%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP004_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 : n003.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 11:27:44 AM UTC 2026
% Result : Theorem 4.57s 1.66s
% Output : Refutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 447 ( 10 equ)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 243 ( 104 ~; 104 |; 17 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 253 ( 253 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 95 !; 4 ?; 99 :)
% 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_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_10,type,
c_2Epred__set_2ESUBSET: del > $i ).
tff(func_def_12,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_14,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_15,type,
c_2Ebool_2EIN: del > $i ).
tff(func_def_16,type,
c_2Epred__set_2ECHOICE: del > $i ).
tff(func_def_17,type,
c_2Epred__set_2EDELETE: del > $i ).
tff(func_def_18,type,
c_2Epred__set_2EREST: del > $i ).
tff(func_def_19,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_20,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_21,type,
sK0: del ).
tff(func_def_23,type,
sK2: ( del * $i * $i ) > $i ).
tff(func_def_24,type,
sK3: ( 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(f20,axiom,
! [X0: del] : mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
tff(f22,axiom,
! [X0: del] : mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
tff(f27,axiom,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> ! [X2: $i] :
( mem(X2,arr(X0,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3: $i] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
=> p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
tff(f28,axiom,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> ! [X2: $i] :
( mem(X2,X0)
=> ! [X3: $i] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& ( X2 != X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
tff(f29,axiom,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
tff(f30,conjecture,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
tff(f31,negated_conjecture,
~ ! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
tff(f32,plain,
? [X0: del,X1: $i] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1))
& mem(X1,arr(X0,bool)) ),
inference(ennf_transformation,[],[f31]) ).
tff(f35,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(f36,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(ennf_transformation,[],[f27]) ).
tff(f37,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(flattening,[],[f36]) ).
tff(f38,plain,
! [X0: del,X1: $i] :
( ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(ennf_transformation,[],[f29]) ).
tff(f41,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& ( X2 != X3 ) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) ),
inference(ennf_transformation,[],[f28]) ).
tff(f42,plain,
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1))
& mem(sK1,arr(sK0,bool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
tff(f44,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ? [X3: $i] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0) ) )
& ( ! [X3: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(nnf_transformation,[],[f37]) ).
tff(f45,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ? [X3: $i] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0) ) )
& ( ! [X4: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(rectify,[],[f44]) ).
tff(f46,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
& mem(sK2(X0,X1,X2),X0) ) )
& ( ! [X4: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f45]) ).
tff(f48,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ( X2 = X3 ) )
& ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& ( X2 != X3 ) )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) ),
inference(nnf_transformation,[],[f41]) ).
tff(f49,plain,
! [X0: del,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ( X2 = X3 ) )
& ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
& ( X2 != X3 ) )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) ),
inference(flattening,[],[f48]) ).
tff(f50,plain,
mem(sK1,arr(sK0,bool)),
inference(cnf_transformation,[],[f42]) ).
tff(f51,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1)),
inference(cnf_transformation,[],[f42]) ).
tff(f54,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,[],[f35]) ).
tff(f56,plain,
! [X2: $i,X0: del,X1: $i] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| mem(sK2(X0,X1,X2),X0)
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool)) ),
inference(cnf_transformation,[],[f46]) ).
tff(f57,plain,
! [X2: $i,X0: del,X1: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool)) ),
inference(cnf_transformation,[],[f46]) ).
tff(f58,plain,
! [X2: $i,X0: del,X1: $i] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool)) ),
inference(cnf_transformation,[],[f46]) ).
tff(f60,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
inference(cnf_transformation,[],[f38]) ).
tff(f61,plain,
! [X0: del] : mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))),
inference(cnf_transformation,[],[f22]) ).
tff(f65,plain,
! [X2: $i,X3: $i,X0: del,X1: $i] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ mem(X3,X0)
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f68,plain,
! [X0: del] : mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)),
inference(cnf_transformation,[],[f20]) ).
tff(f74,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Epred__set_2ECHOICE(X1),X0),X1)
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[],[f54,f68]) ).
tff(f76,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Epred__set_2EREST(X1),X0),arr(X1,bool))
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[],[f54,f61]) ).
tff(f81,plain,
ap(c_2Epred__set_2EREST(sK0),sK1) = ap(ap(c_2Epred__set_2EDELETE(sK0),sK1),ap(c_2Epred__set_2ECHOICE(sK0),sK1)),
inference(resolution,[],[f60,f50]) ).
tff(f97,definition,
( spl4_1
<=> mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f98,plain,
( mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f97]) ).
tff(f99,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| spl4_1 ),
inference(avatar_component_clause,[],[f97]) ).
tff(f116,plain,
! [X2: $i,X3: $i,X0: del,X1: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3)),X1))
| ~ mem(X2,X0)
| ~ mem(sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3),X0)
| ~ mem(X1,arr(X0,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2)),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),arr(X0,bool)) ),
inference(resolution,[],[f65,f57]) ).
tff(f119,plain,
! [X2: $i,X3: $i,X0: del,X1: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X3)),X1))
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2)),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),arr(X0,bool)) ),
inference(forward_subsumption_resolution,[],[f116,f56]) ).
tff(f159,plain,
( ~ mem(sK1,arr(sK0,bool))
| spl4_1 ),
inference(resolution,[],[f76,f99]) ).
tff(f164,plain,
( $false
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f159,f50]) ).
tff(f165,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f164]) ).
tff(f293,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK0),sK2(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0)),sK1))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK0),sK1),sK0)
| ~ mem(sK1,arr(sK0,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),X0))
| ~ mem(X0,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool)) ),
inference(superposition,[],[f119,f81]) ).
tff(f299,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK0),sK2(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0)),sK1))
| ~ mem(sK1,arr(sK0,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),X0))
| ~ mem(X0,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool)) ),
inference(forward_subsumption_resolution,[],[f293,f74]) ).
tff(f306,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK0),sK2(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0)),sK1))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),X0))
| ~ mem(X0,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool)) ),
inference(forward_subsumption_resolution,[],[f299,f50]) ).
tff(f318,plain,
( ! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK0),sK2(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0)),sK1))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),X0))
| ~ mem(X0,arr(sK0,bool)) )
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f306,f98]) ).
tff(f319,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1))
| ~ mem(sK1,arr(sK0,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1))
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ spl4_1 ),
inference(resolution,[],[f318,f58]) ).
tff(f321,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1))
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ spl4_1 ),
inference(duplicate_literal_removal,[],[f319]) ).
tff(f323,plain,
( ~ mem(sK1,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f321,f51]) ).
tff(f324,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f323,f50]) ).
tff(f325,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f324,f98]) ).
tff(f326,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f325]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f165]) ).
cnf(s6,plain,
~ spl4_1,
inference(sat_conversion,[],[f326]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6]) ).
tff(f327,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n003.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 27 11:52:04 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 4.57/1.66 % (384418)Detected formulas, will run a generic FOF schedule.
% 4.57/1.66 % (384499)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=180119143:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.57/1.66 % (384498)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3660472182:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.57/1.66 % (384500)dis-21_1_sil=8000:lcm=predicate:random_seed=224049558: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)
% 4.57/1.66 % (384494)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=3146598531:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.57/1.66 % (384496)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=2093266032:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.57/1.66 % (384495)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=2562462102:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.57/1.66 % (384497)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4124878715:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.57/1.66 % (384497)Refutation not found, incomplete strategy
% 4.57/1.66 % (384497)------------------------------
% 4.57/1.66 % (384497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.66 % (384497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.66 % (384497)CaDiCaL version: 2.1.3
% 4.57/1.66 % (384497)Termination reason: Refutation not found, incomplete strategy
% 4.57/1.66 % (384497)Time elapsed: 0.004 s
% 4.57/1.66 % (384497)Peak memory usage: 88 MB
% 4.57/1.66 % (384497)Instructions burned: 2 (million)
% 4.57/1.66 % (384499)Instruction limit reached!
% 4.57/1.66 % (384499)------------------------------
% 4.57/1.66 % (384499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.66 % (384499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.66 % (384499)CaDiCaL version: 2.1.3
% 4.57/1.66 % (384499)Termination reason: Instruction limit
% 4.57/1.66 % (384499)Termination phase: Saturation
% 4.57/1.66 % (384499)Time elapsed: 0.083 s
% 4.57/1.66 % (384499)Peak memory usage: 89 MB
% 4.57/1.66 % (384499)Instructions burned: 140 (million)
% 4.57/1.66 % (384498)Instruction limit reached!
% 4.57/1.66 % (384498)------------------------------
% 4.57/1.66 % (384498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.66 % (384498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.66 % (384498)CaDiCaL version: 2.1.3
% 4.57/1.66 % (384498)Termination reason: Instruction limit
% 4.57/1.66 % (384498)Termination phase: Saturation
% 4.57/1.66 % (384498)Time elapsed: 0.101 s
% 4.57/1.66 % (384498)Peak memory usage: 88 MB
% 4.57/1.66 % (384498)Instructions burned: 119 (million)
% 4.57/1.66 % (384500)Instruction limit reached!
% 4.57/1.66 % (384500)------------------------------
% 4.57/1.66 % (384500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.66 % (384500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.66 % (384500)CaDiCaL version: 2.1.3
% 4.57/1.66 % (384500)Termination reason: Instruction limit
% 4.57/1.66 % (384500)Termination phase: Saturation
% 4.57/1.66 % (384500)Time elapsed: 0.106 s
% 4.57/1.66 % (384500)Peak memory usage: 89 MB
% 4.57/1.66 % (384500)Instructions burned: 130 (million)
% 4.57/1.66 % (384568)lrs+10_1_sil=8000:sp=occurrence:random_seed=2827202689:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.57/1.66 % (384568)First to succeed.
% 4.57/1.66 % (384568)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-384418"
% 4.57/1.66 % (384497)------------------------------
% 4.57/1.66 % (384497)------------------------------
% 4.57/1.66 % (384581)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2644549820:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.57/1.66 % (384575)lrs+10_1_sil=32000:urr=on:br=off:random_seed=475290493:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.57/1.66 % (384581)Also succeeded, but the first one will report.
% 4.57/1.66 % (384575)Instruction limit reached!
% 4.57/1.66 % (384575)------------------------------
% 4.57/1.66 % (384575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.66 % (384575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.66 % (384575)CaDiCaL version: 2.1.3
% 4.57/1.66 % (384575)Termination reason: Instruction limit
% 4.57/1.66 % (384575)Termination phase: Saturation
% 4.57/1.66 % (384575)Time elapsed: 0.103 s
% 4.57/1.66 % (384575)Peak memory usage: 89 MB
% 4.57/1.66 % (384575)Instructions burned: 158 (million)
% 4.57/1.66 % (384623)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=1790553049:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 4.57/1.66 % (384623)Also succeeded, but the first one will report.
% 4.57/1.66 % (384568)Refutation found. Thanks to Tanya!
% 4.57/1.66 % SZS status Theorem for theBenchmark
% 4.57/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 6.21/1.86 % (384568)------------------------------
% 6.21/1.86 % (384568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.21/1.86 % (384568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.21/1.86 % (384568)CaDiCaL version: 2.1.3
% 6.21/1.86 % (384568)Termination reason: Refutation
% 6.21/1.86 % (384568)Time elapsed: 0.029 s
% 6.21/1.86 % (384568)Peak memory usage: 90 MB
% 6.21/1.86 % (384568)Instructions burned: 24 (million)
% 6.21/1.86 % (384568)------------------------------
% 6.21/1.86 % (384568)------------------------------
% 6.21/1.86 % (384418)Success in time 0.801 s
% 6.21/1.86 % Vampire exiting
%------------------------------------------------------------------------------