%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET996+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:42:29 PM UTC 2026
% Result : Theorem 2.80s 1.34s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 104 ( 33 unt; 2 def)
% Number of atoms : 315 ( 79 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 357 ( 146 ~; 135 |; 55 &)
% ( 11 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 171 ( 1 sgn 154 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f7,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f13,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_dom(X0))
& relation(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f14,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_rng(X0))
& relation(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f23,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f24,axiom,
! [X0,X1,X2] :
( element(X2,X0)
=> ? [X3] :
( relation(X3)
& function(X3)
& relation_dom(X3) = X1
& ! [X4] :
( in(X4,X1)
=> apply(X3,X4) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_16_2__funct_1) ).
fof(f25,conjecture,
! [X0,X1] :
~ ( ~ ( X0 = empty_set
& X1 != empty_set )
& ! [X2] :
( ( relation(X2)
& function(X2) )
=> ~ ( X1 = relation_dom(X2)
& subset(relation_rng(X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1] :
~ ( ~ ( X0 = empty_set
& X1 != empty_set )
& ! [X2] :
( ( relation(X2)
& function(X2) )
=> ~ ( X1 = relation_dom(X2)
& subset(relation_rng(X2),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f29,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f30,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f33,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X0)
& X0 != X1
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f36,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f23]) ).
fof(f37,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f38,plain,
? [X0,X1] :
( ( empty_set != X0
| empty_set = X1 )
& ! [X2] :
( relation_dom(X2) != X1
| ~ subset(relation_rng(X2),X0)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f39,plain,
? [X0,X1] :
( ( empty_set != X0
| empty_set = X1 )
& ! [X2] :
( relation_dom(X2) != X1
| ~ subset(relation_rng(X2),X0)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ empty(X0)
| X0 = X1
| ~ empty(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f41,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ? [X3] :
( relation(X3)
& function(X3)
& relation_dom(X3) = X1
& ! [X4] :
( apply(X3,X4) = X2
| ~ in(X4,X1) ) )
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( ( empty(relation_rng(X0))
& relation(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f48,plain,
! [X0] :
( ( empty(relation_dom(X0))
& relation(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f51,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f54,plain,
( ( empty_set != sK0
| empty_set = sK1 )
& ! [X2] :
( relation_dom(X2) != sK1
| ~ subset(relation_rng(X2),sK0)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f39]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( relation(sK2(X1,X2))
& function(sK2(X1,X2))
& relation_dom(sK2(X1,X2)) = X1
& ! [X4] :
( apply(sK2(X1,X2),X4) = X2
| ~ in(X4,X1) ) )
| ~ element(X2,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X1,X2))],[f42]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK3(X0,X1) )
| ~ in(sK3(X0,X1),X1) )
& ( ( in(sK4(X0,X1),relation_dom(X0))
& sK3(X0,X1) = apply(X0,sK4(X0,X1)) )
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK5(X0,X5),relation_dom(X0))
& apply(X0,sK5(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f57]) ).
fof(f62,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f63,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f64,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f64]) ).
fof(f66,plain,
! [X2] :
( relation_dom(X2) != sK1
| ~ subset(relation_rng(X2),sK0)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f67,plain,
( empty_set != sK0
| empty_set = sK1 ),
inference(cnf_transformation,[],[f54]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f41]) ).
fof(f70,plain,
! [X2,X0,X1,X4] :
( ~ element(X2,X0)
| ~ in(X4,X1)
| apply(sK2(X1,X2),X4) = X2 ),
inference(cnf_transformation,[],[f55]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| relation_dom(sK2(X1,X2)) = X1 ),
inference(cnf_transformation,[],[f55]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| function(sK2(X1,X2)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| relation(sK2(X1,X2)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f74,plain,
! [X0,X1,X5] :
( apply(X0,sK5(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f75,plain,
! [X0,X1,X5] :
( in(sK5(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X0,X1] :
( in(sK4(X0,X1),relation_dom(X0))
| in(sK3(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f81,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f84,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f88,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f29]) ).
fof(f93,plain,
relation(empty_set),
inference(cnf_transformation,[],[f37]) ).
fof(f94,plain,
empty(empty_set),
inference(cnf_transformation,[],[f37]) ).
fof(f101,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f102,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f103,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f104,plain,
! [X0,X1] :
( in(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f108,plain,
! [X0,X5] :
( in(sK5(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f75]) ).
fof(f109,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| apply(X0,sK5(X0,X5)) = X5
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f74]) ).
fof(f111,definition,
( spl10_1
<=> empty_set = sK1 ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f115,definition,
( spl10_2
<=> empty_set = sK0 ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f117,plain,
( empty_set != sK0
| spl10_2 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f67,f115,f111]) ).
fof(f119,plain,
function(empty_set),
inference(unit_resulting_resolution,[],[f88,f94]) ).
fof(f129,plain,
empty(relation_rng(empty_set)),
inference(unit_resulting_resolution,[],[f81,f94]) ).
fof(f138,plain,
empty(relation_dom(empty_set)),
inference(unit_resulting_resolution,[],[f84,f94]) ).
fof(f141,plain,
empty_set = relation_rng(empty_set),
inference(unit_resulting_resolution,[],[f69,f129]) ).
fof(f168,plain,
empty_set = relation_dom(empty_set),
inference(unit_resulting_resolution,[],[f68,f94,f138]) ).
fof(f206,plain,
( empty_set != sK1
| ~ subset(relation_rng(empty_set),sK0)
| ~ relation(empty_set)
| ~ function(empty_set) ),
inference(superposition,[],[f66,f168]) ).
fof(f207,plain,
( empty_set != sK1
| ~ subset(relation_rng(empty_set),sK0)
| ~ function(empty_set) ),
inference(forward_subsumption_resolution,[],[f206,f93]) ).
fof(f208,plain,
( empty_set != sK1
| ~ subset(relation_rng(empty_set),sK0) ),
inference(forward_subsumption_resolution,[],[f207,f119]) ).
fof(f209,plain,
( ~ subset(empty_set,sK0)
| empty_set != sK1 ),
inference(forward_demodulation,[],[f208,f141]) ).
fof(f210,plain,
empty_set != sK1,
inference(forward_subsumption_resolution,[],[f209,f89]) ).
fof(f211,plain,
~ spl10_1,
inference(avatar_split_clause,[],[f210,f111]) ).
fof(f216,plain,
! [X0] : element(X0,powerset(X0)),
inference(unit_resulting_resolution,[],[f101,f102]) ).
fof(f221,plain,
! [X0,X1] : relation(sK2(X0,X1)),
inference(unit_resulting_resolution,[],[f73,f216]) ).
fof(f222,plain,
! [X0,X1] : function(sK2(X0,X1)),
inference(unit_resulting_resolution,[],[f72,f216]) ).
fof(f224,plain,
! [X0,X1] : relation_dom(sK2(X0,X1)) = X0,
inference(unit_resulting_resolution,[],[f71,f216]) ).
fof(f251,plain,
! [X0] :
( in(sK4(empty_set,X0),empty_set)
| in(sK3(empty_set,X0),X0)
| relation_rng(empty_set) = X0
| ~ relation(empty_set)
| ~ function(empty_set) ),
inference(superposition,[],[f78,f168]) ).
fof(f254,plain,
! [X0] :
( in(sK4(empty_set,X0),empty_set)
| in(sK3(empty_set,X0),X0)
| relation_rng(empty_set) = X0
| ~ function(empty_set) ),
inference(forward_subsumption_resolution,[],[f251,f93]) ).
fof(f256,plain,
! [X0] :
( in(sK4(empty_set,X0),empty_set)
| in(sK3(empty_set,X0),X0)
| relation_rng(empty_set) = X0 ),
inference(forward_subsumption_resolution,[],[f254,f119]) ).
fof(f257,plain,
! [X0] :
( in(sK4(empty_set,X0),empty_set)
| in(sK3(empty_set,X0),X0)
| empty_set = X0 ),
inference(forward_demodulation,[],[f256,f141]) ).
fof(f267,plain,
! [X0] : ~ subset(relation_rng(sK2(sK1,X0)),sK0),
inference(unit_resulting_resolution,[],[f66,f222,f221,f224]) ).
fof(f270,plain,
! [X2,X0,X1] :
( in(sK5(sK2(X0,X1),X2),X0)
| ~ in(X2,relation_rng(sK2(X0,X1)))
| ~ relation(sK2(X0,X1))
| ~ function(sK2(X0,X1)) ),
inference(superposition,[],[f108,f224]) ).
fof(f277,plain,
! [X2,X0,X1] :
( in(sK5(sK2(X0,X1),X2),X0)
| ~ in(X2,relation_rng(sK2(X0,X1)))
| ~ function(sK2(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f270,f221]) ).
fof(f281,plain,
! [X2,X0,X1] :
( in(sK5(sK2(X0,X1),X2),X0)
| ~ in(X2,relation_rng(sK2(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f277,f222]) ).
fof(f283,plain,
! [X0] : ~ in(sK9(relation_rng(sK2(sK1,X0)),sK0),sK0),
inference(unit_resulting_resolution,[],[f105,f267]) ).
fof(f284,plain,
! [X0] : in(sK9(relation_rng(sK2(sK1,X0)),sK0),relation_rng(sK2(sK1,X0))),
inference(unit_resulting_resolution,[],[f104,f267]) ).
fof(f416,plain,
! [X0] : ~ in(sK9(relation_rng(sK2(sK1,X0)),sK0),empty_set),
inference(unit_resulting_resolution,[],[f103,f89,f283]) ).
fof(f440,plain,
! [X0] : in(sK5(sK2(sK1,X0),sK9(relation_rng(sK2(sK1,X0)),sK0)),sK1),
inference(unit_resulting_resolution,[],[f281,f284]) ).
fof(f443,plain,
! [X0] : sK9(relation_rng(sK2(sK1,X0)),sK0) = apply(sK2(sK1,X0),sK5(sK2(sK1,X0),sK9(relation_rng(sK2(sK1,X0)),sK0))),
inference(unit_resulting_resolution,[],[f109,f222,f221,f284]) ).
fof(f653,plain,
! [X0,X1] : apply(sK2(sK1,X0),sK5(sK2(sK1,X1),sK9(relation_rng(sK2(sK1,X1)),sK0))) = X0,
inference(unit_resulting_resolution,[],[f70,f216,f440]) ).
fof(f1114,plain,
! [X0] : sK9(relation_rng(sK2(sK1,X0)),sK0) = X0,
inference(superposition,[],[f443,f653]) ).
fof(f1129,plain,
! [X0] : ~ in(X0,sK0),
inference(superposition,[],[f283,f1114]) ).
fof(f1131,plain,
! [X0] : ~ in(X0,empty_set),
inference(superposition,[],[f416,f1114]) ).
fof(f1158,plain,
( in(sK4(empty_set,sK0),empty_set)
| spl10_2 ),
inference(unit_resulting_resolution,[],[f257,f117,f1129]) ).
fof(f1165,plain,
( $false
| spl10_2 ),
inference(forward_subsumption_resolution,[],[f1158,f1131]) ).
fof(f1166,plain,
spl10_2,
inference(avatar_contradiction_clause,[],[f1165]) ).
cnf(s1,plain,
( spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f118]) ).
cnf(s2,plain,
~ spl10_1,
inference(sat_conversion,[],[f211]) ).
cnf(s3,plain,
spl10_2,
inference(sat_conversion,[],[f1166]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f1169,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET996+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:23:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.80/1.34 % (2965950)Detected formulas, will run a generic FOF schedule.
% 2.80/1.34 % (2965961)dis-21_1_sil=8000:lcm=predicate:random_seed=316626008: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)
% 2.80/1.34 % (2965956)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=2273625273:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.34 % (2965957)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=3064698953:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.34 % (2965955)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=3943433001:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.34 % (2965958)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4115095291:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.34 % (2965959)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1350540521:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.34 % (2965960)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=759604740:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.34 % (2965958)Refutation not found, incomplete strategy
% 2.80/1.34 % (2965958)------------------------------
% 2.80/1.34 % (2965958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.34 % (2965958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.34 % (2965958)CaDiCaL version: 2.1.3
% 2.80/1.34 % (2965958)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.34 % (2965958)Time elapsed: 0.002 s
% 2.80/1.34 % (2965958)Peak memory usage: 88 MB
% 2.80/1.34 % (2965958)Instructions burned: 1 (million)
% 2.80/1.34 % (2965961)Instruction limit reached!
% 2.80/1.34 % (2965961)------------------------------
% 2.80/1.34 % (2965961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.34 % (2965961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.34 % (2965961)CaDiCaL version: 2.1.3
% 2.80/1.34 % (2965961)Termination reason: Instruction limit
% 2.80/1.34 % (2965961)Termination phase: Saturation
% 2.80/1.34 % (2965961)Time elapsed: 0.042 s
% 2.80/1.34 % (2965961)Peak memory usage: 90 MB
% 2.80/1.34 % (2965961)Instructions burned: 131 (million)
% 2.80/1.34 % (2965960)Instruction limit reached!
% 2.80/1.34 % (2965960)------------------------------
% 2.80/1.34 % (2965960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.34 % (2965960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.34 % (2965960)CaDiCaL version: 2.1.3
% 2.80/1.34 % (2965960)Termination reason: Instruction limit
% 2.80/1.34 % (2965960)Termination phase: Saturation
% 2.80/1.34 % (2965960)Time elapsed: 0.060 s
% 2.80/1.34 % (2965960)Peak memory usage: 90 MB
% 2.80/1.34 % (2965960)Instructions burned: 141 (million)
% 2.80/1.34 % (2965959)Instruction limit reached!
% 2.80/1.34 % (2965959)------------------------------
% 2.80/1.34 % (2965959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.34 % (2965959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.34 % (2965959)CaDiCaL version: 2.1.3
% 2.80/1.34 % (2965959)Termination reason: Instruction limit
% 2.80/1.34 % (2965959)Termination phase: Saturation
% 2.80/1.34 % (2965959)Time elapsed: 0.072 s
% 2.80/1.34 % (2965959)Peak memory usage: 88 MB
% 2.80/1.34 % (2965959)Instructions burned: 119 (million)
% 2.80/1.34 % (2965969)lrs+10_1_sil=8000:sp=occurrence:random_seed=2973527488:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.80/1.34 % (2965970)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3526366535:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.80/1.34 % (2965970)First to succeed.
% 2.80/1.34 % (2965970)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2965950"
% 2.80/1.34 % (2965971)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2524086283:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.80/1.34 % (2965958)------------------------------
% 2.80/1.34 % (2965958)------------------------------
% 2.80/1.34 % (2965969)Instruction limit reached!
% 2.80/1.34 % (2965969)------------------------------
% 2.80/1.34 % (2965969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.34 % (2965969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.34 % (2965969)CaDiCaL version: 2.1.3
% 2.80/1.34 % (2965969)Termination reason: Instruction limit
% 2.80/1.34 % (2965969)Termination phase: Saturation
% 2.80/1.34 % (2965969)Time elapsed: 0.165 s
% 2.80/1.34 % (2965969)Peak memory usage: 91 MB
% 2.80/1.34 % (2965969)Instructions burned: 285 (million)
% 2.80/1.34 % (2965970)Refutation found. Thanks to Tanya!
% 2.80/1.34 % SZS status Theorem for theBenchmark
% 2.80/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.53 % (2965970)------------------------------
% 4.03/1.53 % (2965970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.53 % (2965970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.53 % (2965970)CaDiCaL version: 2.1.3
% 4.03/1.53 % (2965970)Termination reason: Refutation
% 4.03/1.53 % (2965970)Time elapsed: 0.013 s
% 4.03/1.53 % (2965970)Peak memory usage: 90 MB
% 4.03/1.53 % (2965970)Instructions burned: 36 (million)
% 4.03/1.53 % (2965970)------------------------------
% 4.03/1.53 % (2965970)------------------------------
% 4.03/1.53 % (2965950)Success in time 0.479 s
% 4.03/1.53 % Vampire exiting
%------------------------------------------------------------------------------