff(f34,axiom,
! [X0: del,X1: $i] :
( mem(X1,X0)
=> ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2ETHE__DEF) ).
tff(f35,axiom,
! [X0: del,X1: del,X2: del,X3: $i] :
( mem(X3,arr(X1,arr(X2,X0)))
=> ! [X4: $i] :
( mem(X4,ty_2Eoption_2Eoption(X1))
=> ! [X5: $i] :
( mem(X5,ty_2Eoption_2Eoption(X2))
=> ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),X5) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),X5))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),X5)))),c_2Eoption_2ENONE(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTION__MAP2__DEF) ).
tff(f36,conjecture,
! [X0: del,X1: del,X2: del,X3: $i] :
( mem(X3,arr(X1,arr(X2,X0)))
=> ! [X4: $i] :
( mem(X4,X1)
=> ! [X5: $i] :
( mem(X5,X2)
=> ( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),ap(c_2Eoption_2ESOME(X2),X5)) = ap(c_2Eoption_2ESOME(X0),ap(ap(X3,X4),X5)) )
& ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0) )
& ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),ap(c_2Eoption_2ESOME(X2),X5)) = c_2Eoption_2ENONE(X0) )
& ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2EOPTION__MAP2__THM) ).
tff(f37,negated_conjecture,
~ ! [X0: del,X1: del,X2: del,X3: $i] :
( mem(X3,arr(X1,arr(X2,X0)))
=> ! [X4: $i] :
( mem(X4,X1)
=> ! [X5: $i] :
( mem(X5,X2)
=> ( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),ap(c_2Eoption_2ESOME(X2),X5)) = ap(c_2Eoption_2ESOME(X0),ap(ap(X3,X4),X5)) )
& ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0) )
& ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),ap(c_2Eoption_2ESOME(X2),X5)) = c_2Eoption_2ENONE(X0) )
& ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) = c_2Eoption_2ENONE(X0) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
tff(f39,plain,
! [X0: del] :
( ! [X1: $i] :
( mem(X1,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) ),
inference(true_and_false_elimination,[],[f33]) ).
tff(f40,plain,
! [X0: del] :
( ! [X1: $i] :
( mem(X1,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) ),
inference(flattening,[],[f39]) ).
tff(f42,plain,
? [X0: del,X1: del,X2: del,X3: $i] :
( ? [X4: $i] :
( ? [X5: $i] :
( ( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),ap(c_2Eoption_2ESOME(X2),X5)) != ap(c_2Eoption_2ESOME(X0),ap(ap(X3,X4),X5)) )
| ( c_2Eoption_2ENONE(X0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),ap(c_2Eoption_2ESOME(X1),X4)),c_2Eoption_2ENONE(X2)) )
| ( c_2Eoption_2ENONE(X0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),ap(c_2Eoption_2ESOME(X2),X5)) )
| ( c_2Eoption_2ENONE(X0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),c_2Eoption_2ENONE(X1)),c_2Eoption_2ENONE(X2)) ) )
& mem(X5,X2) )
& mem(X4,X1) )
& mem(X3,arr(X1,arr(X2,X0))) ),
inference(ennf_transformation,[],[f37]) ).
tff(f47,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f2]) ).
tff(f48,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f47]) ).
tff(f49,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f50,plain,
! [X0: del,X1: del,X2: del,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),X5) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),X5))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),X5)))),c_2Eoption_2ENONE(X0)) )
| ~ mem(X5,ty_2Eoption_2Eoption(X2)) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,arr(X1,arr(X2,X0))) ),
inference(ennf_transformation,[],[f35]) ).
tff(f51,plain,
! [X0: del] :
( ! [X1: $i] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
| ~ mem(X1,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) ),
inference(ennf_transformation,[],[f40]) ).
tff(f52,plain,
! [X0: del,X1: $i] :
( ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X1 )
| ~ mem(X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
tff(f53,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
<=> ( p(X0)
& p(X1) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f21]) ).
tff(f54,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ( ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2ET)),X1),X2) = X1 )
& ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2EF)),X1),X2) = X2 ) )
| ~ mem(X2,X0) )
| ~ mem(X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
tff(f55,plain,
( ( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) != ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)) )
| ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),c_2Eoption_2ENONE(sK2)) )
| ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) )
| ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) ) )
& mem(sK5,sK2)
& mem(sK4,sK1)
& mem(sK3,arr(sK1,arr(sK2,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f42]) ).
tff(f58,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f48]) ).
tff(f59,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X0)
| ~ p(X1) )
& ( ( p(X0)
& p(X1) )
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f53]) ).
tff(f60,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X0)
| ~ p(X1) )
& ( ( p(X0)
& p(X1) )
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f59]) ).
tff(f63,plain,
mem(sK3,arr(sK1,arr(sK2,sK0))),
inference(cnf_transformation,[],[f55]) ).
tff(f64,plain,
mem(sK4,sK1),
inference(cnf_transformation,[],[f55]) ).
tff(f65,plain,
mem(sK5,sK2),
inference(cnf_transformation,[],[f55]) ).
tff(f66,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) != ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)) )
| ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),c_2Eoption_2ENONE(sK2)) )
| ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) )
| ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) ) ),
inference(cnf_transformation,[],[f55]) ).
tff(f72,plain,
! [X0: $i,X1: $i] :
( ~ mem(X1,bool)
| p(X1)
| p(X0)
| ( X0 = X1 )
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f58]) ).
tff(f73,plain,
! [X0: $i,X1: $i] :
( ~ mem(X1,bool)
| ~ p(X1)
| ~ p(X0)
| ( X0 = X1 )
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f58]) ).
tff(f74,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f49]) ).
tff(f75,plain,
! [X0: del] : mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0))),
inference(cnf_transformation,[],[f17]) ).
tff(f76,plain,
! [X2: del,X3: $i,X0: del,X1: del,X4: $i,X5: $i] :
( ~ mem(X3,arr(X1,arr(X2,X0)))
| ~ mem(X5,ty_2Eoption_2Eoption(X2))
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(X0,X1,X2),X3),X4),X5) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(X1),X4)),ap(c_2Eoption_2EIS__SOME(X2),X5))),ap(c_2Eoption_2ESOME(X0),ap(ap(X3,ap(c_2Eoption_2ETHE(X1),X4)),ap(c_2Eoption_2ETHE(X2),X5)))),c_2Eoption_2ENONE(X0)) ) ),
inference(cnf_transformation,[],[f50]) ).
tff(f77,plain,
! [X0: del] : ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))),
inference(cnf_transformation,[],[f51]) ).
tff(f78,plain,
! [X0: del,X1: $i] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)))
| ~ mem(X1,X0) ),
inference(cnf_transformation,[],[f51]) ).
tff(f79,plain,
! [X0: del] : mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0)),
inference(cnf_transformation,[],[f15]) ).
tff(f80,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,X0)
| ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X1)) = X1 ) ),
inference(cnf_transformation,[],[f52]) ).
tff(f82,plain,
! [X0: $i,X1: $i] :
( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f60]) ).
tff(f83,plain,
! [X0: $i,X1: $i] :
( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f60]) ).
tff(f84,plain,
! [X0: $i,X1: $i] :
( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X0)
| ~ p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f60]) ).
tff(f85,plain,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[],[f19]) ).
tff(f94,plain,
p(c_2Ebool_2ET),
inference(cnf_transformation,[],[f14]) ).
tff(f95,plain,
~ p(c_2Ebool_2EF),
inference(cnf_transformation,[],[f11]) ).
tff(f96,plain,
! [X0: del] : mem(c_2Eoption_2EIS__SOME(X0),arr(ty_2Eoption_2Eoption(X0),bool)),
inference(cnf_transformation,[],[f18]) ).
tff(f97,plain,
! [X0: del] : mem(c_2Eoption_2ETHE(X0),arr(ty_2Eoption_2Eoption(X0),X0)),
inference(cnf_transformation,[],[f16]) ).
tff(f98,plain,
! [X2: $i,X0: del,X1: $i] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2EF)),X1),X2) = X2 )
| ~ mem(X2,X0)
| ~ mem(X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
tff(f99,plain,
! [X2: $i,X0: del,X1: $i] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2ET)),X1),X2) = X1 )
| ~ mem(X2,X0)
| ~ mem(X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
tff(f101,plain,
c_2Ebool_2ET = inj__o(fo__c_2Ebool_2ET),
inference(cnf_transformation,[],[f13]) ).
tff(f102,plain,
mem(c_2Ebool_2ET,bool),
inference(cnf_transformation,[],[f12]) ).
tff(f103,plain,
c_2Ebool_2EF = inj__o(fo__c_2Ebool_2EF),
inference(cnf_transformation,[],[f10]) ).
tff(f104,plain,
mem(c_2Ebool_2EF,bool),
inference(cnf_transformation,[],[f9]) ).
tff(f108,plain,
! [X2: $i,X0: del,X1: $i] :
( ~ mem(X2,X0)
| ( ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2EF),X1),X2) = X2 )
| ~ mem(X1,X0) ),
inference(forward_demodulation,[],[f98,f103]) ).
tff(f109,plain,
! [X2: $i,X0: del,X1: $i] :
( ~ mem(X2,X0)
| ( ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2ET),X1),X2) = X1 )
| ~ mem(X1,X0) ),
inference(forward_demodulation,[],[f99,f101]) ).
tff(f111,definition,
( spl7_1
<=> ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f113,plain,
( ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) )
| spl7_1 ),
inference(avatar_component_clause,[],[f111]) ).
tff(f115,definition,
( spl7_2
<=> ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f117,plain,
( ( c_2Eoption_2ENONE(sK0) != ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) )
| spl7_2 ),
inference(avatar_component_clause,[],[f115]) ).
tff(f119,definition,
( spl7_3
<=> ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),c_2Eoption_2ENONE(sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f123,definition,
( spl7_4
<=> ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f126,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f66,f123,f119,f115,f111]) ).
tff(f127,plain,
! [X0: $i,X1: $i] :
( ~ mem(X1,ty_2Eoption_2Eoption(sK1))
| ~ mem(X0,ty_2Eoption_2Eoption(sK2))
| ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),X1),X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),X1)),ap(c_2Eoption_2EIS__SOME(sK2),X0))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),X1)),ap(c_2Eoption_2ETHE(sK2),X0)))),c_2Eoption_2ENONE(sK0)) ) ),
inference(resolution,[],[f76,f63]) ).
tff(f128,plain,
! [X0: $i] :
( mem(ap(sK3,X0),arr(sK2,sK0))
| ~ mem(X0,sK1) ),
inference(resolution,[],[f74,f63]) ).
tff(f129,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Eoption_2ESOME(X1),X0),ty_2Eoption_2Eoption(X1))
| ~ mem(X0,X1) ),
inference(resolution,[],[f75,f74]) ).
tff(f131,plain,
sK5 = ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)),
inference(resolution,[],[f80,f65]) ).
tff(f133,plain,
sK4 = ap(c_2Eoption_2ETHE(sK1),ap(c_2Eoption_2ESOME(sK1),sK4)),
inference(resolution,[],[f64,f80]) ).
tff(f136,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Eoption_2ETHE(X1),X0),X1)
| ~ mem(X0,ty_2Eoption_2Eoption(X1)) ),
inference(resolution,[],[f97,f74]) ).
tff(f144,plain,
! [X0: $i,X1: $i] :
( mem(ap(ap(sK3,X0),X1),sK0)
| ~ mem(X1,sK2)
| ~ mem(X0,sK1) ),
inference(resolution,[],[f128,f74]) ).
tff(f145,plain,
! [X0: $i] :
( ~ mem(X0,sK1)
| ( ap(sK3,X0) = ap(c_2Eoption_2ETHE(arr(sK2,sK0)),ap(c_2Eoption_2ESOME(arr(sK2,sK0)),ap(sK3,X0))) ) ),
inference(resolution,[],[f128,f80]) ).
tff(f152,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,ty_2Eoption_2Eoption(X0))
| ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2ET),X1),c_2Eoption_2ENONE(X0)) = X1 ) ),
inference(resolution,[],[f109,f79]) ).
tff(f166,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,ty_2Eoption_2Eoption(X0))
| ( c_2Eoption_2ENONE(X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(X0)),c_2Ebool_2EF),X1),c_2Eoption_2ENONE(X0)) ) ),
inference(resolution,[],[f108,f79]) ).
tff(f177,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Eoption_2EIS__SOME(X1),X0),bool)
| ~ mem(X0,ty_2Eoption_2Eoption(X1)) ),
inference(resolution,[],[f96,f74]) ).
tff(f182,plain,
! [X0: $i] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK2))
| ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2EIS__SOME(sK2),X0))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),X0)))),c_2Eoption_2ENONE(sK0)) ) ),
inference(resolution,[],[f127,f79]) ).
tff(f187,plain,
! [X0: $i] :
( p(c_2Ebool_2EF)
| p(X0)
| ( c_2Ebool_2EF = X0 )
| ~ mem(X0,bool) ),
inference(resolution,[],[f104,f72]) ).
tff(f191,plain,
! [X0: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2EF = X0 )
| p(X0) ),
inference(forward_subsumption_resolution,[],[f187,f95]) ).
tff(f196,plain,
! [X0: $i] :
( ~ p(c_2Ebool_2ET)
| ~ p(X0)
| ( c_2Ebool_2ET = X0 )
| ~ mem(X0,bool) ),
inference(resolution,[],[f102,f73]) ).
tff(f201,plain,
! [X0: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2ET = X0 )
| ~ p(X0) ),
inference(forward_subsumption_resolution,[],[f196,f94]) ).
tff(f234,plain,
! [X2: del,X3: $i,X0: $i,X1: del] :
( mem(ap(ap(c_2Eoption_2ETHE(arr(X1,X2)),X0),X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,ty_2Eoption_2Eoption(arr(X1,X2))) ),
inference(resolution,[],[f136,f74]) ).
tff(f250,plain,
! [X0: $i,X1: del] :
( ~ p(ap(c_2Eoption_2EIS__SOME(X1),X0))
| ( c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(X1),X0) )
| ~ mem(X0,ty_2Eoption_2Eoption(X1)) ),
inference(resolution,[],[f177,f201]) ).
tff(f251,plain,
! [X0: $i,X1: del] :
( p(ap(c_2Eoption_2EIS__SOME(X1),X0))
| ( c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(X1),X0) )
| ~ mem(X0,ty_2Eoption_2Eoption(X1)) ),
inference(resolution,[],[f177,f191]) ).
tff(f316,plain,
! [X0: $i] :
( mem(ap(c_2Ebool_2E_2F_5C,X0),arr(bool,bool))
| ~ mem(X0,bool) ),
inference(resolution,[],[f85,f74]) ).
tff(f321,plain,
! [X0: $i,X1: $i] :
( mem(ap(ap(c_2Ebool_2E_2F_5C,X0),X1),bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[],[f316,f74]) ).
tff(f328,plain,
! [X0: del] :
( ( c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) )
| ~ mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0)) ),
inference(resolution,[],[f251,f77]) ).
tff(f329,plain,
! [X0: del] : ( c_2Ebool_2EF = ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)) ),
inference(forward_subsumption_resolution,[],[f328,f79]) ).
tff(f424,plain,
! [X0: del,X1: $i] :
( ( c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) )
| ~ mem(ap(c_2Eoption_2ESOME(X0),X1),ty_2Eoption_2Eoption(X0))
| ~ mem(X1,X0) ),
inference(resolution,[],[f250,f78]) ).
tff(f428,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,X0)
| ( c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X1)) ) ),
inference(forward_subsumption_resolution,[],[f424,f129]) ).
tff(f451,plain,
c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(sK1),ap(c_2Eoption_2ESOME(sK1),sK4)),
inference(resolution,[],[f428,f64]) ).
tff(f452,plain,
c_2Ebool_2ET = ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)),
inference(resolution,[],[f428,f65]) ).
tff(f582,plain,
! [X0: $i,X1: $i] :
( p(ap(ap(c_2Ebool_2E_2F_5C,X1),X0))
| ~ mem(X1,bool)
| ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X1),X0) )
| ~ mem(X0,bool) ),
inference(resolution,[],[f321,f191]) ).
tff(f585,plain,
! [X0: $i,X1: $i] :
( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X0))
| ~ mem(X1,bool)
| ( c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,X1),X0) )
| ~ mem(X0,bool) ),
inference(resolution,[],[f321,f201]) ).
tff(f869,definition,
( spl7_9
<=> mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)),ty_2Eoption_2Eoption(sK0)) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
tff(f870,plain,
( mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)),ty_2Eoption_2Eoption(sK0))
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f869]) ).
tff(f871,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)),ty_2Eoption_2Eoption(sK0))
| spl7_9 ),
inference(avatar_component_clause,[],[f869]) ).
tff(f873,definition,
( spl7_10
<=> mem(ap(ap(sK3,sK4),sK5),sK0) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
tff(f874,plain,
( ~ mem(ap(ap(sK3,sK4),sK5),sK0)
| spl7_10 ),
inference(avatar_component_clause,[],[f873]) ).
tff(f877,plain,
( ~ mem(ap(ap(sK3,sK4),sK5),sK0)
| spl7_9 ),
inference(resolution,[],[f871,f129]) ).
tff(f878,plain,
( ~ spl7_10
| spl7_9 ),
inference(avatar_split_clause,[],[f877,f869,f873]) ).
tff(f879,plain,
( ~ mem(sK5,sK2)
| ~ mem(sK4,sK1)
| spl7_10 ),
inference(resolution,[],[f874,f144]) ).
tff(f880,plain,
( ~ mem(sK4,sK1)
| spl7_10 ),
inference(forward_subsumption_resolution,[],[f879,f65]) ).
tff(f881,plain,
( $false
| spl7_10 ),
inference(forward_subsumption_resolution,[],[f880,f64]) ).
tff(f882,plain,
spl7_10,
inference(avatar_contradiction_clause,[],[f881]) ).
tff(f889,plain,
( ( ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_9 ),
inference(resolution,[],[f870,f152]) ).
tff(f1011,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)),
inference(resolution,[],[f182,f79]) ).
tff(f1020,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1))),c_2Ebool_2EF)),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)),
inference(forward_demodulation,[],[f1011,f329]) ).
tff(f1025,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)),
inference(forward_demodulation,[],[f1020,f329]) ).
tff(f1048,plain,
! [X0: $i,X1: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1) )
| ~ mem(X1,bool)
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[],[f582,f83]) ).
tff(f1049,plain,
! [X0: $i,X1: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1) )
| ~ mem(X1,bool)
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[],[f582,f82]) ).
tff(f1050,plain,
! [X0: $i,X1: $i] :
( ~ mem(X1,bool)
| ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1) )
| ~ mem(X0,bool)
| p(X1) ),
inference(duplicate_literal_removal,[],[f1049]) ).
tff(f1051,plain,
! [X0: $i,X1: $i] :
( ~ mem(X1,bool)
| ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),X1) )
| ~ mem(X0,bool)
| p(X0) ),
inference(duplicate_literal_removal,[],[f1048]) ).
tff(f1054,plain,
ap(sK3,sK4) = ap(c_2Eoption_2ETHE(arr(sK2,sK0)),ap(c_2Eoption_2ESOME(arr(sK2,sK0)),ap(sK3,sK4))),
inference(resolution,[],[f145,f64]) ).
tff(f1057,plain,
! [X0: $i] :
( mem(ap(ap(sK3,sK4),X0),sK0)
| ~ mem(X0,sK2)
| ~ mem(ap(c_2Eoption_2ESOME(arr(sK2,sK0)),ap(sK3,sK4)),ty_2Eoption_2Eoption(arr(sK2,sK0))) ),
inference(superposition,[],[f234,f1054]) ).
tff(f1059,definition,
( spl7_11
<=> mem(ap(c_2Eoption_2ESOME(arr(sK2,sK0)),ap(sK3,sK4)),ty_2Eoption_2Eoption(arr(sK2,sK0))) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
tff(f1061,plain,
( ~ mem(ap(c_2Eoption_2ESOME(arr(sK2,sK0)),ap(sK3,sK4)),ty_2Eoption_2Eoption(arr(sK2,sK0)))
| spl7_11 ),
inference(avatar_component_clause,[],[f1059]) ).
tff(f1063,definition,
( spl7_12
<=> ! [X0: $i] :
( mem(ap(ap(sK3,sK4),X0),sK0)
| ~ mem(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
tff(f1064,plain,
( ! [X0: $i] :
( mem(ap(ap(sK3,sK4),X0),sK0)
| ~ mem(X0,sK2) )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f1063]) ).
tff(f1065,plain,
( ~ spl7_11
| spl7_12 ),
inference(avatar_split_clause,[],[f1057,f1063,f1059]) ).
tff(f1067,definition,
( spl7_13
<=> mem(ap(sK3,sK4),arr(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
tff(f1068,plain,
( ~ mem(ap(sK3,sK4),arr(sK2,sK0))
| spl7_13 ),
inference(avatar_component_clause,[],[f1067]) ).
tff(f1071,plain,
( ~ mem(ap(sK3,sK4),arr(sK2,sK0))
| spl7_11 ),
inference(resolution,[],[f1061,f129]) ).
tff(f1072,plain,
( ~ spl7_13
| spl7_11 ),
inference(avatar_split_clause,[],[f1071,f1059,f1067]) ).
tff(f1073,plain,
( ~ mem(sK4,sK1)
| spl7_13 ),
inference(resolution,[],[f1068,f128]) ).
tff(f1074,plain,
( $false
| spl7_13 ),
inference(forward_subsumption_resolution,[],[f1073,f64]) ).
tff(f1075,plain,
spl7_13,
inference(avatar_contradiction_clause,[],[f1074]) ).
tff(f1138,plain,
! [X0: $i,X1: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,X0),X1) )
| ~ mem(X1,bool)
| ~ p(X0)
| ~ p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[],[f585,f84]) ).
tff(f1139,plain,
! [X0: $i,X1: $i] :
( ~ mem(X1,bool)
| ( c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,X0),X1) )
| ~ mem(X0,bool)
| ~ p(X0)
| ~ p(X1) ),
inference(duplicate_literal_removal,[],[f1138]) ).
tff(f1147,plain,
! [X0: $i] :
( ( c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2ET) )
| ~ mem(X0,bool)
| ~ p(X0)
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[],[f1139,f102]) ).
tff(f1149,plain,
! [X0: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2ET) )
| ~ p(X0) ),
inference(forward_subsumption_resolution,[],[f1147,f94]) ).
tff(f1283,plain,
! [X0: $i] :
( ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2EF) )
| ~ mem(X0,bool)
| p(c_2Ebool_2EF) ),
inference(resolution,[],[f1050,f104]) ).
tff(f1286,plain,
! [X0: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2EF) ) ),
inference(forward_subsumption_resolution,[],[f1283,f95]) ).
tff(f1292,plain,
c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),
inference(resolution,[],[f1286,f104]) ).
tff(f1293,plain,
c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),
inference(resolution,[],[f1286,f102]) ).
tff(f1295,plain,
ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)),
inference(superposition,[],[f1025,f1292]) ).
tff(f1339,definition,
( spl7_17
<=> mem(ap(c_2Eoption_2ESOME(sK2),sK5),ty_2Eoption_2Eoption(sK2)) ),
introduced(definition,[new_symbols(definition,[spl7_17])],[avatar_definition]) ).
tff(f1340,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK2),sK5),ty_2Eoption_2Eoption(sK2))
| spl7_17 ),
inference(avatar_component_clause,[],[f1339]) ).
tff(f1341,plain,
( mem(ap(c_2Eoption_2ESOME(sK2),sK5),ty_2Eoption_2Eoption(sK2))
| ~ spl7_17 ),
inference(avatar_component_clause,[],[f1339]) ).
tff(f1349,definition,
( spl7_19
<=> mem(ap(c_2Eoption_2ESOME(sK1),sK4),ty_2Eoption_2Eoption(sK1)) ),
introduced(definition,[new_symbols(definition,[spl7_19])],[avatar_definition]) ).
tff(f1350,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK1),sK4),ty_2Eoption_2Eoption(sK1))
| spl7_19 ),
inference(avatar_component_clause,[],[f1349]) ).
tff(f1351,plain,
( mem(ap(c_2Eoption_2ESOME(sK1),sK4),ty_2Eoption_2Eoption(sK1))
| ~ spl7_19 ),
inference(avatar_component_clause,[],[f1349]) ).
tff(f1401,plain,
( ( c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET) )
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[],[f1149,f102]) ).
tff(f1403,plain,
c_2Ebool_2ET = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET),
inference(forward_subsumption_resolution,[],[f1401,f94]) ).
tff(f1457,plain,
! [X0: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2ET) )
| p(X0) ),
inference(resolution,[],[f1051,f102]) ).
tff(f1464,plain,
( ( c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET) )
| p(c_2Ebool_2EF) ),
inference(resolution,[],[f1457,f104]) ).
tff(f1467,plain,
c_2Ebool_2EF = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),
inference(forward_subsumption_resolution,[],[f1464,f95]) ).
tff(f1811,plain,
( ~ mem(sK5,sK2)
| spl7_17 ),
inference(resolution,[],[f1340,f129]) ).
tff(f1812,plain,
( $false
| spl7_17 ),
inference(forward_subsumption_resolution,[],[f1811,f65]) ).
tff(f1813,plain,
spl7_17,
inference(avatar_contradiction_clause,[],[f1812]) ).
tff(f1815,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17 ),
inference(resolution,[],[f1341,f182]) ).
tff(f1842,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17 ),
inference(forward_demodulation,[],[f1815,f131]) ).
tff(f1844,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),c_2Eoption_2ENONE(sK1))),c_2Ebool_2ET)),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17 ),
inference(forward_demodulation,[],[f1842,f452]) ).
tff(f1845,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17 ),
inference(forward_demodulation,[],[f1844,f329]) ).
tff(f1846,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17 ),
inference(forward_demodulation,[],[f1845,f1467]) ).
tff(f1879,plain,
( ~ mem(sK4,sK1)
| spl7_19 ),
inference(resolution,[],[f1350,f129]) ).
tff(f1880,plain,
( $false
| spl7_19 ),
inference(forward_subsumption_resolution,[],[f1879,f64]) ).
tff(f1881,plain,
spl7_19,
inference(avatar_contradiction_clause,[],[f1880]) ).
tff(f1883,plain,
( ! [X0: $i] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK2))
| ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),ap(c_2Eoption_2ESOME(sK1),sK4))),ap(c_2Eoption_2EIS__SOME(sK2),X0))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),ap(c_2Eoption_2ESOME(sK1),sK4))),ap(c_2Eoption_2ETHE(sK2),X0)))),c_2Eoption_2ENONE(sK0)) ) )
| ~ spl7_19 ),
inference(resolution,[],[f1351,f127]) ).
tff(f1910,plain,
( ! [X0: $i] :
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(sK1),ap(c_2Eoption_2ESOME(sK1),sK4))),ap(c_2Eoption_2EIS__SOME(sK2),X0))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),X0)))),c_2Eoption_2ENONE(sK0)) )
| ~ mem(X0,ty_2Eoption_2Eoption(sK2)) )
| ~ spl7_19 ),
inference(forward_demodulation,[],[f1883,f133]) ).
tff(f1912,plain,
( ! [X0: $i] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK2))
| ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),X0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK2),X0))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),X0)))),c_2Eoption_2ENONE(sK0)) ) )
| ~ spl7_19 ),
inference(forward_demodulation,[],[f1910,f451]) ).
tff(f3172,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),ap(c_2Eoption_2ESOME(sK2),sK5))))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17
| ~ spl7_19 ),
inference(resolution,[],[f1912,f1341]) ).
tff(f3177,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),c_2Eoption_2ENONE(sK2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK2),c_2Eoption_2ENONE(sK2)))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_19 ),
inference(resolution,[],[f1912,f79]) ).
tff(f3183,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),c_2Eoption_2ENONE(sK2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3177,f329]) ).
tff(f3184,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),ap(c_2Eoption_2EIS__SOME(sK2),ap(c_2Eoption_2ESOME(sK2),sK5)))),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3172,f131]) ).
tff(f3185,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),c_2Eoption_2ENONE(sK2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3183,f1293]) ).
tff(f3186,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2ET)),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3184,f452]) ).
tff(f3187,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2ET),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_17
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3186,f1403]) ).
tff(f3188,plain,
( ( ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),ap(c_2Eoption_2ESOME(sK2),sK5)) = ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),sK5)) )
| ~ spl7_9
| ~ spl7_17
| ~ spl7_19 ),
inference(forward_demodulation,[],[f3187,f889]) ).
tff(f3189,plain,
( spl7_4
| ~ spl7_9
| ~ spl7_17
| ~ spl7_19 ),
inference(avatar_split_clause,[],[f3188,f1349,f1339,f869,f123]) ).
tff(f3485,definition,
( spl7_25
<=> mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5)),ty_2Eoption_2Eoption(sK0)) ),
introduced(definition,[new_symbols(definition,[spl7_25])],[avatar_definition]) ).
tff(f3486,plain,
( mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5)),ty_2Eoption_2Eoption(sK0))
| ~ spl7_25 ),
inference(avatar_component_clause,[],[f3485]) ).
tff(f3487,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5)),ty_2Eoption_2Eoption(sK0))
| spl7_25 ),
inference(avatar_component_clause,[],[f3485]) ).
tff(f3494,definition,
( spl7_27
<=> mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)))),ty_2Eoption_2Eoption(sK0)) ),
introduced(definition,[new_symbols(definition,[spl7_27])],[avatar_definition]) ).
tff(f3495,plain,
( mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)))),ty_2Eoption_2Eoption(sK0))
| ~ spl7_27 ),
inference(avatar_component_clause,[],[f3494]) ).
tff(f3496,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)))),ty_2Eoption_2Eoption(sK0))
| spl7_27 ),
inference(avatar_component_clause,[],[f3494]) ).
tff(f3503,definition,
( spl7_29
<=> mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)))),ty_2Eoption_2Eoption(sK0)) ),
introduced(definition,[new_symbols(definition,[spl7_29])],[avatar_definition]) ).
tff(f3504,plain,
( mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)))),ty_2Eoption_2Eoption(sK0))
| ~ spl7_29 ),
inference(avatar_component_clause,[],[f3503]) ).
tff(f3505,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)))),ty_2Eoption_2Eoption(sK0))
| spl7_29 ),
inference(avatar_component_clause,[],[f3503]) ).
tff(f3512,plain,
( ~ mem(ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),sK0)
| spl7_29 ),
inference(resolution,[],[f3505,f129]) ).
tff(f3513,plain,
( ~ mem(ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))),sK0)
| spl7_27 ),
inference(resolution,[],[f3496,f129]) ).
tff(f3514,plain,
( ~ mem(ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5),sK0)
| spl7_25 ),
inference(resolution,[],[f3487,f129]) ).
tff(f3516,plain,
( ~ mem(ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)),sK2)
| ~ spl7_12
| spl7_29 ),
inference(resolution,[],[f3512,f1064]) ).
tff(f3517,plain,
( ~ mem(c_2Eoption_2ENONE(sK2),ty_2Eoption_2Eoption(sK2))
| ~ spl7_12
| spl7_29 ),
inference(resolution,[],[f3516,f136]) ).
tff(f3518,plain,
( $false
| ~ spl7_12
| spl7_29 ),
inference(forward_subsumption_resolution,[],[f3517,f79]) ).
tff(f3519,plain,
( ~ spl7_12
| spl7_29 ),
inference(avatar_contradiction_clause,[],[f3518]) ).
tff(f3525,plain,
( ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,sK4),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_29 ),
inference(resolution,[],[f3504,f166]) ).
tff(f3725,plain,
( ~ mem(ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)),sK2)
| ~ mem(ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1)),sK1)
| spl7_27 ),
inference(resolution,[],[f3513,f144]) ).
tff(f3727,definition,
( spl7_39
<=> mem(ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl7_39])],[avatar_definition]) ).
tff(f3728,plain,
( mem(ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1)),sK1)
| ~ spl7_39 ),
inference(avatar_component_clause,[],[f3727]) ).
tff(f3729,plain,
( ~ mem(ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1)),sK1)
| spl7_39 ),
inference(avatar_component_clause,[],[f3727]) ).
tff(f3731,definition,
( spl7_40
<=> mem(ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)),sK2) ),
introduced(definition,[new_symbols(definition,[spl7_40])],[avatar_definition]) ).
tff(f3733,plain,
( ~ mem(ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2)),sK2)
| spl7_40 ),
inference(avatar_component_clause,[],[f3731]) ).
tff(f3734,plain,
( ~ spl7_39
| ~ spl7_40
| spl7_27 ),
inference(avatar_split_clause,[],[f3725,f3494,f3731,f3727]) ).
tff(f3735,plain,
( ~ mem(c_2Eoption_2ENONE(sK1),ty_2Eoption_2Eoption(sK1))
| spl7_39 ),
inference(resolution,[],[f3729,f136]) ).
tff(f3736,plain,
( $false
| spl7_39 ),
inference(forward_subsumption_resolution,[],[f3735,f79]) ).
tff(f3737,plain,
spl7_39,
inference(avatar_contradiction_clause,[],[f3736]) ).
tff(f3763,plain,
( ~ mem(c_2Eoption_2ENONE(sK2),ty_2Eoption_2Eoption(sK2))
| spl7_40 ),
inference(resolution,[],[f3733,f136]) ).
tff(f3764,plain,
( $false
| spl7_40 ),
inference(forward_subsumption_resolution,[],[f3763,f79]) ).
tff(f3765,plain,
spl7_40,
inference(avatar_contradiction_clause,[],[f3764]) ).
tff(f3824,plain,
( ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),ap(c_2Eoption_2ETHE(sK2),c_2Eoption_2ENONE(sK2))))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_27 ),
inference(resolution,[],[f3495,f166]) ).
tff(f3997,plain,
( ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),c_2Eoption_2ENONE(sK2)) )
| ~ spl7_27 ),
inference(superposition,[],[f3824,f1295]) ).
tff(f4002,plain,
( $false
| spl7_1
| ~ spl7_27 ),
inference(forward_subsumption_resolution,[],[f3997,f113]) ).
tff(f4003,plain,
( spl7_1
| ~ spl7_27 ),
inference(avatar_contradiction_clause,[],[f4002]) ).
tff(f4055,plain,
( ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),ap(c_2Eoption_2ESOME(sK1),sK4)),c_2Eoption_2ENONE(sK2)) )
| ~ spl7_19
| ~ spl7_29 ),
inference(superposition,[],[f3185,f3525]) ).
tff(f4057,plain,
( spl7_3
| ~ spl7_19
| ~ spl7_29 ),
inference(avatar_split_clause,[],[f4055,f3503,f1349,f119]) ).
tff(f6586,plain,
( ~ mem(sK5,sK2)
| ~ mem(ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1)),sK1)
| spl7_25 ),
inference(resolution,[],[f3514,f144]) ).
tff(f6587,plain,
( ~ mem(ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1)),sK1)
| spl7_25 ),
inference(forward_subsumption_resolution,[],[f6586,f65]) ).
tff(f6588,plain,
( $false
| spl7_25
| ~ spl7_39 ),
inference(forward_subsumption_resolution,[],[f6587,f3728]) ).
tff(f6589,plain,
( spl7_25
| ~ spl7_39 ),
inference(avatar_contradiction_clause,[],[f6588]) ).
tff(f6604,plain,
( ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(sK0)),c_2Ebool_2EF),ap(c_2Eoption_2ESOME(sK0),ap(ap(sK3,ap(c_2Eoption_2ETHE(sK1),c_2Eoption_2ENONE(sK1))),sK5))),c_2Eoption_2ENONE(sK0)) )
| ~ spl7_25 ),
inference(resolution,[],[f3486,f166]) ).
tff(f6865,plain,
( ( c_2Eoption_2ENONE(sK0) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(sK0,sK1,sK2),sK3),c_2Eoption_2ENONE(sK1)),ap(c_2Eoption_2ESOME(sK2),sK5)) )
| ~ spl7_17
| ~ spl7_25 ),
inference(superposition,[],[f6604,f1846]) ).
tff(f6870,plain,
( $false
| spl7_2
| ~ spl7_17
| ~ spl7_25 ),
inference(forward_subsumption_resolution,[],[f6865,f117]) ).
tff(f6871,plain,
( spl7_2
| ~ spl7_17
| ~ spl7_25 ),
inference(avatar_contradiction_clause,[],[f6870]) ).
cnf(s1,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f126]) ).
cnf(s7,plain,
( spl7_9
| ~ spl7_10 ),
inference(sat_conversion,[],[f878]) ).
cnf(s8,plain,
spl7_10,
inference(sat_conversion,[],[f882]) ).
cnf(s9,plain,
( ~ spl7_11
| spl7_12 ),
inference(sat_conversion,[],[f1065]) ).
cnf(s11,plain,
( spl7_11
| ~ spl7_13 ),
inference(sat_conversion,[],[f1072]) ).
cnf(s12,plain,
spl7_13,
inference(sat_conversion,[],[f1075]) ).
cnf(s18,plain,
spl7_17,
inference(sat_conversion,[],[f1813]) ).
cnf(s20,plain,
spl7_19,
inference(sat_conversion,[],[f1881]) ).
cnf(s28,plain,
( spl7_4
| ~ spl7_9
| ~ spl7_17
| ~ spl7_19 ),
inference(sat_conversion,[],[f3189]) ).
cnf(s33,plain,
( ~ spl7_12
| spl7_29 ),
inference(sat_conversion,[],[f3519]) ).
cnf(s40,plain,
( spl7_27
| ~ spl7_39
| ~ spl7_40 ),
inference(sat_conversion,[],[f3734]) ).
cnf(s41,plain,
spl7_39,
inference(sat_conversion,[],[f3737]) ).
cnf(s42,plain,
spl7_40,
inference(sat_conversion,[],[f3765]) ).
cnf(s50,plain,
( spl7_1
| ~ spl7_27 ),
inference(sat_conversion,[],[f4003]) ).
cnf(s51,plain,
( spl7_3
| ~ spl7_19
| ~ spl7_29 ),
inference(sat_conversion,[],[f4057]) ).
cnf(s58,plain,
( spl7_25
| ~ spl7_39 ),
inference(sat_conversion,[],[f6589]) ).
cnf(s64,plain,
( spl7_2
| ~ spl7_17
| ~ spl7_25 ),
inference(sat_conversion,[],[f6871]) ).
cnf(s65,plain,
spl7_25,
inference(rat,[],[s58,s41]) ).
cnf(s67,plain,
spl7_27,
inference(rat,[],[s40,s42,s41]) ).
cnf(s68,plain,
spl7_1,
inference(rat,[],[s50,s67]) ).
cnf(s79,plain,
spl7_2,
inference(rat,[],[s64,s65,s18]) ).
cnf(s82,plain,
spl7_11,
inference(rat,[],[s11,s12]) ).
cnf(s83,plain,
spl7_12,
inference(rat,[],[s9,s82]) ).
cnf(s85,plain,
spl7_29,
inference(rat,[],[s33,s83]) ).
cnf(s88,plain,
spl7_3,
inference(rat,[],[s51,s20,s85]) ).
cnf(s91,plain,
spl7_9,
inference(rat,[],[s7,s8]) ).
cnf(s92,plain,
spl7_4,
inference(rat,[],[s28,s20,s18,s91]) ).
cnf(s94,plain,
$false,
inference(rat,[],[s1,s92,s88,s79,s68]) ).
tff(f6872,plain,
$false,
inference(avatar_sat_refutation,[],[s94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP002_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 11:50:57 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 12.12/2.65 % (2704327)Detected formulas, will run a generic FOF schedule.
% 12.12/2.65 % (2704334)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=723148396:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.12/2.65 % (2704337)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1213981855:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.12/2.65 % (2704335)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1828926648:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.12/2.65 % (2704338)dis-21_1_sil=8000:lcm=predicate:random_seed=3906418817: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)
% 12.12/2.65 % (2704332)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=2141342400:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.12/2.65 % (2704333)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=3414082771:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.12/2.65 % (2704336)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3686767287:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.12/2.65 % (2704335)Refutation not found, incomplete strategy
% 12.12/2.65 % (2704335)------------------------------
% 12.12/2.65 % (2704335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.12/2.65 % (2704335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.12/2.65 % (2704335)CaDiCaL version: 2.1.3
% 12.12/2.65 % (2704335)Termination reason: Refutation not found, incomplete strategy
% 12.12/2.65 % (2704335)Time elapsed: 0.003 s
% 12.12/2.65 % (2704335)Peak memory usage: 88 MB
% 12.12/2.65 % (2704335)Instructions burned: 2 (million)
% 12.12/2.65 % (2704338)Instruction limit reached!
% 12.12/2.65 % (2704338)------------------------------
% 12.12/2.65 % (2704338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.12/2.65 % (2704338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.12/2.65 % (2704338)CaDiCaL version: 2.1.3
% 12.12/2.65 % (2704338)Termination reason: Instruction limit
% 12.12/2.65 % (2704338)Termination phase: Saturation
% 12.12/2.65 % (2704338)Time elapsed: 0.051 s
% 12.12/2.65 % (2704338)Peak memory usage: 88 MB
% 12.12/2.65 % (2704338)Instructions burned: 130 (million)
% 12.12/2.65 % (2704336)Instruction limit reached!
% 12.12/2.65 % (2704336)------------------------------
% 12.12/2.65 % (2704336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.12/2.65 % (2704336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.12/2.65 % (2704336)CaDiCaL version: 2.1.3
% 12.12/2.65 % (2704336)Termination reason: Instruction limit
% 12.12/2.65 % (2704336)Termination phase: Saturation
% 12.12/2.65 % (2704336)Time elapsed: 0.070 s
% 12.12/2.65 % (2704336)Peak memory usage: 88 MB
% 12.12/2.65 % (2704336)Instructions burned: 120 (million)
% 12.12/2.65 % (2704337)Instruction limit reached!
% 12.12/2.65 % (2704337)------------------------------
% 12.12/2.65 % (2704337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.12/2.65 % (2704337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.12/2.65 % (2704337)CaDiCaL version: 2.1.3
% 12.12/2.65 % (2704337)Termination reason: Instruction limit
% 12.12/2.65 % (2704337)Termination phase: Saturation
% 12.12/2.65 % (2704337)Time elapsed: 0.094 s
% 12.12/2.65 % (2704337)Peak memory usage: 90 MB
% 12.12/2.65 % (2704337)Instructions burned: 139 (million)
% 12.12/2.65 % (2704346)lrs+10_1_sil=8000:sp=occurrence:random_seed=634015683:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.12/2.65 % (2704347)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1945880517:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.12/2.65 % (2704348)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4138956917:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.12/2.65 % (2704335)------------------------------
% 12.12/2.65 % (2704335)------------------------------
% 12.12/2.65 % (2704347)Instruction limit reached!
% 12.12/2.65 % (2704347)------------------------------
% 12.12/2.65 % (2704347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.70/3.26 % (2704347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.70/3.26 % (2704347)CaDiCaL version: 2.1.3
% 16.70/3.26 % (2704347)Termination reason: Instruction limit
% 16.70/3.26 % (2704347)Termination phase: Saturation
% 16.70/3.26 % (2704347)Time elapsed: 0.090 s
% 16.70/3.26 % (2704347)Peak memory usage: 90 MB
% 16.70/3.26 % (2704347)Instructions burned: 158 (million)
% 16.70/3.26 % (2704352)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=2310864226:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 16.70/3.26 % (2704346)Instruction limit reached!
% 16.70/3.26 % (2704346)------------------------------
% 16.70/3.26 % (2704346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.70/3.26 % (2704346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.70/3.26 % (2704346)CaDiCaL version: 2.1.3
% 16.70/3.26 % (2704346)Termination reason: Instruction limit
% 16.70/3.26 % (2704346)Termination phase: Saturation
% 16.70/3.26 % (2704346)Time elapsed: 0.176 s
% 16.70/3.26 % (2704346)Peak memory usage: 92 MB
% 16.70/3.26 % (2704346)Instructions burned: 285 (million)
% 16.70/3.26 % (2704353)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=245644275:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 16.70/3.26 % (2704352)Instruction limit reached!
% 16.70/3.26 % (2704352)------------------------------
% 16.70/3.26 % (2704352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.70/3.26 % (2704352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.70/3.26 % (2704352)CaDiCaL version: 2.1.3
% 16.70/3.26 % (2704352)Termination reason: Instruction limit
% 16.70/3.26 % (2704352)Termination phase: Saturation
% 16.70/3.26 % (2704352)Time elapsed: 0.078 s
% 16.70/3.26 % (2704352)Peak memory usage: 92 MB
% 16.70/3.26 % (2704352)Instructions burned: 250 (million)
% 16.70/3.26 % (2704353)Refutation not found, incomplete strategy
% 16.70/3.26 % (2704353)------------------------------
% 16.70/3.26 % (2704353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.70/3.26 % (2704353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.70/3.26 % (2704353)CaDiCaL version: 2.1.3
% 16.70/3.26 % (2704353)Termination reason: Refutation not found, incomplete strategy
% 16.70/3.26 % (2704353)Time elapsed: 0.003 s
% 16.70/3.26 % (2704353)Peak memory usage: 88 MB
% 16.70/3.26 % (2704353)Instructions burned: 4 (million)
% 16.70/3.26 % (2704348)Instruction limit reached!
% 16.70/3.26 % (2704348)------------------------------
% 16.70/3.26 % (2704348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.70/3.26 % (2704348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.70/3.26 % (2704348)CaDiCaL version: 2.1.3
% 16.70/3.26 % (2704348)Termination reason: Instruction limit
% 16.70/3.26 % (2704348)Termination phase: Saturation
% 16.70/3.26 % (2704348)Time elapsed: 0.217 s
% 16.70/3.26 % (2704348)Peak memory usage: 91 MB
% 16.70/3.26 % (2704348)Instructions burned: 325 (million)
% 16.70/3.26 % (2704355)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2752393118:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 16.70/3.26 % (2704357)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2954052520:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 16.70/3.26 % (2704357)Instruction limit reached!
% 16.70/3.26 % (2704357)------------------------------
% 16.70/3.26 % (2704357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.70/3.26 % (2704357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.70/3.26 % (2704357)CaDiCaL version: 2.1.3
% 16.70/3.26 % (2704357)Termination reason: Instruction limit
% 16.70/3.26 % (2704357)Termination phase: Saturation
% 16.70/3.26 % (2704357)Time elapsed: 0.045 s
% 16.70/3.26 % (2704357)Peak memory usage: 90 MB
% 16.70/3.26 % (2704357)Instructions burned: 115 (million)
% 16.70/3.26 % (2704358)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1152108707:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 16.70/3.26 % (2704358)Instruction limit reached!
% 16.70/3.26 % (2704358)------------------------------
% 16.70/3.26 % (2704358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.70/3.26 % (2704358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.70/3.26 % (2704358)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704358)Termination reason: Instruction limit
% 28.86/5.33 % (2704358)Termination phase: Saturation
% 28.86/5.33 % (2704358)Time elapsed: 0.064 s
% 28.86/5.33 % (2704358)Peak memory usage: 89 MB
% 28.86/5.33 % (2704358)Instructions burned: 128 (million)
% 28.86/5.33 % (2704361)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1494270867:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 28.86/5.33 % (2704353)------------------------------
% 28.86/5.33 % (2704353)------------------------------
% 28.86/5.33 % (2704361)Instruction limit reached!
% 28.86/5.33 % (2704361)------------------------------
% 28.86/5.33 % (2704361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704361)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704361)Termination reason: Instruction limit
% 28.86/5.33 % (2704361)Termination phase: Saturation
% 28.86/5.33 % (2704361)Time elapsed: 0.037 s
% 28.86/5.33 % (2704361)Peak memory usage: 89 MB
% 28.86/5.33 % (2704361)Instructions burned: 117 (million)
% 28.86/5.33 % (2704366)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1194787651:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 28.86/5.33 % (2704365)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=93903626:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 28.86/5.33 % (2704364)lrs+10_1_sil=8000:sp=occurrence:random_seed=2188053764:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 28.86/5.33 % (2704365)Refutation not found, incomplete strategy
% 28.86/5.33 % (2704365)------------------------------
% 28.86/5.33 % (2704365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704365)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704365)Termination reason: Refutation not found, incomplete strategy
% 28.86/5.33 % (2704365)Time elapsed: 0.003 s
% 28.86/5.33 % (2704365)Peak memory usage: 88 MB
% 28.86/5.33 % (2704365)Instructions burned: 3 (million)
% 28.86/5.33 % (2704365)------------------------------
% 28.86/5.33 % (2704365)------------------------------
% 28.86/5.33 % (2704370)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3218084635:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 28.86/5.33 % (2704370)Instruction limit reached!
% 28.86/5.33 % (2704370)------------------------------
% 28.86/5.33 % (2704370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704370)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704370)Termination reason: Instruction limit
% 28.86/5.33 % (2704370)Termination phase: Saturation
% 28.86/5.33 % (2704370)Time elapsed: 0.070 s
% 28.86/5.33 % (2704370)Peak memory usage: 90 MB
% 28.86/5.33 % (2704370)Instructions burned: 134 (million)
% 28.86/5.33 % (2704364)Instruction limit reached!
% 28.86/5.33 % (2704364)------------------------------
% 28.86/5.33 % (2704364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704364)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704364)Termination reason: Instruction limit
% 28.86/5.33 % (2704364)Termination phase: Saturation
% 28.86/5.33 % (2704364)Time elapsed: 0.507 s
% 28.86/5.33 % (2704364)Peak memory usage: 100 MB
% 28.86/5.33 % (2704364)Instructions burned: 908 (million)
% 28.86/5.33 % (2704372)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2713073422:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 28.86/5.33 % (2704373)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=736878485:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 28.86/5.33 % (2704372)Instruction limit reached!
% 28.86/5.33 % (2704372)------------------------------
% 28.86/5.33 % (2704372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704372)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704372)Termination reason: Instruction limit
% 28.86/5.33 % (2704372)Termination phase: Saturation
% 28.86/5.33 % (2704372)Time elapsed: 0.275 s
% 28.86/5.33 % (2704372)Peak memory usage: 90 MB
% 28.86/5.33 % (2704372)Instructions burned: 593 (million)
% 28.86/5.33 % (2704376)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=1113964886:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2982 on theBenchmark for (2982ds/125Mi)
% 28.86/5.33 % (2704355)Instruction limit reached!
% 28.86/5.33 % (2704355)------------------------------
% 28.86/5.33 % (2704355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704355)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704355)Termination reason: Instruction limit
% 28.86/5.33 % (2704355)Termination phase: Saturation
% 28.86/5.33 % (2704355)Time elapsed: 1.292 s
% 28.86/5.33 % (2704355)Peak memory usage: 134 MB
% 28.86/5.33 % (2704355)Instructions burned: 2351 (million)
% 28.86/5.33 % (2704376)Instruction limit reached!
% 28.86/5.33 % (2704376)------------------------------
% 28.86/5.33 % (2704376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704376)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704376)Termination reason: Instruction limit
% 28.86/5.33 % (2704376)Termination phase: Saturation
% 28.86/5.33 % (2704376)Time elapsed: 0.079 s
% 28.86/5.33 % (2704376)Peak memory usage: 91 MB
% 28.86/5.33 % (2704376)Instructions burned: 125 (million)
% 28.86/5.33 % (2704378)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2926044080:i=134:gtgl=5:slsql=off:gtg=exists_sym_2980 on theBenchmark for (2980ds/134Mi)
% 28.86/5.33 % (2704379)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=4214797043:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2979 on theBenchmark for (2979ds/141Mi)
% 28.86/5.33 % (2704378)Instruction limit reached!
% 28.86/5.33 % (2704378)------------------------------
% 28.86/5.33 % (2704378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704378)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704378)Termination reason: Instruction limit
% 28.86/5.33 % (2704378)Termination phase: Saturation
% 28.86/5.33 % (2704378)Time elapsed: 0.084 s
% 28.86/5.33 % (2704378)Peak memory usage: 91 MB
% 28.86/5.33 % (2704378)Instructions burned: 134 (million)
% 28.86/5.33 % (2704379)Instruction limit reached!
% 28.86/5.33 % (2704379)------------------------------
% 28.86/5.33 % (2704379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704379)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704379)Termination reason: Instruction limit
% 28.86/5.33 % (2704379)Termination phase: Saturation
% 28.86/5.33 % (2704379)Time elapsed: 0.085 s
% 28.86/5.33 % (2704379)Peak memory usage: 91 MB
% 28.86/5.33 % (2704379)Instructions burned: 141 (million)
% 28.86/5.33 % (2704382)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1252741155:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2978 on theBenchmark for (2978ds/431Mi)
% 28.86/5.33 % (2704382)Refutation not found, incomplete strategy
% 28.86/5.33 % (2704382)------------------------------
% 28.86/5.33 % (2704382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704382)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704382)Termination reason: Refutation not found, incomplete strategy
% 28.86/5.33 % (2704382)Time elapsed: 0.003 s
% 28.86/5.33 % (2704382)Peak memory usage: 89 MB
% 28.86/5.33 % (2704382)Instructions burned: 3 (million)
% 28.86/5.33 % (2704383)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=1864395916:i=6060:aac=none:ins=25_2977 on theBenchmark for (2977ds/6060Mi)
% 28.86/5.33 % (2704366)Instruction limit reached!
% 28.86/5.33 % (2704366)------------------------------
% 28.86/5.33 % (2704366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704366)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704366)Termination reason: Instruction limit
% 28.86/5.33 % (2704366)Termination phase: Saturation
% 28.86/5.33 % (2704366)Time elapsed: 1.468 s
% 28.86/5.33 % (2704366)Peak memory usage: 141 MB
% 28.86/5.33 % (2704366)Instructions burned: 5204 (million)
% 28.86/5.33 % (2704396)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=2889484543:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2975 on theBenchmark for (2975ds/150Mi)
% 28.86/5.33 % (2704382)------------------------------
% 28.86/5.33 % (2704382)------------------------------
% 28.86/5.33 % (2704396)Instruction limit reached!
% 28.86/5.33 % (2704396)------------------------------
% 28.86/5.33 % (2704396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704396)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704396)Termination reason: Instruction limit
% 28.86/5.33 % (2704396)Termination phase: Saturation
% 28.86/5.33 % (2704396)Time elapsed: 0.046 s
% 28.86/5.33 % (2704396)Peak memory usage: 91 MB
% 28.86/5.33 % (2704396)Instructions burned: 151 (million)
% 28.86/5.33 % (2704436)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=2242823022:i=667:av=off:fsr=off_2974 on theBenchmark for (2974ds/667Mi)
% 28.86/5.33 % (2704432)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=1910808842:i=14155:bd=all_2974 on theBenchmark for (2974ds/14155Mi)
% 28.86/5.33 % (2704436)Instruction limit reached!
% 28.86/5.33 % (2704436)------------------------------
% 28.86/5.33 % (2704436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704436)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704436)Termination reason: Instruction limit
% 28.86/5.33 % (2704436)Termination phase: Saturation
% 28.86/5.33 % (2704436)Time elapsed: 0.144 s
% 28.86/5.33 % (2704436)Peak memory usage: 89 MB
% 28.86/5.33 % (2704436)Instructions burned: 669 (million)
% 28.86/5.33 % (2704476)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=3338804072:s2a=on:i=185:s2at=1.8:fdi=4_2972 on theBenchmark for (2972ds/185Mi)
% 28.86/5.33 % (2704476)Instruction limit reached!
% 28.86/5.33 % (2704476)------------------------------
% 28.86/5.33 % (2704476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704476)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704476)Termination reason: Instruction limit
% 28.86/5.33 % (2704476)Termination phase: Saturation
% 28.86/5.33 % (2704476)Time elapsed: 0.057 s
% 28.86/5.33 % (2704476)Peak memory usage: 91 MB
% 28.86/5.33 % (2704476)Instructions burned: 187 (million)
% 28.86/5.33 % (2704514)dis+1010_14_anc=all:to=lpo:sil=8000:sp=arity:slsq=on:random_seed=4193761111:i=193:ins=10:fsr=off:ss=axioms:fsd=on_2970 on theBenchmark for (2970ds/193Mi)
% 28.86/5.33 % (2704514)Instruction limit reached!
% 28.86/5.33 % (2704514)------------------------------
% 28.86/5.33 % (2704514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.86/5.33 % (2704514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.86/5.33 % (2704514)CaDiCaL version: 2.1.3
% 28.86/5.33 % (2704514)Termination reason: Instruction limit
% 28.86/5.33 % (2704514)Termination phase: Saturation
% 28.86/5.33 % (2704514)Time elapsed: 0.057 s
% 28.86/5.33 % (2704514)Peak memory usage: 89 MB
% 28.86/5.33 % (2704514)Instructions burned: 196 (million)
% 28.86/5.33 % (2704516)dis+1011_7_sil=8000:sp=occurrence:sos=all:fd=off:random_seed=1367001905:st=5.3:i=4850:sd=4:av=off:sup=off:ss=included:sgt=16_2969 on theBenchmark for (2969ds/4850Mi)
% 28.86/5.33 % (2704373)First to succeed.
% 28.86/5.33 % (2704373)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2704327"
% 28.86/5.33 % (2704373)Refutation found. Thanks to Tanya!
% 28.86/5.33 % SZS status Theorem for theBenchmark
% 28.86/5.33 % SZS output start Proof for theBenchmark
% See solution above
% 32.29/5.52 % (2704373)------------------------------
% 32.29/5.52 % (2704373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.29/5.52 % (2704373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.29/5.52 % (2704373)CaDiCaL version: 2.1.3
% 32.29/5.52 % (2704373)Termination reason: Refutation
% 32.29/5.52 % (2704373)Time elapsed: 2.612 s
% 32.29/5.52 % (2704373)Peak memory usage: 160 MB
% 32.29/5.52 % (2704373)Instructions burned: 4300 (million)
% 32.29/5.52 % (2704373)------------------------------
% 32.29/5.52 % (2704373)------------------------------
% 32.29/5.52 % (2704327)Success in time 4.478 s
% 32.29/5.52 % Vampire exiting
%------------------------------------------------------------------------------