%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n004.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 11:33:55 AM UTC 2026
% Result : Theorem 0.98s 0.59s
% Output : Refutation 0.98s
% 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 : 21 ( 21 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 * $i * $i ) > $i ).
tff(func_def_22,type,
sK1: ( del * $i ) > $i ).
tff(func_def_23,type,
sK2: ( del * $i * $i ) > $i ).
tff(func_def_24,type,
sK3: del ).
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/Axioms/ITP001/ITP001_2.ax',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: del,X2: $i] :
( ! [X3: $i] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
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) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(ennf_transformation,[],[f27]) ).
tff(f46,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,[],[f45]) ).
tff(f47,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(f48,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(f49,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(f61,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,[],[f46]) ).
tff(f62,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,[],[f61]) ).
tff(f63,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))],[f62]) ).
tff(f64,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,[],[f47]) ).
tff(f65,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,[],[f64]) ).
tff(f66,plain,
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
& mem(sK4,arr(sK3,bool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f49]) ).
tff(f67,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,[],[f32]) ).
tff(f93,plain,
! [X0: del] : mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)),
inference(cnf_transformation,[],[f20]) ).
tff(f95,plain,
! [X0: del] : mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))),
inference(cnf_transformation,[],[f22]) ).
tff(f104,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,[],[f63]) ).
tff(f105,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,[],[f63]) ).
tff(f106,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,[],[f63]) ).
tff(f108,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,[],[f65]) ).
tff(f110,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,[],[f48]) ).
tff(f111,plain,
mem(sK4,arr(sK3,bool)),
inference(cnf_transformation,[],[f66]) ).
tff(f112,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4)),
inference(cnf_transformation,[],[f66]) ).
tff(f154,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Epred__set_2ECHOICE(X1),X0),X1)
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[],[f67,f93]) ).
tff(f156,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Epred__set_2EREST(X1),X0),arr(X1,bool))
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[],[f67,f95]) ).
tff(f278,plain,
ap(c_2Epred__set_2EREST(sK3),sK4) = ap(ap(c_2Epred__set_2EDELETE(sK3),sK4),ap(c_2Epred__set_2ECHOICE(sK3),sK4)),
inference(resolution,[],[f110,f111]) ).
tff(f290,definition,
( spl5_9
<=> mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool)) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
tff(f291,plain,
( mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f290]) ).
tff(f292,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| spl5_9 ),
inference(avatar_component_clause,[],[f290]) ).
tff(f321,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,[],[f108,f105]) ).
tff(f324,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,[],[f321,f104]) ).
tff(f554,plain,
( ~ mem(sK4,arr(sK3,bool))
| spl5_9 ),
inference(resolution,[],[f156,f292]) ).
tff(f563,plain,
( $false
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f554,f111]) ).
tff(f564,plain,
spl5_9,
inference(avatar_contradiction_clause,[],[f563]) ).
tff(f1136,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(sK4,arr(sK3,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool)) ),
inference(superposition,[],[f324,f278]) ).
tff(f1139,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| ~ mem(sK4,arr(sK3,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool)) ),
inference(forward_subsumption_resolution,[],[f1136,f154]) ).
tff(f1145,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool)) ),
inference(forward_subsumption_resolution,[],[f1139,f111]) ).
tff(f1149,plain,
( ! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,ap(c_2Epred__set_2EREST(sK3),sK4),X0)),sK4))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),X0))
| ~ mem(X0,arr(sK3,bool)) )
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1145,f291]) ).
tff(f1343,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
| ~ mem(sK4,arr(sK3,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
| ~ mem(sK4,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ spl5_9 ),
inference(resolution,[],[f1149,f106]) ).
tff(f1347,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
| ~ mem(sK4,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ spl5_9 ),
inference(duplicate_literal_removal,[],[f1343]) ).
tff(f1350,plain,
( ~ mem(sK4,arr(sK3,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1347,f112]) ).
tff(f1352,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK3),sK4),arr(sK3,bool))
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1350,f111]) ).
tff(f1353,plain,
( $false
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f1352,f291]) ).
tff(f1354,plain,
~ spl5_9,
inference(avatar_contradiction_clause,[],[f1353]) ).
cnf(s10,plain,
spl5_9,
inference(sat_conversion,[],[f564]) ).
cnf(s30,plain,
~ spl5_9,
inference(sat_conversion,[],[f1354]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s10,s30]) ).
tff(f1355,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 11:49:52 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.44 Running first-order model finding
% 0.12/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.98/0.59 % (3380846)Will run a generic schedule for satisfiability detection.
% 0.98/0.59 % (3380852)% WARNING: option uhcvi not known.
% 0.98/0.59 % (3380852)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3871697175:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.98/0.59 % (3380851)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=972762180_2999 on theBenchmark for (2999ds/0Mi)
% 0.98/0.59 % (3380853)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3376692721:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.98/0.59 % (3380854)dis+10_1_sil=32000:sp=arity:random_seed=309644945:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.98/0.59 % (3380855)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=391507139:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.98/0.59 % (3380856)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1573643465:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.98/0.59 % (3380857)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2689847641:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.98/0.59 % TRYING [1,1,1]
% 0.98/0.59 % TRYING [1,2,1]
% 0.98/0.59 % TRYING [2,2,1]
% 0.98/0.59 % TRYING [1,3,1]
% 0.98/0.59 % TRYING [1,2,2]
% 0.98/0.59 % TRYING [2,2,2]
% 0.98/0.59 % TRYING [1,3,2]
% 0.98/0.59 % TRYING [3,2,1]
% 0.98/0.59 % TRYING [2,3,1]
% 0.98/0.59 % (3380854) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3380846-3380854"...
% 0.98/0.59 % TRYING [2,3,2]
% 0.98/0.59 % (3380854)...printing done.
% 0.98/0.59 % (3380854)Refutation found. Thanks to Tanya!
% 0.98/0.59 % SZS status Theorem for theBenchmark
% 0.98/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.98/0.59 % (3380854)------------------------------
% 0.98/0.59 % (3380854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.59 % (3380854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.59 % (3380854)CaDiCaL version: 2.1.3
% 0.98/0.59 % (3380854)Termination reason: Refutation
% 0.98/0.59 % (3380854)Time elapsed: 0.093 s
% 0.98/0.59 % (3380854)Peak memory usage: 13 MB
% 0.98/0.59 % (3380854)Instructions burned: 90 (million)
% 0.98/0.59 % (3380846)Success in time 0.136 s
% 0.98/0.59 % Vampire exiting
%------------------------------------------------------------------------------