%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU016+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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:04 PM UTC 2026
% Result : Theorem 16.97s 3.24s
% Output : Refutation 17.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 58
% Syntax : Number of formulae : 523 ( 60 unt; 37 def)
% Number of atoms : 2292 ( 479 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 3174 (1405 ~;1538 |; 150 &)
% ( 44 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 38 ( 36 usr; 30 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 11 con; 0-2 aty)
% Number of variables : 461 ( 0 sgn 429 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f7,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f9,axiom,
! [X0,X1] :
( ( empty(X0)
& relation(X1) )
=> ( empty(relation_composition(X1,X0))
& relation(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f16,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f18,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_dom(X0))
& relation(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f30,axiom,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = singleton(empty_set)
& ! [X2] :
( in(X2,singleton(empty_set))
=> apply(X1,X2) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e3_38_2__funct_1) ).
fof(f31,axiom,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = singleton(empty_set)
& ! [X2] :
( in(X2,singleton(empty_set))
=> apply(X1,X2) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e6_38_2__funct_1) ).
fof(f32,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( relation_dom(X1) = singleton(X0)
=> relation_rng(X1) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f37,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f39,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f40,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( subset(relation_rng(X1),relation_dom(X0))
& subset(relation_rng(X2),relation_dom(X0))
& relation_dom(X1) = relation_dom(X2)
& relation_composition(X1,X0) = relation_composition(X2,X0) )
=> X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( subset(relation_rng(X1),relation_dom(X0))
& subset(relation_rng(X2),relation_dom(X0))
& relation_dom(X1) = relation_dom(X2)
& relation_composition(X1,X0) = relation_composition(X2,X0) )
=> X1 = X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f45,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f47,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f54,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(f55,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,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f57,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ( empty(relation_composition(X1,X0))
& relation(relation_composition(X1,X0)) )
| ~ empty(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f61,plain,
! [X0,X1] :
( ( empty(relation_composition(X1,X0))
& relation(relation_composition(X1,X0)) )
| ~ empty(X0)
| ~ relation(X1) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f63,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f65,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0] :
( ( empty(relation_dom(X0))
& relation(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f73,plain,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = singleton(empty_set)
& ! [X2] :
( apply(X1,X2) = X0
| ~ in(X2,singleton(empty_set)) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f74,plain,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = singleton(empty_set)
& ! [X2] :
( apply(X1,X2) = X0
| ~ in(X2,singleton(empty_set)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f75,plain,
! [X0,X1] :
( relation_rng(X1) = singleton(apply(X1,X0))
| singleton(X0) != relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f76,plain,
! [X0,X1] :
( relation_rng(X1) = singleton(apply(X1,X0))
| singleton(X0) != relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f75]) ).
fof(f78,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f83,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
? [X0] :
( ( one_to_one(X0)
<~> ! [X1] :
( ! [X2] :
( X1 = X2
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ subset(relation_rng(X2),relation_dom(X0))
| relation_dom(X1) != relation_dom(X2)
| relation_composition(X1,X0) != relation_composition(X2,X0)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f87,plain,
? [X0] :
( ( one_to_one(X0)
<~> ! [X1] :
( ! [X2] :
( X1 = X2
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ subset(relation_rng(X2),relation_dom(X0))
| relation_dom(X1) != relation_dom(X2)
| relation_composition(X1,X0) != relation_composition(X2,X0)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f89,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f88]) ).
fof(f92,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X0,X2) != apply(X1,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X0,X2) != apply(X1,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f97,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f97]) ).
fof(f99,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,[],[f55]) ).
fof(f100,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,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK1(X0,X1) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK2(X0,X1),relation_dom(X0))
& sK1(X0,X1) = apply(X0,sK2(X0,X1)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK3(X0,X5),relation_dom(X0))
& apply(X0,sK3(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f100]) ).
fof(f102,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f103,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK4(X0) != sK5(X0)
& in(sK4(X0),relation_dom(X0))
& in(sK5(X0),relation_dom(X0))
& apply(X0,sK4(X0)) = apply(X0,sK5(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0))],[f103]) ).
fof(f114,plain,
! [X0] :
( relation(sK15(X0))
& function(sK15(X0))
& singleton(empty_set) = relation_dom(sK15(X0))
& ! [X2] :
( apply(sK15(X0),X2) = X0
| ~ in(X2,singleton(empty_set)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f73]) ).
fof(f115,plain,
! [X0] :
( relation(sK16(X0))
& function(sK16(X0))
& singleton(empty_set) = relation_dom(sK16(X0))
& ! [X2] :
( apply(sK16(X0),X2) = X0
| ~ in(X2,singleton(empty_set)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f74]) ).
fof(f116,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f117,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f118,plain,
? [X0] :
( ( ? [X1] :
( ? [X2] :
( X1 != X2
& subset(relation_rng(X1),relation_dom(X0))
& subset(relation_rng(X2),relation_dom(X0))
& relation_dom(X1) = relation_dom(X2)
& relation_composition(X1,X0) = relation_composition(X2,X0)
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) )
| ~ one_to_one(X0) )
& ( ! [X1] :
( ! [X2] :
( X1 = X2
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ subset(relation_rng(X2),relation_dom(X0))
| relation_dom(X1) != relation_dom(X2)
| relation_composition(X1,X0) != relation_composition(X2,X0)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) )
| one_to_one(X0) )
& relation(X0)
& function(X0) ),
inference(nnf_transformation,[],[f87]) ).
fof(f119,plain,
? [X0] :
( ( ? [X1] :
( ? [X2] :
( X1 != X2
& subset(relation_rng(X1),relation_dom(X0))
& subset(relation_rng(X2),relation_dom(X0))
& relation_dom(X1) = relation_dom(X2)
& relation_composition(X1,X0) = relation_composition(X2,X0)
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) )
| ~ one_to_one(X0) )
& ( ! [X1] :
( ! [X2] :
( X1 = X2
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ subset(relation_rng(X2),relation_dom(X0))
| relation_dom(X1) != relation_dom(X2)
| relation_composition(X1,X0) != relation_composition(X2,X0)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) )
| one_to_one(X0) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f118]) ).
fof(f120,plain,
? [X0] :
( ( ? [X1] :
( ? [X2] :
( X1 != X2
& subset(relation_rng(X1),relation_dom(X0))
& subset(relation_rng(X2),relation_dom(X0))
& relation_dom(X1) = relation_dom(X2)
& relation_composition(X1,X0) = relation_composition(X2,X0)
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) )
| ~ one_to_one(X0) )
& ( ! [X3] :
( ! [X4] :
( X3 = X4
| ~ subset(relation_rng(X3),relation_dom(X0))
| ~ subset(relation_rng(X4),relation_dom(X0))
| relation_dom(X3) != relation_dom(X4)
| relation_composition(X3,X0) != relation_composition(X4,X0)
| ~ relation(X4)
| ~ function(X4) )
| ~ relation(X3)
| ~ function(X3) )
| one_to_one(X0) )
& relation(X0)
& function(X0) ),
inference(rectify,[],[f119]) ).
fof(f121,plain,
( ( ( sK18 != sK19
& subset(relation_rng(sK18),relation_dom(sK17))
& subset(relation_rng(sK19),relation_dom(sK17))
& relation_dom(sK18) = relation_dom(sK19)
& relation_composition(sK18,sK17) = relation_composition(sK19,sK17)
& relation(sK19)
& function(sK19)
& relation(sK18)
& function(sK18) )
| ~ one_to_one(sK17) )
& ( ! [X3] :
( ! [X4] :
( X3 = X4
| ~ subset(relation_rng(X3),relation_dom(sK17))
| ~ subset(relation_rng(X4),relation_dom(sK17))
| relation_dom(X3) != relation_dom(X4)
| relation_composition(X3,sK17) != relation_composition(X4,sK17)
| ~ relation(X4)
| ~ function(X4) )
| ~ relation(X3)
| ~ function(X3) )
| one_to_one(sK17) )
& relation(sK17)
& function(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f120]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ( apply(X0,sK20(X0,X1)) != apply(X1,sK20(X0,X1))
& in(sK20(X0,X1),relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X0,X1))],[f95]) ).
fof(f126,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f127,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f132,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f136,plain,
! [X3,X0,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| X3 = X4
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f137,plain,
! [X0] :
( ~ relation(X0)
| apply(X0,sK4(X0)) = apply(X0,sK5(X0))
| one_to_one(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f138,plain,
! [X0] :
( in(sK5(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f139,plain,
! [X0] :
( in(sK4(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f140,plain,
! [X0] :
( sK4(X0) != sK5(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f141,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f144,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ empty(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f147,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f154,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f157,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f176,plain,
! [X2,X0] :
( ~ in(X2,singleton(empty_set))
| apply(sK15(X0),X2) = X0 ),
inference(cnf_transformation,[],[f114]) ).
fof(f177,plain,
! [X0] : singleton(empty_set) = relation_dom(sK15(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f178,plain,
! [X0] : function(sK15(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f179,plain,
! [X0] : relation(sK15(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f180,plain,
! [X2,X0] :
( ~ in(X2,singleton(empty_set))
| apply(sK16(X0),X2) = X0 ),
inference(cnf_transformation,[],[f115]) ).
fof(f181,plain,
! [X0] : singleton(empty_set) = relation_dom(sK16(X0)),
inference(cnf_transformation,[],[f115]) ).
fof(f182,plain,
! [X0] : function(sK16(X0)),
inference(cnf_transformation,[],[f115]) ).
fof(f183,plain,
! [X0] : relation(sK16(X0)),
inference(cnf_transformation,[],[f115]) ).
fof(f184,plain,
! [X0,X1] :
( singleton(X0) != relation_dom(X1)
| relation_rng(X1) = singleton(apply(X1,X0))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f188,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f190,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f192,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f193,plain,
! [X0,X1] :
( ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f194,plain,
function(sK17),
inference(cnf_transformation,[],[f121]) ).
fof(f195,plain,
relation(sK17),
inference(cnf_transformation,[],[f121]) ).
fof(f196,plain,
! [X3,X4] :
( X3 = X4
| ~ subset(relation_rng(X3),relation_dom(sK17))
| ~ subset(relation_rng(X4),relation_dom(sK17))
| relation_dom(X3) != relation_dom(X4)
| relation_composition(X3,sK17) != relation_composition(X4,sK17)
| ~ relation(X4)
| ~ function(X4)
| ~ relation(X3)
| ~ function(X3)
| one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f197,plain,
( function(sK18)
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f198,plain,
( relation(sK18)
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f199,plain,
( function(sK19)
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f200,plain,
( relation(sK19)
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f201,plain,
( relation_composition(sK18,sK17) = relation_composition(sK19,sK17)
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f202,plain,
( relation_dom(sK18) = relation_dom(sK19)
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f203,plain,
( subset(relation_rng(sK19),relation_dom(sK17))
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f204,plain,
( subset(relation_rng(sK18),relation_dom(sK17))
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f205,plain,
( sK18 != sK19
| ~ one_to_one(sK17) ),
inference(cnf_transformation,[],[f121]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f209,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f211,plain,
! [X0,X1] :
( relation_dom(X0) != relation_dom(X1)
| X0 = X1
| in(sK20(X0,X1),relation_dom(X0))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f212,plain,
! [X0,X1] :
( apply(X0,sK20(X0,X1)) != apply(X1,sK20(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f213,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f127]) ).
fof(f214,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f213]) ).
fof(f215,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f126]) ).
fof(f216,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f132]) ).
fof(f217,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f216]) ).
fof(f220,definition,
sF21 = relation_rng(sK18),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f221,plain,
relation_rng(sK18) = sF21,
inference(reorient_equations,[],[f220]) ).
fof(f222,definition,
sF22 = relation_dom(sK17),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f223,plain,
relation_dom(sK17) = sF22,
inference(reorient_equations,[],[f222]) ).
fof(f224,plain,
( subset(sF21,sF22)
| ~ one_to_one(sK17) ),
inference(definition_folding,[],[f204,f223,f221]) ).
fof(f225,definition,
sF23 = relation_rng(sK19),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f226,plain,
relation_rng(sK19) = sF23,
inference(reorient_equations,[],[f225]) ).
fof(f227,plain,
( subset(sF23,sF22)
| ~ one_to_one(sK17) ),
inference(definition_folding,[],[f203,f223,f226]) ).
fof(f228,definition,
sF24 = relation_dom(sK18),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f229,plain,
relation_dom(sK18) = sF24,
inference(reorient_equations,[],[f228]) ).
fof(f230,definition,
sF25 = relation_dom(sK19),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f231,plain,
relation_dom(sK19) = sF25,
inference(reorient_equations,[],[f230]) ).
fof(f232,plain,
( sF24 = sF25
| ~ one_to_one(sK17) ),
inference(definition_folding,[],[f202,f231,f229]) ).
fof(f233,definition,
sF26 = relation_composition(sK18,sK17),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f234,plain,
relation_composition(sK18,sK17) = sF26,
inference(reorient_equations,[],[f233]) ).
fof(f235,definition,
sF27 = relation_composition(sK19,sK17),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f236,plain,
relation_composition(sK19,sK17) = sF27,
inference(reorient_equations,[],[f235]) ).
fof(f237,plain,
( sF26 = sF27
| ~ one_to_one(sK17) ),
inference(definition_folding,[],[f201,f236,f234]) ).
fof(f238,definition,
! [X3] : sF28(X3) = relation_composition(X3,sK17),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f239,plain,
! [X3] : relation_composition(X3,sK17) = sF28(X3),
inference(reorient_equations,[],[f238]) ).
fof(f240,plain,
! [X3,X4] :
( X3 = X4
| ~ subset(relation_rng(X3),sF22)
| ~ subset(relation_rng(X4),sF22)
| relation_dom(X3) != relation_dom(X4)
| sF28(X3) != sF28(X4)
| ~ relation(X4)
| ~ function(X4)
| ~ relation(X3)
| ~ function(X3)
| one_to_one(sK17) ),
inference(definition_folding,[],[f196,f239,f239,f223,f223]) ).
fof(f242,definition,
( spl29_1
<=> one_to_one(sK17) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f243,plain,
( ~ one_to_one(sK17)
| spl29_1 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f244,plain,
( one_to_one(sK17)
| ~ spl29_1 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f246,definition,
( spl29_2
<=> ! [X4,X3] :
( X3 = X4
| ~ function(X3)
| ~ relation(X3)
| ~ function(X4)
| ~ relation(X4)
| sF28(X3) != sF28(X4)
| relation_dom(X3) != relation_dom(X4)
| ~ subset(relation_rng(X4),sF22)
| ~ subset(relation_rng(X3),sF22) ) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f247,plain,
( ! [X3,X4] :
( sF28(X3) != sF28(X4)
| ~ function(X3)
| ~ relation(X3)
| ~ function(X4)
| ~ relation(X4)
| X3 = X4
| relation_dom(X3) != relation_dom(X4)
| ~ subset(relation_rng(X4),sF22)
| ~ subset(relation_rng(X3),sF22) )
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( spl29_1
| spl29_2 ),
inference(avatar_split_clause,[],[f240,f246,f242]) ).
fof(f250,definition,
( spl29_3
<=> function(sK18) ),
introduced(definition,[new_symbols(definition,[spl29_3])],[avatar_definition]) ).
fof(f252,plain,
( function(sK18)
| ~ spl29_3 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl29_1
| spl29_3 ),
inference(avatar_split_clause,[],[f197,f250,f242]) ).
fof(f255,definition,
( spl29_4
<=> relation(sK18) ),
introduced(definition,[new_symbols(definition,[spl29_4])],[avatar_definition]) ).
fof(f257,plain,
( relation(sK18)
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,plain,
( ~ spl29_1
| spl29_4 ),
inference(avatar_split_clause,[],[f198,f255,f242]) ).
fof(f260,definition,
( spl29_5
<=> function(sK19) ),
introduced(definition,[new_symbols(definition,[spl29_5])],[avatar_definition]) ).
fof(f262,plain,
( function(sK19)
| ~ spl29_5 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f263,plain,
( ~ spl29_1
| spl29_5 ),
inference(avatar_split_clause,[],[f199,f260,f242]) ).
fof(f265,definition,
( spl29_6
<=> relation(sK19) ),
introduced(definition,[new_symbols(definition,[spl29_6])],[avatar_definition]) ).
fof(f267,plain,
( relation(sK19)
| ~ spl29_6 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f268,plain,
( ~ spl29_1
| spl29_6 ),
inference(avatar_split_clause,[],[f200,f265,f242]) ).
fof(f270,definition,
( spl29_7
<=> sF26 = sF27 ),
introduced(definition,[new_symbols(definition,[spl29_7])],[avatar_definition]) ).
fof(f272,plain,
( sF26 = sF27
| ~ spl29_7 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,plain,
( ~ spl29_1
| spl29_7 ),
inference(avatar_split_clause,[],[f237,f270,f242]) ).
fof(f275,definition,
( spl29_8
<=> sF24 = sF25 ),
introduced(definition,[new_symbols(definition,[spl29_8])],[avatar_definition]) ).
fof(f277,plain,
( sF24 = sF25
| ~ spl29_8 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f278,plain,
( ~ spl29_1
| spl29_8 ),
inference(avatar_split_clause,[],[f232,f275,f242]) ).
fof(f280,definition,
( spl29_9
<=> subset(sF23,sF22) ),
introduced(definition,[new_symbols(definition,[spl29_9])],[avatar_definition]) ).
fof(f282,plain,
( subset(sF23,sF22)
| ~ spl29_9 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,plain,
( ~ spl29_1
| spl29_9 ),
inference(avatar_split_clause,[],[f227,f280,f242]) ).
fof(f285,definition,
( spl29_10
<=> subset(sF21,sF22) ),
introduced(definition,[new_symbols(definition,[spl29_10])],[avatar_definition]) ).
fof(f287,plain,
( subset(sF21,sF22)
| ~ spl29_10 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,plain,
( ~ spl29_1
| spl29_10 ),
inference(avatar_split_clause,[],[f224,f285,f242]) ).
fof(f290,definition,
( spl29_11
<=> sK18 = sK19 ),
introduced(definition,[new_symbols(definition,[spl29_11])],[avatar_definition]) ).
fof(f292,plain,
( sK18 != sK19
| spl29_11 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f293,plain,
( ~ spl29_1
| ~ spl29_11 ),
inference(avatar_split_clause,[],[f205,f290,f242]) ).
fof(f298,plain,
! [X0] :
( ~ subset(relation_rng(X0),sF22)
| relation_dom(X0) = relation_dom(relation_composition(X0,sK17))
| ~ relation(sK17)
| ~ relation(X0) ),
inference(superposition,[],[f193,f223]) ).
fof(f309,plain,
! [X0] :
( ~ subset(relation_rng(X0),sF22)
| relation_dom(X0) = relation_dom(relation_composition(X0,sK17))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f298,f195]) ).
fof(f312,plain,
! [X0] :
( ~ subset(relation_rng(X0),sF22)
| relation_dom(X0) = relation_dom(sF28(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f309,f239]) ).
fof(f322,plain,
sF26 = sF28(sK18),
inference(superposition,[],[f239,f234]) ).
fof(f326,plain,
sF27 = sF28(sK19),
inference(superposition,[],[f239,f236]) ).
fof(f330,plain,
( ~ subset(sF23,sF22)
| relation_dom(sK19) = relation_dom(sF28(sK19))
| ~ relation(sK19) ),
inference(superposition,[],[f312,f226]) ).
fof(f331,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(sF28(X0)))
| apply(sK17,apply(X0,X1)) = apply(sF28(X0),X1)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[],[f186,f239]) ).
fof(f334,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(sF28(X0)))
| apply(sK17,apply(X0,X1)) = apply(sF28(X0),X1)
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK17) ),
inference(forward_subsumption_resolution,[],[f331,f195]) ).
fof(f335,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(sF28(X0)))
| apply(sK17,apply(X0,X1)) = apply(sF28(X0),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f334,f194]) ).
fof(f336,plain,
! [X0] :
( relation(sF28(X0))
| ~ relation(X0)
| ~ relation(sK17) ),
inference(superposition,[],[f141,f239]) ).
fof(f339,plain,
! [X0] :
( relation(sF28(X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f336,f195]) ).
fof(f341,plain,
( in(sK4(sK17),sF22)
| one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[],[f139,f223]) ).
fof(f350,plain,
( in(sK5(sK17),sF22)
| one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[],[f138,f223]) ).
fof(f367,plain,
! [X0] :
( function(sF28(X0))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[],[f147,f239]) ).
fof(f370,plain,
! [X0] :
( function(sF28(X0))
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK17) ),
inference(forward_subsumption_resolution,[],[f367,f195]) ).
fof(f371,plain,
! [X0] :
( function(sF28(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f370,f194]) ).
fof(f378,plain,
! [X0] :
( relation_dom(X0) != sF24
| sK18 = X0
| in(sK20(X0,sK18),relation_dom(X0))
| ~ relation(sK18)
| ~ function(sK18)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f211,f229]) ).
fof(f379,plain,
! [X0] :
( relation_dom(X0) != sF25
| sK19 = X0
| in(sK20(X0,sK19),relation_dom(X0))
| ~ relation(sK19)
| ~ function(sK19)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f211,f231]) ).
fof(f386,plain,
( apply(sK17,sK4(sK17)) = apply(sK17,sK5(sK17))
| one_to_one(sK17)
| ~ function(sK17) ),
inference(resolution,[],[f137,f195]) ).
fof(f402,plain,
! [X0] :
( in(apply(sK18,X0),sF21)
| ~ in(X0,relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f217,f221]) ).
fof(f403,plain,
! [X0] :
( in(apply(sK19,X0),sF23)
| ~ in(X0,relation_dom(sK19))
| ~ relation(sK19)
| ~ function(sK19) ),
inference(superposition,[],[f217,f226]) ).
fof(f430,plain,
! [X0] :
( ~ in(X0,relation_dom(sF26))
| apply(sK17,apply(sK18,X0)) = apply(sF26,X0)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[],[f335,f322]) ).
fof(f431,plain,
! [X0] :
( ~ in(X0,relation_dom(sF27))
| apply(sK17,apply(sK19,X0)) = apply(sF27,X0)
| ~ relation(sK19)
| ~ function(sK19) ),
inference(superposition,[],[f335,f326]) ).
fof(f455,plain,
! [X0,X1] :
( singleton(X0) != singleton(empty_set)
| relation_rng(sK15(X1)) = singleton(apply(sK15(X1),X0))
| ~ relation(sK15(X1))
| ~ function(sK15(X1)) ),
inference(superposition,[],[f184,f177]) ).
fof(f456,plain,
! [X2,X0,X1] :
( ~ in(X0,singleton(empty_set))
| apply(relation_composition(sK15(X1),X2),X0) = apply(X2,apply(sK15(X1),X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(sK15(X1))
| ~ function(sK15(X1)) ),
inference(superposition,[],[f187,f177]) ).
fof(f469,plain,
! [X2,X0,X1] :
( ~ in(X0,singleton(empty_set))
| apply(relation_composition(sK15(X1),X2),X0) = apply(X2,apply(sK15(X1),X0))
| ~ relation(X2)
| ~ function(X2)
| ~ function(sK15(X1)) ),
inference(forward_subsumption_resolution,[],[f456,f179]) ).
fof(f470,plain,
! [X0,X1] :
( singleton(X0) != singleton(empty_set)
| relation_rng(sK15(X1)) = singleton(apply(sK15(X1),X0))
| ~ function(sK15(X1)) ),
inference(forward_subsumption_resolution,[],[f455,f179]) ).
fof(f478,plain,
! [X2,X0,X1] :
( ~ in(X0,singleton(empty_set))
| apply(relation_composition(sK15(X1),X2),X0) = apply(X2,apply(sK15(X1),X0))
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f469,f178]) ).
fof(f479,plain,
! [X0,X1] :
( singleton(X0) != singleton(empty_set)
| relation_rng(sK15(X1)) = singleton(apply(sK15(X1),X0)) ),
inference(forward_subsumption_resolution,[],[f470,f178]) ).
fof(f501,plain,
! [X0,X1] :
( relation_dom(X1) != singleton(empty_set)
| sK16(X0) = X1
| in(sK20(sK16(X0),X1),singleton(empty_set))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(sK16(X0))
| ~ function(sK16(X0)) ),
inference(superposition,[],[f211,f181]) ).
fof(f502,plain,
! [X0,X1] :
( relation_dom(X0) != singleton(empty_set)
| sK16(X1) = X0
| in(sK20(X0,sK16(X1)),relation_dom(X0))
| ~ relation(sK16(X1))
| ~ function(sK16(X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f211,f181]) ).
fof(f507,plain,
! [X0,X1] :
( relation_dom(X0) != singleton(empty_set)
| sK16(X1) = X0
| in(sK20(X0,sK16(X1)),relation_dom(X0))
| ~ function(sK16(X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f502,f183]) ).
fof(f508,plain,
! [X0,X1] :
( relation_dom(X1) != singleton(empty_set)
| sK16(X0) = X1
| in(sK20(sK16(X0),X1),singleton(empty_set))
| ~ relation(X1)
| ~ function(X1)
| ~ function(sK16(X0)) ),
inference(forward_subsumption_resolution,[],[f501,f183]) ).
fof(f515,plain,
! [X0,X1] :
( relation_dom(X0) != singleton(empty_set)
| sK16(X1) = X0
| in(sK20(X0,sK16(X1)),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f507,f182]) ).
fof(f516,plain,
! [X0,X1] :
( relation_dom(X1) != singleton(empty_set)
| sK16(X0) = X1
| in(sK20(sK16(X0),X1),singleton(empty_set))
| ~ relation(X1)
| ~ function(X1) ),
inference(forward_subsumption_resolution,[],[f508,f182]) ).
fof(f537,definition,
( spl29_20
<=> empty(sF22) ),
introduced(definition,[new_symbols(definition,[spl29_20])],[avatar_definition]) ).
fof(f538,plain,
( empty(sF22)
| ~ spl29_20 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f539,plain,
( ~ empty(sF22)
| spl29_20 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f620,plain,
( ~ empty(sF22)
| empty(sK17)
| ~ relation(sK17) ),
inference(superposition,[],[f154,f223]) ).
fof(f651,plain,
( relation_dom(sK19) = relation_dom(sF28(sK19))
| ~ relation(sK19)
| ~ spl29_9 ),
inference(forward_subsumption_resolution,[],[f330,f282]) ).
fof(f659,plain,
( ! [X0] :
( relation_dom(X0) != sF25
| sK19 = X0
| in(sK20(X0,sK19),relation_dom(X0))
| ~ function(sK19)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl29_6 ),
inference(forward_subsumption_resolution,[],[f379,f267]) ).
fof(f662,plain,
( ! [X0] :
( in(apply(sK19,X0),sF23)
| ~ in(X0,relation_dom(sK19))
| ~ function(sK19) )
| ~ spl29_6 ),
inference(forward_subsumption_resolution,[],[f403,f267]) ).
fof(f664,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF27))
| apply(sK17,apply(sK19,X0)) = apply(sF27,X0)
| ~ function(sK19) )
| ~ spl29_6 ),
inference(forward_subsumption_resolution,[],[f431,f267]) ).
fof(f685,plain,
( ! [X0] :
( relation_dom(X0) != sF24
| sK18 = X0
| in(sK20(X0,sK18),relation_dom(X0))
| ~ function(sK18)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f378,f257]) ).
fof(f688,plain,
( ! [X0] :
( in(apply(sK18,X0),sF21)
| ~ in(X0,relation_dom(sK18))
| ~ function(sK18) )
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f402,f257]) ).
fof(f690,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF26))
| apply(sK17,apply(sK18,X0)) = apply(sF26,X0)
| ~ function(sK18) )
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f430,f257]) ).
fof(f703,plain,
( relation_dom(sK19) = relation_dom(sF28(sK19))
| ~ spl29_6
| ~ spl29_9 ),
inference(forward_subsumption_resolution,[],[f651,f267]) ).
fof(f748,definition,
( spl29_32
<=> empty(sK17) ),
introduced(definition,[new_symbols(definition,[spl29_32])],[avatar_definition]) ).
fof(f749,plain,
( empty(sK17)
| ~ spl29_32 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f750,plain,
( ~ empty(sK17)
| spl29_32 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f759,plain,
( relation_dom(sK19) = relation_dom(sF27)
| ~ spl29_6
| ~ spl29_9 ),
inference(forward_demodulation,[],[f703,f326]) ).
fof(f836,plain,
( relation_dom(sK19) = relation_dom(sF26)
| ~ spl29_6
| ~ spl29_7
| ~ spl29_9 ),
inference(forward_demodulation,[],[f759,f272]) ).
fof(f887,plain,
( sF25 = relation_dom(sF26)
| ~ spl29_6
| ~ spl29_7
| ~ spl29_9 ),
inference(forward_demodulation,[],[f836,f231]) ).
fof(f941,plain,
( in(sK4(sK17),sF22)
| ~ relation(sK17)
| ~ function(sK17)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f341,f243]) ).
fof(f942,plain,
( in(sK5(sK17),sF22)
| ~ relation(sK17)
| ~ function(sK17)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f350,f243]) ).
fof(f946,plain,
( in(sK4(sK17),sF22)
| ~ function(sK17)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f941,f195]) ).
fof(f947,plain,
( in(sK5(sK17),sF22)
| ~ function(sK17)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f942,f195]) ).
fof(f949,plain,
( in(sK4(sK17),sF22)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f946,f194]) ).
fof(f950,plain,
( in(sK5(sK17),sF22)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f947,f194]) ).
fof(f1354,plain,
! [X0] : relation_rng(sK15(X0)) = singleton(apply(sK15(X0),empty_set)),
inference(equality_resolution,[],[f479]) ).
fof(f1361,plain,
! [X0,X1] :
( singleton(empty_set) != singleton(empty_set)
| sK15(X0) = sK16(X1)
| in(sK20(sK15(X0),sK16(X1)),singleton(empty_set))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) ),
inference(superposition,[],[f515,f177]) ).
fof(f1368,plain,
! [X0,X1] :
( sK15(X0) = sK16(X1)
| in(sK20(sK15(X0),sK16(X1)),singleton(empty_set))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) ),
inference(trivial_inequality_removal,[],[f1361]) ).
fof(f1370,plain,
! [X0,X1] :
( sK15(X0) = sK16(X1)
| in(sK20(sK15(X0),sK16(X1)),singleton(empty_set))
| ~ function(sK15(X0)) ),
inference(forward_subsumption_resolution,[],[f1368,f179]) ).
fof(f1372,plain,
! [X0,X1] :
( in(sK20(sK15(X0),sK16(X1)),singleton(empty_set))
| sK15(X0) = sK16(X1) ),
inference(forward_subsumption_resolution,[],[f1370,f178]) ).
fof(f1679,definition,
( spl29_106
<=> empty(sF26) ),
introduced(definition,[new_symbols(definition,[spl29_106])],[avatar_definition]) ).
fof(f1680,plain,
( empty(sF26)
| ~ spl29_106 ),
inference(avatar_component_clause,[],[f1679]) ).
fof(f1681,plain,
( ~ empty(sF26)
| spl29_106 ),
inference(avatar_component_clause,[],[f1679]) ).
fof(f1849,plain,
! [X0] : apply(sK15(X0),empty_set) = X0,
inference(resolution,[],[f176,f214]) ).
fof(f1862,plain,
! [X2,X0,X1] :
( apply(sK15(X0),sK20(sK15(X1),sK16(X2))) = X0
| sK15(X1) = sK16(X2) ),
inference(resolution,[],[f176,f1372]) ).
fof(f1993,plain,
! [X2,X0,X1] :
( apply(sK16(X0),sK20(sK15(X1),sK16(X2))) = X0
| sK15(X1) = sK16(X2) ),
inference(resolution,[],[f180,f1372]) ).
fof(f2032,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f206,f192]) ).
fof(f2035,plain,
( ! [X0] :
( ~ in(X0,sF23)
| element(X0,sF22) )
| ~ spl29_9 ),
inference(resolution,[],[f2032,f282]) ).
fof(f2046,plain,
( empty(sF25)
| ~ empty(sF26)
| ~ spl29_6
| ~ spl29_7
| ~ spl29_9 ),
inference(superposition,[],[f157,f887]) ).
fof(f2115,plain,
! [X0,X1] :
( apply(relation_composition(sK15(X0),X1),empty_set) = apply(X1,apply(sK15(X0),empty_set))
| ~ relation(X1)
| ~ function(X1) ),
inference(resolution,[],[f478,f214]) ).
fof(f2134,plain,
! [X0,X1] :
( ~ relation(X1)
| apply(X1,X0) = apply(relation_composition(sK15(X0),X1),empty_set)
| ~ function(X1) ),
inference(forward_demodulation,[],[f2115,f1849]) ).
fof(f2145,plain,
! [X0] :
( apply(sK17,X0) = apply(relation_composition(sK15(X0),sK17),empty_set)
| ~ function(sK17) ),
inference(resolution,[],[f2134,f195]) ).
fof(f2153,plain,
! [X0] : apply(sK17,X0) = apply(relation_composition(sK15(X0),sK17),empty_set),
inference(forward_subsumption_resolution,[],[f2145,f194]) ).
fof(f2156,plain,
! [X0] : apply(sK17,X0) = apply(sF28(sK15(X0)),empty_set),
inference(forward_demodulation,[],[f2153,f239]) ).
fof(f3353,plain,
! [X0,X1] :
( apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| relation_dom(sK16(X0)) != relation_dom(sK15(X1))
| sK16(X0) = sK15(X1)
| ~ relation(sK16(X0))
| ~ function(sK16(X0))
| ~ relation(sK15(X1))
| ~ function(sK15(X1))
| sK16(X0) = sK15(X1) ),
inference(superposition,[],[f212,f1993]) ).
fof(f3358,plain,
! [X0,X1] :
( apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| relation_dom(sK16(X0)) != relation_dom(sK15(X1))
| sK16(X0) = sK15(X1)
| ~ relation(sK16(X0))
| ~ function(sK16(X0))
| ~ relation(sK15(X1))
| ~ function(sK15(X1)) ),
inference(duplicate_literal_removal,[],[f3353]) ).
fof(f3361,plain,
! [X0,X1] :
( apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| relation_dom(sK16(X0)) != relation_dom(sK15(X1))
| sK16(X0) = sK15(X1)
| ~ function(sK16(X0))
| ~ relation(sK15(X1))
| ~ function(sK15(X1)) ),
inference(forward_subsumption_resolution,[],[f3358,f183]) ).
fof(f3364,plain,
! [X0,X1] :
( apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| relation_dom(sK16(X0)) != relation_dom(sK15(X1))
| sK16(X0) = sK15(X1)
| ~ relation(sK15(X1))
| ~ function(sK15(X1)) ),
inference(forward_subsumption_resolution,[],[f3361,f182]) ).
fof(f3367,plain,
! [X0,X1] :
( apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| relation_dom(sK16(X0)) != relation_dom(sK15(X1))
| sK16(X0) = sK15(X1)
| ~ function(sK15(X1)) ),
inference(forward_subsumption_resolution,[],[f3364,f179]) ).
fof(f3370,plain,
! [X0,X1] :
( apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| relation_dom(sK16(X0)) != relation_dom(sK15(X1))
| sK16(X0) = sK15(X1) ),
inference(forward_subsumption_resolution,[],[f3367,f178]) ).
fof(f3373,plain,
! [X0,X1] :
( singleton(empty_set) != relation_dom(sK16(X0))
| apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| sK16(X0) = sK15(X1) ),
inference(forward_demodulation,[],[f3370,f177]) ).
fof(f3376,plain,
! [X0,X1] :
( apply(sK15(X1),sK20(sK15(X1),sK16(X0))) != X0
| sK16(X0) = sK15(X1) ),
inference(forward_subsumption_resolution,[],[f3373,f181]) ).
fof(f3401,plain,
! [X0,X1] :
( X0 != X1
| sK15(X0) = sK16(X1)
| sK15(X0) = sK16(X1) ),
inference(superposition,[],[f3376,f1862]) ).
fof(f3408,plain,
! [X0,X1] :
( X0 != X1
| sK15(X0) = sK16(X1) ),
inference(duplicate_literal_removal,[],[f3401]) ).
fof(f3423,plain,
! [X0] : sK15(X0) = sK16(X0),
inference(equality_resolution,[],[f3408]) ).
fof(f3690,plain,
! [X0] : singleton(X0) = relation_rng(sK15(X0)),
inference(superposition,[],[f1354,f1849]) ).
fof(f3731,plain,
! [X0] :
( ~ subset(singleton(X0),sF22)
| relation_dom(sK15(X0)) = relation_dom(sF28(sK15(X0)))
| ~ relation(sK15(X0)) ),
inference(superposition,[],[f312,f3690]) ).
fof(f3738,plain,
! [X0] :
( ~ subset(singleton(X0),sF22)
| relation_dom(sK15(X0)) = relation_dom(sF28(sK15(X0))) ),
inference(forward_subsumption_resolution,[],[f3731,f179]) ).
fof(f3747,plain,
! [X0] :
( ~ subset(singleton(X0),sF22)
| singleton(empty_set) = relation_dom(sF28(sK15(X0))) ),
inference(forward_demodulation,[],[f3738,f177]) ).
fof(f4598,plain,
( empty(sF27)
| ~ empty(sK17)
| ~ relation(sK19) ),
inference(superposition,[],[f144,f236]) ).
fof(f12862,plain,
! [X0] :
( ~ in(X0,sF22)
| singleton(empty_set) = relation_dom(sF28(sK15(X0))) ),
inference(resolution,[],[f3747,f190]) ).
fof(f12880,plain,
( singleton(empty_set) = relation_dom(sF28(sK15(sK4(sK17))))
| spl29_1 ),
inference(resolution,[],[f12862,f949]) ).
fof(f12881,plain,
( singleton(empty_set) = relation_dom(sF28(sK15(sK5(sK17))))
| spl29_1 ),
inference(resolution,[],[f12862,f950]) ).
fof(f12938,plain,
( ! [X0] :
( singleton(empty_set) != singleton(empty_set)
| sK16(X0) = sF28(sK15(sK5(sK17)))
| in(sK20(sK16(X0),sF28(sK15(sK5(sK17)))),singleton(empty_set))
| ~ relation(sF28(sK15(sK5(sK17))))
| ~ function(sF28(sK15(sK5(sK17)))) )
| spl29_1 ),
inference(superposition,[],[f516,f12881]) ).
fof(f12960,plain,
( ! [X0] :
( sK16(X0) = sF28(sK15(sK5(sK17)))
| in(sK20(sK16(X0),sF28(sK15(sK5(sK17)))),singleton(empty_set))
| ~ relation(sF28(sK15(sK5(sK17))))
| ~ function(sF28(sK15(sK5(sK17)))) )
| spl29_1 ),
inference(trivial_inequality_removal,[],[f12938]) ).
fof(f12969,definition,
( spl29_302
<=> function(sF28(sK15(sK5(sK17)))) ),
introduced(definition,[new_symbols(definition,[spl29_302])],[avatar_definition]) ).
fof(f12970,plain,
( function(sF28(sK15(sK5(sK17))))
| ~ spl29_302 ),
inference(avatar_component_clause,[],[f12969]) ).
fof(f12971,plain,
( ~ function(sF28(sK15(sK5(sK17))))
| spl29_302 ),
inference(avatar_component_clause,[],[f12969]) ).
fof(f12973,definition,
( spl29_303
<=> relation(sF28(sK15(sK5(sK17)))) ),
introduced(definition,[new_symbols(definition,[spl29_303])],[avatar_definition]) ).
fof(f12974,plain,
( relation(sF28(sK15(sK5(sK17))))
| ~ spl29_303 ),
inference(avatar_component_clause,[],[f12973]) ).
fof(f12975,plain,
( ~ relation(sF28(sK15(sK5(sK17))))
| spl29_303 ),
inference(avatar_component_clause,[],[f12973]) ).
fof(f13077,plain,
( ! [X0] :
( sK15(X0) = sF28(sK15(sK5(sK17)))
| in(sK20(sK16(X0),sF28(sK15(sK5(sK17)))),singleton(empty_set))
| ~ relation(sF28(sK15(sK5(sK17))))
| ~ function(sF28(sK15(sK5(sK17)))) )
| spl29_1 ),
inference(forward_demodulation,[],[f12960,f3423]) ).
fof(f13080,definition,
( spl29_327
<=> ! [X0] :
( sK15(X0) = sF28(sK15(sK5(sK17)))
| in(sK20(sK15(X0),sF28(sK15(sK5(sK17)))),singleton(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[spl29_327])],[avatar_definition]) ).
fof(f13081,plain,
( ! [X0] :
( in(sK20(sK15(X0),sF28(sK15(sK5(sK17)))),singleton(empty_set))
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_327 ),
inference(avatar_component_clause,[],[f13080]) ).
fof(f13138,plain,
( ! [X0] :
( in(sK20(sK15(X0),sF28(sK15(sK5(sK17)))),singleton(empty_set))
| sK15(X0) = sF28(sK15(sK5(sK17)))
| ~ relation(sF28(sK15(sK5(sK17))))
| ~ function(sF28(sK15(sK5(sK17)))) )
| spl29_1 ),
inference(forward_demodulation,[],[f13077,f3423]) ).
fof(f13142,plain,
( ~ spl29_302
| ~ spl29_303
| spl29_327
| spl29_1 ),
inference(avatar_split_clause,[],[f13138,f242,f13080,f12973,f12969]) ).
fof(f13145,plain,
( ~ relation(sK15(sK5(sK17)))
| spl29_303 ),
inference(resolution,[],[f12975,f339]) ).
fof(f13146,plain,
( $false
| spl29_303 ),
inference(forward_subsumption_resolution,[],[f13145,f179]) ).
fof(f13147,plain,
spl29_303,
inference(avatar_contradiction_clause,[],[f13146]) ).
fof(f13149,plain,
( ~ relation(sK15(sK5(sK17)))
| ~ function(sK15(sK5(sK17)))
| spl29_302 ),
inference(resolution,[],[f12971,f371]) ).
fof(f13150,plain,
( ~ function(sK15(sK5(sK17)))
| spl29_302 ),
inference(forward_subsumption_resolution,[],[f13149,f179]) ).
fof(f13151,plain,
( $false
| spl29_302 ),
inference(forward_subsumption_resolution,[],[f13150,f178]) ).
fof(f13152,plain,
spl29_302,
inference(avatar_contradiction_clause,[],[f13151]) ).
fof(f13168,plain,
( ! [X0] :
( empty_set = sK20(sK15(X0),sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_327 ),
inference(resolution,[],[f13081,f215]) ).
fof(f13320,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK5(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17)))
| ~ relation(sF28(sK15(sK5(sK17))))
| ~ function(sF28(sK15(sK5(sK17))))
| ~ relation(sK15(X0))
| ~ function(sK15(X0))
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_327 ),
inference(superposition,[],[f212,f13168]) ).
fof(f13321,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK5(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17)))
| ~ relation(sF28(sK15(sK5(sK17))))
| ~ function(sF28(sK15(sK5(sK17))))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) )
| ~ spl29_327 ),
inference(duplicate_literal_removal,[],[f13320]) ).
fof(f13323,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK5(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17)))
| ~ function(sF28(sK15(sK5(sK17))))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) )
| ~ spl29_303
| ~ spl29_327 ),
inference(forward_subsumption_resolution,[],[f13321,f12974]) ).
fof(f13324,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK5(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17)))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) )
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327 ),
inference(forward_subsumption_resolution,[],[f13323,f12970]) ).
fof(f13325,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK5(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17)))
| ~ function(sK15(X0)) )
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327 ),
inference(forward_subsumption_resolution,[],[f13324,f179]) ).
fof(f13326,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK5(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327 ),
inference(forward_subsumption_resolution,[],[f13325,f178]) ).
fof(f13327,plain,
( ! [X0] :
( apply(sK17,sK5(sK17)) != apply(sK15(X0),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327 ),
inference(forward_demodulation,[],[f13326,f2156]) ).
fof(f13328,plain,
( ! [X0] :
( apply(sK17,sK5(sK17)) != X0
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK5(sK17))))
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327 ),
inference(forward_demodulation,[],[f13327,f1849]) ).
fof(f13403,definition,
( spl29_344
<=> subset(singleton(sK5(sK17)),sF22) ),
introduced(definition,[new_symbols(definition,[spl29_344])],[avatar_definition]) ).
fof(f13404,plain,
( subset(singleton(sK5(sK17)),sF22)
| ~ spl29_344 ),
inference(avatar_component_clause,[],[f13403]) ).
fof(f13405,plain,
( ~ subset(singleton(sK5(sK17)),sF22)
| spl29_344 ),
inference(avatar_component_clause,[],[f13403]) ).
fof(f13411,plain,
( ~ in(sK5(sK17),sF22)
| spl29_344 ),
inference(resolution,[],[f13405,f190]) ).
fof(f13412,plain,
( $false
| spl29_1
| spl29_344 ),
inference(forward_subsumption_resolution,[],[f13411,f950]) ).
fof(f13413,plain,
( spl29_1
| spl29_344 ),
inference(avatar_contradiction_clause,[],[f13412]) ).
fof(f13414,plain,
( singleton(empty_set) = relation_dom(sF28(sK15(sK5(sK17))))
| ~ spl29_344 ),
inference(resolution,[],[f13404,f3747]) ).
fof(f13517,plain,
( ! [X0] :
( singleton(empty_set) != singleton(empty_set)
| sK16(X0) = sF28(sK15(sK4(sK17)))
| in(sK20(sK16(X0),sF28(sK15(sK4(sK17)))),singleton(empty_set))
| ~ relation(sF28(sK15(sK4(sK17))))
| ~ function(sF28(sK15(sK4(sK17)))) )
| spl29_1 ),
inference(superposition,[],[f516,f12880]) ).
fof(f13539,plain,
( ! [X0] :
( sK16(X0) = sF28(sK15(sK4(sK17)))
| in(sK20(sK16(X0),sF28(sK15(sK4(sK17)))),singleton(empty_set))
| ~ relation(sF28(sK15(sK4(sK17))))
| ~ function(sF28(sK15(sK4(sK17)))) )
| spl29_1 ),
inference(trivial_inequality_removal,[],[f13517]) ).
fof(f13548,definition,
( spl29_350
<=> function(sF28(sK15(sK4(sK17)))) ),
introduced(definition,[new_symbols(definition,[spl29_350])],[avatar_definition]) ).
fof(f13549,plain,
( function(sF28(sK15(sK4(sK17))))
| ~ spl29_350 ),
inference(avatar_component_clause,[],[f13548]) ).
fof(f13550,plain,
( ~ function(sF28(sK15(sK4(sK17))))
| spl29_350 ),
inference(avatar_component_clause,[],[f13548]) ).
fof(f13552,definition,
( spl29_351
<=> relation(sF28(sK15(sK4(sK17)))) ),
introduced(definition,[new_symbols(definition,[spl29_351])],[avatar_definition]) ).
fof(f13553,plain,
( relation(sF28(sK15(sK4(sK17))))
| ~ spl29_351 ),
inference(avatar_component_clause,[],[f13552]) ).
fof(f13554,plain,
( ~ relation(sF28(sK15(sK4(sK17))))
| spl29_351 ),
inference(avatar_component_clause,[],[f13552]) ).
fof(f13641,plain,
( ! [X0] :
( sK15(X0) = sF28(sK15(sK4(sK17)))
| in(sK20(sK16(X0),sF28(sK15(sK4(sK17)))),singleton(empty_set))
| ~ relation(sF28(sK15(sK4(sK17))))
| ~ function(sF28(sK15(sK4(sK17)))) )
| spl29_1 ),
inference(forward_demodulation,[],[f13539,f3423]) ).
fof(f13644,definition,
( spl29_371
<=> ! [X0] :
( sK15(X0) = sF28(sK15(sK4(sK17)))
| in(sK20(sK15(X0),sF28(sK15(sK4(sK17)))),singleton(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[spl29_371])],[avatar_definition]) ).
fof(f13645,plain,
( ! [X0] :
( in(sK20(sK15(X0),sF28(sK15(sK4(sK17)))),singleton(empty_set))
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_371 ),
inference(avatar_component_clause,[],[f13644]) ).
fof(f13702,plain,
( ! [X0] :
( in(sK20(sK15(X0),sF28(sK15(sK4(sK17)))),singleton(empty_set))
| sK15(X0) = sF28(sK15(sK4(sK17)))
| ~ relation(sF28(sK15(sK4(sK17))))
| ~ function(sF28(sK15(sK4(sK17)))) )
| spl29_1 ),
inference(forward_demodulation,[],[f13641,f3423]) ).
fof(f13706,plain,
( ~ spl29_350
| ~ spl29_351
| spl29_371
| spl29_1 ),
inference(avatar_split_clause,[],[f13702,f242,f13644,f13552,f13548]) ).
fof(f13709,plain,
( ~ relation(sK15(sK4(sK17)))
| spl29_351 ),
inference(resolution,[],[f13554,f339]) ).
fof(f13710,plain,
( $false
| spl29_351 ),
inference(forward_subsumption_resolution,[],[f13709,f179]) ).
fof(f13711,plain,
spl29_351,
inference(avatar_contradiction_clause,[],[f13710]) ).
fof(f13713,plain,
( ~ relation(sK15(sK4(sK17)))
| ~ function(sK15(sK4(sK17)))
| spl29_350 ),
inference(resolution,[],[f13550,f371]) ).
fof(f13714,plain,
( ~ function(sK15(sK4(sK17)))
| spl29_350 ),
inference(forward_subsumption_resolution,[],[f13713,f179]) ).
fof(f13715,plain,
( $false
| spl29_350 ),
inference(forward_subsumption_resolution,[],[f13714,f178]) ).
fof(f13716,plain,
spl29_350,
inference(avatar_contradiction_clause,[],[f13715]) ).
fof(f13732,plain,
( ! [X0] :
( empty_set = sK20(sK15(X0),sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_371 ),
inference(resolution,[],[f13645,f215]) ).
fof(f13879,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK4(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17)))
| ~ relation(sF28(sK15(sK4(sK17))))
| ~ function(sF28(sK15(sK4(sK17))))
| ~ relation(sK15(X0))
| ~ function(sK15(X0))
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_371 ),
inference(superposition,[],[f212,f13732]) ).
fof(f13880,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK4(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17)))
| ~ relation(sF28(sK15(sK4(sK17))))
| ~ function(sF28(sK15(sK4(sK17))))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) )
| ~ spl29_371 ),
inference(duplicate_literal_removal,[],[f13879]) ).
fof(f13882,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK4(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17)))
| ~ function(sF28(sK15(sK4(sK17))))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) )
| ~ spl29_351
| ~ spl29_371 ),
inference(forward_subsumption_resolution,[],[f13880,f13553]) ).
fof(f13883,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK4(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17)))
| ~ relation(sK15(X0))
| ~ function(sK15(X0)) )
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371 ),
inference(forward_subsumption_resolution,[],[f13882,f13549]) ).
fof(f13884,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK4(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17)))
| ~ function(sK15(X0)) )
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371 ),
inference(forward_subsumption_resolution,[],[f13883,f179]) ).
fof(f13885,plain,
( ! [X0] :
( apply(sK15(X0),empty_set) != apply(sF28(sK15(sK4(sK17))),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371 ),
inference(forward_subsumption_resolution,[],[f13884,f178]) ).
fof(f13886,plain,
( ! [X0] :
( apply(sK17,sK4(sK17)) != apply(sK15(X0),empty_set)
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371 ),
inference(forward_demodulation,[],[f13885,f2156]) ).
fof(f13887,plain,
( ! [X0] :
( apply(sK17,sK4(sK17)) != X0
| relation_dom(sK15(X0)) != relation_dom(sF28(sK15(sK4(sK17))))
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371 ),
inference(forward_demodulation,[],[f13886,f1849]) ).
fof(f13945,definition,
( spl29_384
<=> sK15(sK4(sK17)) = sK15(sK5(sK17)) ),
introduced(definition,[new_symbols(definition,[spl29_384])],[avatar_definition]) ).
fof(f13947,plain,
( sK15(sK4(sK17)) = sK15(sK5(sK17))
| ~ spl29_384 ),
inference(avatar_component_clause,[],[f13945]) ).
fof(f13949,definition,
( spl29_385
<=> subset(singleton(sK4(sK17)),sF22) ),
introduced(definition,[new_symbols(definition,[spl29_385])],[avatar_definition]) ).
fof(f13950,plain,
( subset(singleton(sK4(sK17)),sF22)
| ~ spl29_385 ),
inference(avatar_component_clause,[],[f13949]) ).
fof(f13951,plain,
( ~ subset(singleton(sK4(sK17)),sF22)
| spl29_385 ),
inference(avatar_component_clause,[],[f13949]) ).
fof(f13961,plain,
( ~ in(sK4(sK17),sF22)
| spl29_385 ),
inference(resolution,[],[f13951,f190]) ).
fof(f13962,plain,
( $false
| spl29_1
| spl29_385 ),
inference(forward_subsumption_resolution,[],[f13961,f949]) ).
fof(f13963,plain,
( spl29_1
| spl29_385 ),
inference(avatar_contradiction_clause,[],[f13962]) ).
fof(f13964,plain,
( singleton(empty_set) = relation_dom(sF28(sK15(sK4(sK17))))
| ~ spl29_385 ),
inference(resolution,[],[f13950,f3747]) ).
fof(f14003,plain,
( sK5(sK17) = apply(sK15(sK4(sK17)),empty_set)
| ~ spl29_384 ),
inference(superposition,[],[f1849,f13947]) ).
fof(f14079,plain,
( sK4(sK17) = sK5(sK17)
| ~ spl29_384 ),
inference(forward_demodulation,[],[f14003,f1849]) ).
fof(f14164,plain,
( ! [X0] :
( relation_dom(X0) != sF25
| sK19 = X0
| in(sK20(X0,sK19),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl29_5
| ~ spl29_6 ),
inference(forward_subsumption_resolution,[],[f659,f262]) ).
fof(f14167,plain,
( ! [X0] :
( in(apply(sK19,X0),sF23)
| ~ in(X0,relation_dom(sK19)) )
| ~ spl29_5
| ~ spl29_6 ),
inference(forward_subsumption_resolution,[],[f662,f262]) ).
fof(f14169,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF27))
| apply(sK17,apply(sK19,X0)) = apply(sF27,X0) )
| ~ spl29_5
| ~ spl29_6 ),
inference(forward_subsumption_resolution,[],[f664,f262]) ).
fof(f14269,plain,
( ! [X0] :
( relation_dom(X0) != sF24
| sK18 = X0
| in(sK20(X0,sK18),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl29_3
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f685,f252]) ).
fof(f14271,plain,
( ! [X0] :
( in(apply(sK18,X0),sF21)
| ~ in(X0,relation_dom(sK18)) )
| ~ spl29_3
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f688,f252]) ).
fof(f14273,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF26))
| apply(sK17,apply(sK18,X0)) = apply(sF26,X0) )
| ~ spl29_3
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f690,f252]) ).
fof(f14393,plain,
( ! [X0] :
( singleton(empty_set) != relation_dom(sF28(sK15(sK5(sK17))))
| apply(sK17,sK5(sK17)) != X0
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327 ),
inference(forward_demodulation,[],[f13328,f177]) ).
fof(f14394,plain,
( ! [X0] :
( singleton(empty_set) != relation_dom(sF28(sK15(sK4(sK17))))
| apply(sK17,sK4(sK17)) != X0
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371 ),
inference(forward_demodulation,[],[f13887,f177]) ).
fof(f14415,plain,
( ! [X0] :
( relation_dom(X0) != sF24
| sK19 = X0
| in(sK20(X0,sK19),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8 ),
inference(forward_demodulation,[],[f14164,f277]) ).
fof(f14418,plain,
( ! [X0] :
( ~ in(X0,sF25)
| in(apply(sK19,X0),sF23) )
| ~ spl29_5
| ~ spl29_6 ),
inference(forward_demodulation,[],[f14167,f231]) ).
fof(f14420,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF26))
| apply(sK17,apply(sK19,X0)) = apply(sF27,X0) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7 ),
inference(forward_demodulation,[],[f14169,f272]) ).
fof(f14516,plain,
( ! [X0] :
( in(apply(sK18,X0),sF21)
| ~ in(X0,sF24) )
| ~ spl29_3
| ~ spl29_4 ),
inference(forward_demodulation,[],[f14271,f229]) ).
fof(f14518,plain,
( ! [X0] :
( ~ in(X0,sF25)
| apply(sK17,apply(sK18,X0)) = apply(sF26,X0) )
| ~ spl29_3
| ~ spl29_4
| ~ spl29_6
| ~ spl29_7
| ~ spl29_9 ),
inference(forward_demodulation,[],[f14273,f887]) ).
fof(f14618,plain,
( ! [X0] :
( apply(sK17,sK5(sK17)) != X0
| sK15(X0) = sF28(sK15(sK5(sK17))) )
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327
| ~ spl29_344 ),
inference(forward_subsumption_resolution,[],[f14393,f13414]) ).
fof(f14619,plain,
( ! [X0] :
( apply(sK17,sK4(sK17)) != X0
| sK15(X0) = sF28(sK15(sK4(sK17))) )
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371
| ~ spl29_385 ),
inference(forward_subsumption_resolution,[],[f14394,f13964]) ).
fof(f14631,plain,
( ! [X0] :
( in(apply(sK19,X0),sF23)
| ~ in(X0,sF24) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8 ),
inference(forward_demodulation,[],[f14418,f277]) ).
fof(f14633,plain,
( ! [X0] :
( ~ in(X0,sF25)
| apply(sK17,apply(sK19,X0)) = apply(sF27,X0) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_9 ),
inference(forward_demodulation,[],[f14420,f887]) ).
fof(f14720,plain,
( ! [X0] :
( ~ in(X0,sF24)
| apply(sK17,apply(sK18,X0)) = apply(sF26,X0) )
| ~ spl29_3
| ~ spl29_4
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9 ),
inference(forward_demodulation,[],[f14518,f277]) ).
fof(f14831,plain,
( ! [X0] :
( ~ in(X0,sF24)
| apply(sK17,apply(sK19,X0)) = apply(sF27,X0) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9 ),
inference(forward_demodulation,[],[f14633,f277]) ).
fof(f15006,plain,
( ! [X0] :
( ~ in(X0,sF24)
| apply(sF26,X0) = apply(sK17,apply(sK19,X0)) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9 ),
inference(forward_demodulation,[],[f14831,f272]) ).
fof(f15395,plain,
( ! [X0] :
( ~ in(X0,sF21)
| element(X0,sF22) )
| ~ spl29_10 ),
inference(resolution,[],[f287,f2032]) ).
fof(f15546,plain,
( ! [X0] :
( element(apply(sK19,X0),sF22)
| ~ in(X0,sF24) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_9 ),
inference(resolution,[],[f14631,f2035]) ).
fof(f16128,plain,
( sF24 != sF25
| sK18 = sK19
| in(sK20(sK19,sK18),sF25)
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl29_3
| ~ spl29_4 ),
inference(superposition,[],[f14269,f231]) ).
fof(f16131,plain,
( sK18 = sK19
| in(sK20(sK19,sK18),sF25)
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_8 ),
inference(forward_subsumption_resolution,[],[f16128,f277]) ).
fof(f16133,plain,
( in(sK20(sK19,sK18),sF25)
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_8
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f16131,f292]) ).
fof(f16135,plain,
( in(sK20(sK19,sK18),sF25)
| ~ function(sK19)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f16133,f267]) ).
fof(f16137,plain,
( in(sK20(sK19,sK18),sF25)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f16135,f262]) ).
fof(f16147,plain,
( in(sK20(sK19,sK18),sF24)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(forward_demodulation,[],[f16137,f277]) ).
fof(f16160,plain,
( ~ empty(sF24)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(resolution,[],[f16147,f209]) ).
fof(f16795,plain,
( sF24 != sF24
| sK18 = sK19
| in(sK20(sK18,sK19),sF24)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8 ),
inference(superposition,[],[f14415,f229]) ).
fof(f16797,plain,
( sK18 = sK19
| in(sK20(sK18,sK19),sF24)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8 ),
inference(trivial_inequality_removal,[],[f16795]) ).
fof(f16799,plain,
( in(sK20(sK18,sK19),sF24)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f16797,f292]) ).
fof(f16801,plain,
( in(sK20(sK18,sK19),sF24)
| ~ function(sK18)
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f16799,f257]) ).
fof(f16803,plain,
( in(sK20(sK18,sK19),sF24)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f16801,f252]) ).
fof(f16810,plain,
( apply(sF26,sK20(sK18,sK19)) = apply(sK17,apply(sK19,sK20(sK18,sK19)))
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11 ),
inference(resolution,[],[f16803,f15006]) ).
fof(f16811,plain,
( apply(sF26,sK20(sK18,sK19)) = apply(sK17,apply(sK18,sK20(sK18,sK19)))
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11 ),
inference(resolution,[],[f16803,f14720]) ).
fof(f16837,definition,
( spl29_490
<=> in(apply(sK18,sK20(sK18,sK19)),sF22) ),
introduced(definition,[new_symbols(definition,[spl29_490])],[avatar_definition]) ).
fof(f16838,plain,
( in(apply(sK18,sK20(sK18,sK19)),sF22)
| ~ spl29_490 ),
inference(avatar_component_clause,[],[f16837]) ).
fof(f16839,plain,
( ~ in(apply(sK18,sK20(sK18,sK19)),sF22)
| spl29_490 ),
inference(avatar_component_clause,[],[f16837]) ).
fof(f17144,plain,
( sF28(sK15(sK5(sK17))) = sK15(apply(sK17,sK5(sK17)))
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327
| ~ spl29_344 ),
inference(equality_resolution,[],[f14618]) ).
fof(f17345,definition,
( spl29_542
<=> in(apply(sK19,sK20(sK18,sK19)),sF22) ),
introduced(definition,[new_symbols(definition,[spl29_542])],[avatar_definition]) ).
fof(f17346,plain,
( in(apply(sK19,sK20(sK18,sK19)),sF22)
| ~ spl29_542 ),
inference(avatar_component_clause,[],[f17345]) ).
fof(f17347,plain,
( ~ in(apply(sK19,sK20(sK18,sK19)),sF22)
| spl29_542 ),
inference(avatar_component_clause,[],[f17345]) ).
fof(f17386,plain,
( sF28(sK15(sK4(sK17))) = sK15(apply(sK17,sK4(sK17)))
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371
| ~ spl29_385 ),
inference(equality_resolution,[],[f14619]) ).
fof(f17447,plain,
( ! [X0] :
( element(apply(sK18,X0),sF22)
| ~ in(X0,sF24) )
| ~ spl29_3
| ~ spl29_4
| ~ spl29_10 ),
inference(resolution,[],[f15395,f14516]) ).
fof(f19378,plain,
( ! [X0] :
( ~ in(X0,sF24)
| in(apply(sK19,X0),sF22)
| empty(sF22) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_9 ),
inference(resolution,[],[f15546,f188]) ).
fof(f19384,plain,
( ! [X0] :
( in(apply(sK19,X0),sF22)
| ~ in(X0,sF24) )
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_9
| spl29_20 ),
inference(forward_subsumption_resolution,[],[f19378,f539]) ).
fof(f19385,plain,
( ~ in(sK20(sK18,sK19),sF24)
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_9
| spl29_20
| spl29_542 ),
inference(resolution,[],[f19384,f17347]) ).
fof(f19421,plain,
( $false
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_9
| spl29_11
| spl29_20
| spl29_542 ),
inference(forward_subsumption_resolution,[],[f19385,f16803]) ).
fof(f19422,plain,
( ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_9
| spl29_11
| spl29_20
| spl29_542 ),
inference(avatar_contradiction_clause,[],[f19421]) ).
fof(f19426,plain,
( empty(sK17)
| ~ relation(sK17)
| ~ spl29_20 ),
inference(forward_subsumption_resolution,[],[f620,f538]) ).
fof(f19459,plain,
( ~ relation(sK17)
| ~ spl29_20
| spl29_32 ),
inference(forward_subsumption_resolution,[],[f19426,f750]) ).
fof(f19472,plain,
( $false
| ~ spl29_20
| spl29_32 ),
inference(forward_subsumption_resolution,[],[f19459,f195]) ).
fof(f19473,plain,
( ~ spl29_20
| spl29_32 ),
inference(avatar_contradiction_clause,[],[f19472]) ).
fof(f19647,plain,
( ! [X0] :
( apply(sK17,X0) != apply(sF26,sK20(sK18,sK19))
| ~ in(apply(sK18,sK20(sK18,sK19)),relation_dom(sK17))
| ~ in(X0,relation_dom(sK17))
| apply(sK18,sK20(sK18,sK19)) = X0
| ~ one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17) )
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11 ),
inference(superposition,[],[f136,f16811]) ).
fof(f19648,plain,
( ! [X0] :
( apply(sK17,X0) != apply(sF26,sK20(sK18,sK19))
| ~ in(apply(sK18,sK20(sK18,sK19)),relation_dom(sK17))
| ~ in(X0,relation_dom(sK17))
| apply(sK18,sK20(sK18,sK19)) = X0
| ~ relation(sK17)
| ~ function(sK17) )
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f19647,f244]) ).
fof(f19653,plain,
( ! [X0] :
( apply(sK17,X0) != apply(sF26,sK20(sK18,sK19))
| ~ in(apply(sK18,sK20(sK18,sK19)),relation_dom(sK17))
| ~ in(X0,relation_dom(sK17))
| apply(sK18,sK20(sK18,sK19)) = X0
| ~ function(sK17) )
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f19648,f195]) ).
fof(f19658,plain,
( ! [X0] :
( apply(sK17,X0) != apply(sF26,sK20(sK18,sK19))
| ~ in(apply(sK18,sK20(sK18,sK19)),relation_dom(sK17))
| ~ in(X0,relation_dom(sK17))
| apply(sK18,sK20(sK18,sK19)) = X0 )
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11 ),
inference(forward_subsumption_resolution,[],[f19653,f194]) ).
fof(f19834,plain,
( ! [X0] :
( ~ in(apply(sK18,sK20(sK18,sK19)),sF22)
| apply(sK17,X0) != apply(sF26,sK20(sK18,sK19))
| ~ in(X0,relation_dom(sK17))
| apply(sK18,sK20(sK18,sK19)) = X0 )
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11 ),
inference(forward_demodulation,[],[f19658,f223]) ).
fof(f21451,plain,
( ! [X0] :
( ~ in(X0,sF24)
| in(apply(sK18,X0),sF22)
| empty(sF22) )
| ~ spl29_3
| ~ spl29_4
| ~ spl29_10 ),
inference(resolution,[],[f17447,f188]) ).
fof(f21455,plain,
( ! [X0] :
( in(apply(sK18,X0),sF22)
| ~ in(X0,sF24) )
| ~ spl29_3
| ~ spl29_4
| ~ spl29_10
| spl29_20 ),
inference(forward_subsumption_resolution,[],[f21451,f539]) ).
fof(f21456,plain,
( ~ in(sK20(sK18,sK19),sF24)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_10
| spl29_20
| spl29_490 ),
inference(resolution,[],[f21455,f16839]) ).
fof(f21499,plain,
( $false
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_10
| spl29_11
| spl29_20
| spl29_490 ),
inference(forward_subsumption_resolution,[],[f21456,f16803]) ).
fof(f21500,plain,
( ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_10
| spl29_11
| spl29_20
| spl29_490 ),
inference(avatar_contradiction_clause,[],[f21499]) ).
fof(f24008,plain,
( ! [X0] :
( apply(sK17,X0) != apply(sF26,sK20(sK18,sK19))
| ~ in(X0,relation_dom(sK17))
| apply(sK18,sK20(sK18,sK19)) = X0 )
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11
| ~ spl29_490 ),
inference(forward_subsumption_resolution,[],[f19834,f16838]) ).
fof(f31738,plain,
( ! [X0] :
( apply(sK17,X0) != apply(sF26,sK20(sK18,sK19))
| ~ in(X0,sF22)
| apply(sK18,sK20(sK18,sK19)) = X0 )
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11
| ~ spl29_490 ),
inference(forward_demodulation,[],[f24008,f223]) ).
fof(f31814,definition,
( spl29_840
<=> apply(sK19,sK20(sK18,sK19)) = apply(sK18,sK20(sK18,sK19)) ),
introduced(definition,[new_symbols(definition,[spl29_840])],[avatar_definition]) ).
fof(f31816,plain,
( apply(sK19,sK20(sK18,sK19)) = apply(sK18,sK20(sK18,sK19))
| ~ spl29_840 ),
inference(avatar_component_clause,[],[f31814]) ).
fof(f31889,plain,
( apply(sF26,sK20(sK18,sK19)) != apply(sF26,sK20(sK18,sK19))
| ~ in(apply(sK19,sK20(sK18,sK19)),sF22)
| apply(sK19,sK20(sK18,sK19)) = apply(sK18,sK20(sK18,sK19))
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11
| ~ spl29_490 ),
inference(superposition,[],[f31738,f16810]) ).
fof(f31891,plain,
( ~ in(apply(sK19,sK20(sK18,sK19)),sF22)
| apply(sK19,sK20(sK18,sK19)) = apply(sK18,sK20(sK18,sK19))
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11
| ~ spl29_490 ),
inference(trivial_inequality_removal,[],[f31889]) ).
fof(f31893,plain,
( apply(sK19,sK20(sK18,sK19)) = apply(sK18,sK20(sK18,sK19))
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11
| ~ spl29_490
| ~ spl29_542 ),
inference(forward_subsumption_resolution,[],[f31891,f17346]) ).
fof(f31896,plain,
( spl29_840
| ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11
| ~ spl29_490
| ~ spl29_542 ),
inference(avatar_split_clause,[],[f31893,f17345,f16837,f290,f280,f275,f270,f265,f260,f255,f250,f242,f31814]) ).
fof(f31907,plain,
( apply(sK18,sK20(sK18,sK19)) != apply(sK18,sK20(sK18,sK19))
| relation_dom(sK18) != relation_dom(sK19)
| sK18 = sK19
| ~ relation(sK19)
| ~ function(sK19)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl29_840 ),
inference(superposition,[],[f212,f31816]) ).
fof(f31919,plain,
( relation_dom(sK18) != relation_dom(sK19)
| sK18 = sK19
| ~ relation(sK19)
| ~ function(sK19)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl29_840 ),
inference(trivial_inequality_removal,[],[f31907]) ).
fof(f31929,plain,
( relation_dom(sK18) != relation_dom(sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ relation(sK18)
| ~ function(sK18)
| spl29_11
| ~ spl29_840 ),
inference(forward_subsumption_resolution,[],[f31919,f292]) ).
fof(f31939,plain,
( relation_dom(sK18) != relation_dom(sK19)
| ~ function(sK19)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl29_6
| spl29_11
| ~ spl29_840 ),
inference(forward_subsumption_resolution,[],[f31929,f267]) ).
fof(f31945,plain,
( relation_dom(sK18) != relation_dom(sK19)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl29_5
| ~ spl29_6
| spl29_11
| ~ spl29_840 ),
inference(forward_subsumption_resolution,[],[f31939,f262]) ).
fof(f31951,plain,
( relation_dom(sK18) != relation_dom(sK19)
| ~ function(sK18)
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| spl29_11
| ~ spl29_840 ),
inference(forward_subsumption_resolution,[],[f31945,f257]) ).
fof(f31955,plain,
( relation_dom(sK18) != relation_dom(sK19)
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| spl29_11
| ~ spl29_840 ),
inference(forward_subsumption_resolution,[],[f31951,f252]) ).
fof(f31959,plain,
( relation_dom(sK18) != sF25
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| spl29_11
| ~ spl29_840 ),
inference(forward_demodulation,[],[f31955,f231]) ).
fof(f31963,plain,
( relation_dom(sK18) != sF24
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11
| ~ spl29_840 ),
inference(forward_demodulation,[],[f31959,f277]) ).
fof(f31966,plain,
( $false
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11
| ~ spl29_840 ),
inference(forward_subsumption_resolution,[],[f31963,f229]) ).
fof(f31967,plain,
( ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11
| ~ spl29_840 ),
inference(avatar_contradiction_clause,[],[f31966]) ).
fof(f31988,plain,
( empty(sF27)
| ~ relation(sK19)
| ~ spl29_32 ),
inference(forward_subsumption_resolution,[],[f4598,f749]) ).
fof(f32051,plain,
( empty(sF27)
| ~ spl29_6
| ~ spl29_32 ),
inference(forward_subsumption_resolution,[],[f31988,f267]) ).
fof(f32072,plain,
( empty(sF26)
| ~ spl29_6
| ~ spl29_7
| ~ spl29_32 ),
inference(forward_demodulation,[],[f32051,f272]) ).
fof(f32084,plain,
( $false
| ~ spl29_6
| ~ spl29_7
| ~ spl29_32
| spl29_106 ),
inference(forward_subsumption_resolution,[],[f32072,f1681]) ).
fof(f32085,plain,
( ~ spl29_6
| ~ spl29_7
| ~ spl29_32
| spl29_106 ),
inference(avatar_contradiction_clause,[],[f32084]) ).
fof(f32101,plain,
( empty(sF25)
| ~ spl29_6
| ~ spl29_7
| ~ spl29_9
| ~ spl29_106 ),
inference(forward_subsumption_resolution,[],[f2046,f1680]) ).
fof(f32122,definition,
( spl29_848
<=> empty(sF24) ),
introduced(definition,[new_symbols(definition,[spl29_848])],[avatar_definition]) ).
fof(f32144,plain,
( ~ spl29_848
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11 ),
inference(avatar_split_clause,[],[f16160,f290,f275,f265,f260,f255,f250,f32122]) ).
fof(f32200,plain,
( empty(sF24)
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| ~ spl29_106 ),
inference(forward_demodulation,[],[f32101,f277]) ).
fof(f32254,plain,
( spl29_848
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| ~ spl29_106 ),
inference(avatar_split_clause,[],[f32200,f1679,f280,f275,f270,f265,f32122]) ).
fof(f32444,plain,
( apply(sK17,sK4(sK17)) = apply(sK17,sK5(sK17))
| ~ function(sK17)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f386,f243]) ).
fof(f32527,plain,
( apply(sK17,sK4(sK17)) = apply(sK17,sK5(sK17))
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f32444,f194]) ).
fof(f33428,plain,
( sF28(sK15(sK5(sK17))) = sK15(apply(sK17,sK4(sK17)))
| spl29_1
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327
| ~ spl29_344 ),
inference(superposition,[],[f17144,f32527]) ).
fof(f33507,definition,
( spl29_864
<=> sF28(sK15(sK4(sK17))) = sF28(sK15(sK5(sK17))) ),
introduced(definition,[new_symbols(definition,[spl29_864])],[avatar_definition]) ).
fof(f33509,plain,
( sF28(sK15(sK4(sK17))) = sF28(sK15(sK5(sK17)))
| ~ spl29_864 ),
inference(avatar_component_clause,[],[f33507]) ).
fof(f33574,plain,
( sF28(sK15(sK4(sK17))) = sF28(sK15(sK5(sK17)))
| spl29_1
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327
| ~ spl29_344
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371
| ~ spl29_385 ),
inference(forward_demodulation,[],[f33428,f17386]) ).
fof(f33597,plain,
( spl29_864
| spl29_1
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327
| ~ spl29_344
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371
| ~ spl29_385 ),
inference(avatar_split_clause,[],[f33574,f13949,f13644,f13552,f13548,f13403,f13080,f12973,f12969,f242,f33507]) ).
fof(f36092,definition,
( spl29_992
<=> sK4(sK17) = sK5(sK17) ),
introduced(definition,[new_symbols(definition,[spl29_992])],[avatar_definition]) ).
fof(f36093,plain,
( sK4(sK17) = sK5(sK17)
| ~ spl29_992 ),
inference(avatar_component_clause,[],[f36092]) ).
fof(f36094,plain,
( sK4(sK17) != sK5(sK17)
| spl29_992 ),
inference(avatar_component_clause,[],[f36092]) ).
fof(f38568,plain,
( ! [X0] :
( sF28(X0) != sF28(sK15(sK4(sK17)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK15(sK5(sK17)))
| ~ relation(sK15(sK5(sK17)))
| sK15(sK5(sK17)) = X0
| relation_dom(X0) != relation_dom(sK15(sK5(sK17)))
| ~ subset(relation_rng(sK15(sK5(sK17))),sF22)
| ~ subset(relation_rng(X0),sF22) )
| ~ spl29_2
| ~ spl29_864 ),
inference(superposition,[],[f247,f33509]) ).
fof(f38591,plain,
( ! [X0] :
( sF28(X0) != sF28(sK15(sK4(sK17)))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK15(sK5(sK17)))
| sK15(sK5(sK17)) = X0
| relation_dom(X0) != relation_dom(sK15(sK5(sK17)))
| ~ subset(relation_rng(sK15(sK5(sK17))),sF22)
| ~ subset(relation_rng(X0),sF22) )
| ~ spl29_2
| ~ spl29_864 ),
inference(forward_subsumption_resolution,[],[f38568,f178]) ).
fof(f38601,plain,
( ! [X0] :
( sF28(X0) != sF28(sK15(sK4(sK17)))
| ~ function(X0)
| ~ relation(X0)
| sK15(sK5(sK17)) = X0
| relation_dom(X0) != relation_dom(sK15(sK5(sK17)))
| ~ subset(relation_rng(sK15(sK5(sK17))),sF22)
| ~ subset(relation_rng(X0),sF22) )
| ~ spl29_2
| ~ spl29_864 ),
inference(forward_subsumption_resolution,[],[f38591,f179]) ).
fof(f38610,plain,
( ! [X0] :
( relation_dom(X0) != singleton(empty_set)
| sF28(X0) != sF28(sK15(sK4(sK17)))
| ~ function(X0)
| ~ relation(X0)
| sK15(sK5(sK17)) = X0
| ~ subset(relation_rng(sK15(sK5(sK17))),sF22)
| ~ subset(relation_rng(X0),sF22) )
| ~ spl29_2
| ~ spl29_864 ),
inference(forward_demodulation,[],[f38601,f177]) ).
fof(f38615,plain,
( ! [X0] :
( ~ subset(singleton(sK5(sK17)),sF22)
| relation_dom(X0) != singleton(empty_set)
| sF28(X0) != sF28(sK15(sK4(sK17)))
| ~ function(X0)
| ~ relation(X0)
| sK15(sK5(sK17)) = X0
| ~ subset(relation_rng(X0),sF22) )
| ~ spl29_2
| ~ spl29_864 ),
inference(forward_demodulation,[],[f38610,f3690]) ).
fof(f38620,plain,
( ! [X0] :
( sF28(X0) != sF28(sK15(sK4(sK17)))
| relation_dom(X0) != singleton(empty_set)
| ~ function(X0)
| ~ relation(X0)
| sK15(sK5(sK17)) = X0
| ~ subset(relation_rng(X0),sF22) )
| ~ spl29_2
| ~ spl29_344
| ~ spl29_864 ),
inference(forward_subsumption_resolution,[],[f38615,f13404]) ).
fof(f38631,plain,
( singleton(empty_set) != relation_dom(sK15(sK4(sK17)))
| ~ function(sK15(sK4(sK17)))
| ~ relation(sK15(sK4(sK17)))
| sK15(sK4(sK17)) = sK15(sK5(sK17))
| ~ subset(relation_rng(sK15(sK4(sK17))),sF22)
| ~ spl29_2
| ~ spl29_344
| ~ spl29_864 ),
inference(equality_resolution,[],[f38620]) ).
fof(f38632,plain,
( ~ function(sK15(sK4(sK17)))
| ~ relation(sK15(sK4(sK17)))
| sK15(sK4(sK17)) = sK15(sK5(sK17))
| ~ subset(relation_rng(sK15(sK4(sK17))),sF22)
| ~ spl29_2
| ~ spl29_344
| ~ spl29_864 ),
inference(forward_subsumption_resolution,[],[f38631,f177]) ).
fof(f38634,plain,
( ~ relation(sK15(sK4(sK17)))
| sK15(sK4(sK17)) = sK15(sK5(sK17))
| ~ subset(relation_rng(sK15(sK4(sK17))),sF22)
| ~ spl29_2
| ~ spl29_344
| ~ spl29_864 ),
inference(forward_subsumption_resolution,[],[f38632,f178]) ).
fof(f38635,plain,
( sK15(sK4(sK17)) = sK15(sK5(sK17))
| ~ subset(relation_rng(sK15(sK4(sK17))),sF22)
| ~ spl29_2
| ~ spl29_344
| ~ spl29_864 ),
inference(forward_subsumption_resolution,[],[f38634,f179]) ).
fof(f38636,plain,
( ~ subset(singleton(sK4(sK17)),sF22)
| sK15(sK4(sK17)) = sK15(sK5(sK17))
| ~ spl29_2
| ~ spl29_344
| ~ spl29_864 ),
inference(forward_demodulation,[],[f38635,f3690]) ).
fof(f38637,plain,
( sK15(sK4(sK17)) = sK15(sK5(sK17))
| ~ spl29_2
| ~ spl29_344
| ~ spl29_385
| ~ spl29_864 ),
inference(forward_subsumption_resolution,[],[f38636,f13950]) ).
fof(f38638,plain,
( spl29_384
| ~ spl29_2
| ~ spl29_344
| ~ spl29_385
| ~ spl29_864 ),
inference(avatar_split_clause,[],[f38637,f33507,f13949,f13403,f246,f13945]) ).
fof(f38639,plain,
( $false
| ~ spl29_384
| spl29_992 ),
inference(forward_subsumption_resolution,[],[f14079,f36094]) ).
fof(f38640,plain,
( ~ spl29_384
| spl29_992 ),
inference(avatar_contradiction_clause,[],[f38639]) ).
fof(f38784,plain,
( sK4(sK17) != sK4(sK17)
| one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ spl29_992 ),
inference(superposition,[],[f140,f36093]) ).
fof(f38786,plain,
( one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ spl29_992 ),
inference(trivial_inequality_removal,[],[f38784]) ).
fof(f38787,plain,
( ~ relation(sK17)
| ~ function(sK17)
| spl29_1
| ~ spl29_992 ),
inference(forward_subsumption_resolution,[],[f38786,f243]) ).
fof(f38789,plain,
( ~ function(sK17)
| spl29_1
| ~ spl29_992 ),
inference(forward_subsumption_resolution,[],[f38787,f195]) ).
fof(f38790,plain,
( $false
| spl29_1
| ~ spl29_992 ),
inference(forward_subsumption_resolution,[],[f38789,f194]) ).
fof(f38791,plain,
( spl29_1
| ~ spl29_992 ),
inference(avatar_contradiction_clause,[],[f38790]) ).
cnf(s1,plain,
( spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f248]) ).
cnf(s2,plain,
( ~ spl29_1
| spl29_3 ),
inference(sat_conversion,[],[f253]) ).
cnf(s3,plain,
( ~ spl29_1
| spl29_4 ),
inference(sat_conversion,[],[f258]) ).
cnf(s4,plain,
( ~ spl29_1
| spl29_5 ),
inference(sat_conversion,[],[f263]) ).
cnf(s5,plain,
( ~ spl29_1
| spl29_6 ),
inference(sat_conversion,[],[f268]) ).
cnf(s6,plain,
( ~ spl29_1
| spl29_7 ),
inference(sat_conversion,[],[f273]) ).
cnf(s7,plain,
( ~ spl29_1
| spl29_8 ),
inference(sat_conversion,[],[f278]) ).
cnf(s8,plain,
( ~ spl29_1
| spl29_9 ),
inference(sat_conversion,[],[f283]) ).
cnf(s9,plain,
( ~ spl29_1
| spl29_10 ),
inference(sat_conversion,[],[f288]) ).
cnf(s10,plain,
( ~ spl29_1
| ~ spl29_11 ),
inference(sat_conversion,[],[f293]) ).
cnf(s355,plain,
( spl29_1
| ~ spl29_302
| ~ spl29_303
| spl29_327 ),
inference(sat_conversion,[],[f13142]) ).
cnf(s357,plain,
spl29_303,
inference(sat_conversion,[],[f13147]) ).
cnf(s358,plain,
spl29_302,
inference(sat_conversion,[],[f13152]) ).
cnf(s363,plain,
( spl29_1
| spl29_344 ),
inference(sat_conversion,[],[f13413]) ).
cnf(s400,plain,
( spl29_1
| ~ spl29_350
| ~ spl29_351
| spl29_371 ),
inference(sat_conversion,[],[f13706]) ).
cnf(s402,plain,
spl29_351,
inference(sat_conversion,[],[f13711]) ).
cnf(s403,plain,
spl29_350,
inference(sat_conversion,[],[f13716]) ).
cnf(s407,plain,
( spl29_1
| spl29_385 ),
inference(sat_conversion,[],[f13963]) ).
cnf(s675,plain,
( ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_9
| spl29_11
| spl29_20
| spl29_542 ),
inference(sat_conversion,[],[f19422]) ).
cnf(s686,plain,
( ~ spl29_20
| spl29_32 ),
inference(sat_conversion,[],[f19473]) ).
cnf(s780,plain,
( ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| ~ spl29_10
| spl29_11
| spl29_20
| spl29_490 ),
inference(sat_conversion,[],[f21500]) ).
cnf(s1278,plain,
( ~ spl29_1
| ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| spl29_11
| ~ spl29_490
| ~ spl29_542
| spl29_840 ),
inference(sat_conversion,[],[f31896]) ).
cnf(s1281,plain,
( ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11
| ~ spl29_840 ),
inference(sat_conversion,[],[f31967]) ).
cnf(s1313,plain,
( ~ spl29_6
| ~ spl29_7
| ~ spl29_32
| spl29_106 ),
inference(sat_conversion,[],[f32085]) ).
cnf(s1320,plain,
( ~ spl29_3
| ~ spl29_4
| ~ spl29_5
| ~ spl29_6
| ~ spl29_8
| spl29_11
| ~ spl29_848 ),
inference(sat_conversion,[],[f32144]) ).
cnf(s1346,plain,
( ~ spl29_6
| ~ spl29_7
| ~ spl29_8
| ~ spl29_9
| ~ spl29_106
| spl29_848 ),
inference(sat_conversion,[],[f32254]) ).
cnf(s1407,plain,
( spl29_1
| ~ spl29_302
| ~ spl29_303
| ~ spl29_327
| ~ spl29_344
| ~ spl29_350
| ~ spl29_351
| ~ spl29_371
| ~ spl29_385
| spl29_864 ),
inference(sat_conversion,[],[f33597]) ).
cnf(s1683,plain,
( ~ spl29_2
| ~ spl29_344
| spl29_384
| ~ spl29_385
| ~ spl29_864 ),
inference(sat_conversion,[],[f38638]) ).
cnf(s1684,plain,
( ~ spl29_384
| spl29_992 ),
inference(sat_conversion,[],[f38640]) ).
cnf(s1690,plain,
( spl29_1
| ~ spl29_992 ),
inference(sat_conversion,[],[f38791]) ).
cnf(s1692,plain,
( spl29_1
| spl29_371 ),
inference(rat,[],[s400,s402,s403]) ).
cnf(s1724,plain,
( spl29_1
| spl29_327 ),
inference(rat,[],[s355,s357,s358]) ).
cnf(s1774,plain,
spl29_1,
inference(rat,[],[s1683,s1407,s1684,s1,s1724,s363,s1692,s407,s1690,s358,s357,s403,s402]) ).
cnf(s1775,plain,
~ spl29_11,
inference(rat,[],[s10,s1774]) ).
cnf(s1776,plain,
spl29_10,
inference(rat,[],[s9,s1774]) ).
cnf(s1777,plain,
spl29_9,
inference(rat,[],[s8,s1774]) ).
cnf(s1778,plain,
spl29_8,
inference(rat,[],[s7,s1774]) ).
cnf(s1779,plain,
spl29_7,
inference(rat,[],[s6,s1774]) ).
cnf(s1780,plain,
spl29_6,
inference(rat,[],[s5,s1774]) ).
cnf(s1781,plain,
spl29_5,
inference(rat,[],[s4,s1774]) ).
cnf(s1782,plain,
spl29_4,
inference(rat,[],[s3,s1774]) ).
cnf(s1783,plain,
spl29_3,
inference(rat,[],[s2,s1774]) ).
cnf(s1791,plain,
~ spl29_848,
inference(rat,[],[s1320,s1782,s1775,s1778,s1780,s1781,s1783]) ).
cnf(s1792,plain,
~ spl29_840,
inference(rat,[],[s1281,s1782,s1775,s1778,s1780,s1781,s1783]) ).
cnf(s1808,plain,
~ spl29_106,
inference(rat,[],[s1346,s1780,s1779,s1777,s1778,s1791]) ).
cnf(s1813,plain,
~ spl29_32,
inference(rat,[],[s1313,s1780,s1779,s1808]) ).
cnf(s1815,plain,
~ spl29_20,
inference(rat,[],[s686,s1813]) ).
cnf(s1818,plain,
spl29_490,
inference(rat,[],[s780,s1783,s1782,s1775,s1776,s1778,s1780,s1781,s1815]) ).
cnf(s1820,plain,
spl29_542,
inference(rat,[],[s675,s1783,s1782,s1775,s1777,s1778,s1780,s1781,s1815]) ).
cnf(s1823,plain,
$false,
inference(rat,[],[s1278,s1792,s1783,s1782,s1775,s1777,s1778,s1779,s1780,s1781,s1774,s1820,s1818]) ).
fof(f38792,plain,
$false,
inference(avatar_sat_refutation,[],[s1823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU016+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:18:06 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 12.22/2.66 % (3177381)Detected formulas, will run a generic FOF schedule.
% 12.22/2.66 % (3177387)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=295745620:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.22/2.66 % (3177391)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1635396293:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.22/2.66 % (3177390)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3639270752:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.22/2.66 % (3177386)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=970287070:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.22/2.66 % (3177389)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2760923778:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.22/2.66 % (3177388)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=1415542727:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.22/2.66 % (3177392)dis-21_1_sil=8000:lcm=predicate:random_seed=1243716966: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)
% 12.22/2.66 % (3177389)Refutation not found, incomplete strategy
% 12.22/2.66 % (3177389)------------------------------
% 12.22/2.66 % (3177389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.22/2.66 % (3177389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.66 % (3177389)CaDiCaL version: 2.1.3
% 12.22/2.66 % (3177389)Termination reason: Refutation not found, incomplete strategy
% 12.22/2.66 % (3177389)Time elapsed: 0.004 s
% 12.22/2.66 % (3177389)Peak memory usage: 88 MB
% 12.22/2.66 % (3177389)Instructions burned: 4 (million)
% 12.22/2.66 % (3177392)Instruction limit reached!
% 12.22/2.66 % (3177392)------------------------------
% 12.22/2.66 % (3177392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.22/2.66 % (3177392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.66 % (3177392)CaDiCaL version: 2.1.3
% 12.22/2.66 % (3177392)Termination reason: Instruction limit
% 12.22/2.66 % (3177392)Termination phase: Saturation
% 12.22/2.66 % (3177392)Time elapsed: 0.059 s
% 12.22/2.66 % (3177392)Peak memory usage: 88 MB
% 12.22/2.66 % (3177392)Instructions burned: 130 (million)
% 12.22/2.66 % (3177390)Instruction limit reached!
% 12.22/2.66 % (3177390)------------------------------
% 12.22/2.66 % (3177390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.22/2.66 % (3177390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.66 % (3177390)CaDiCaL version: 2.1.3
% 12.22/2.66 % (3177390)Termination reason: Instruction limit
% 12.22/2.66 % (3177390)Termination phase: Saturation
% 12.22/2.66 % (3177390)Time elapsed: 0.069 s
% 12.22/2.66 % (3177390)Peak memory usage: 88 MB
% 12.22/2.66 % (3177390)Instructions burned: 120 (million)
% 12.22/2.66 % (3177391)Instruction limit reached!
% 12.22/2.66 % (3177391)------------------------------
% 12.22/2.66 % (3177391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.22/2.66 % (3177391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.66 % (3177391)CaDiCaL version: 2.1.3
% 12.22/2.66 % (3177391)Termination reason: Instruction limit
% 12.22/2.66 % (3177391)Termination phase: Saturation
% 12.22/2.66 % (3177391)Time elapsed: 0.102 s
% 12.22/2.66 % (3177391)Peak memory usage: 89 MB
% 12.22/2.66 % (3177391)Instructions burned: 140 (million)
% 12.22/2.66 % (3177400)lrs+10_1_sil=8000:sp=occurrence:random_seed=1719500654:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.22/2.66 % (3177401)lrs+10_1_sil=32000:urr=on:br=off:random_seed=414901048:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.22/2.66 % (3177402)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3909153569:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.22/2.66 % (3177389)------------------------------
% 12.22/2.66 % (3177389)------------------------------
% 12.22/2.66 % (3177401)Instruction limit reached!
% 12.22/2.66 % (3177401)------------------------------
% 12.22/2.66 % (3177401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177401)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177401)Termination reason: Instruction limit
% 16.97/3.24 % (3177401)Termination phase: Saturation
% 16.97/3.24 % (3177401)Time elapsed: 0.082 s
% 16.97/3.24 % (3177401)Peak memory usage: 91 MB
% 16.97/3.24 % (3177401)Instructions burned: 157 (million)
% 16.97/3.24 % (3177400)Instruction limit reached!
% 16.97/3.24 % (3177400)------------------------------
% 16.97/3.24 % (3177400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177400)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177400)Termination reason: Instruction limit
% 16.97/3.24 % (3177400)Termination phase: Saturation
% 16.97/3.24 % (3177400)Time elapsed: 0.156 s
% 16.97/3.24 % (3177400)Peak memory usage: 91 MB
% 16.97/3.24 % (3177400)Instructions burned: 285 (million)
% 16.97/3.24 % (3177406)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=3276730375:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 16.97/3.24 % (3177407)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=866059728:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 16.97/3.24 % (3177408)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2717735304:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 16.97/3.24 % (3177407)Refutation not found, incomplete strategy
% 16.97/3.24 % (3177407)------------------------------
% 16.97/3.24 % (3177407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177407)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177407)Termination reason: Refutation not found, incomplete strategy
% 16.97/3.24 % (3177407)Time elapsed: 0.004 s
% 16.97/3.24 % (3177407)Peak memory usage: 88 MB
% 16.97/3.24 % (3177407)Instructions burned: 4 (million)
% 16.97/3.24 % (3177402)Instruction limit reached!
% 16.97/3.24 % (3177402)------------------------------
% 16.97/3.24 % (3177402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177402)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177402)Termination reason: Instruction limit
% 16.97/3.24 % (3177402)Termination phase: Saturation
% 16.97/3.24 % (3177402)Time elapsed: 0.195 s
% 16.97/3.24 % (3177402)Peak memory usage: 91 MB
% 16.97/3.24 % (3177402)Instructions burned: 325 (million)
% 16.97/3.24 % (3177406)Instruction limit reached!
% 16.97/3.24 % (3177406)------------------------------
% 16.97/3.24 % (3177406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177406)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177406)Termination reason: Instruction limit
% 16.97/3.24 % (3177406)Termination phase: Saturation
% 16.97/3.24 % (3177406)Time elapsed: 0.139 s
% 16.97/3.24 % (3177406)Peak memory usage: 93 MB
% 16.97/3.24 % (3177406)Instructions burned: 249 (million)
% 16.97/3.24 % (3177412)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=568461067:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 16.97/3.24 % (3177413)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2132822399:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 16.97/3.24 % (3177412)Instruction limit reached!
% 16.97/3.24 % (3177412)------------------------------
% 16.97/3.24 % (3177412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177412)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177412)Termination reason: Instruction limit
% 16.97/3.24 % (3177412)Termination phase: Saturation
% 16.97/3.24 % (3177412)Time elapsed: 0.078 s
% 16.97/3.24 % (3177412)Peak memory usage: 90 MB
% 16.97/3.24 % (3177412)Instructions burned: 114 (million)
% 16.97/3.24 % (3177407)------------------------------
% 16.97/3.24 % (3177407)------------------------------
% 16.97/3.24 % (3177413)Instruction limit reached!
% 16.97/3.24 % (3177413)------------------------------
% 16.97/3.24 % (3177413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177413)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177413)Termination reason: Instruction limit
% 16.97/3.24 % (3177413)Termination phase: Saturation
% 16.97/3.24 % (3177413)Time elapsed: 0.066 s
% 16.97/3.24 % (3177413)Peak memory usage: 88 MB
% 16.97/3.24 % (3177413)Instructions burned: 128 (million)
% 16.97/3.24 % (3177416)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=969927069:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 16.97/3.24 % (3177417)lrs+10_1_sil=8000:sp=occurrence:random_seed=470864693:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 16.97/3.24 % (3177418)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4287313028:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 16.97/3.24 % (3177416)Instruction limit reached!
% 16.97/3.24 % (3177416)------------------------------
% 16.97/3.24 % (3177416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177416)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177416)Termination reason: Instruction limit
% 16.97/3.24 % (3177416)Termination phase: Saturation
% 16.97/3.24 % (3177416)Time elapsed: 0.064 s
% 16.97/3.24 % (3177416)Peak memory usage: 89 MB
% 16.97/3.24 % (3177416)Instructions burned: 115 (million)
% 16.97/3.24 % (3177418)Refutation not found, incomplete strategy
% 16.97/3.24 % (3177418)------------------------------
% 16.97/3.24 % (3177418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177418)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177418)Termination reason: Refutation not found, incomplete strategy
% 16.97/3.24 % (3177418)Time elapsed: 0.004 s
% 16.97/3.24 % (3177418)Peak memory usage: 88 MB
% 16.97/3.24 % (3177418)Instructions burned: 4 (million)
% 16.97/3.24 % (3177422)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=757478105:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 16.97/3.24 % (3177418)------------------------------
% 16.97/3.24 % (3177418)------------------------------
% 16.97/3.24 % (3177424)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1744681069:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 16.97/3.24 % (3177424)Instruction limit reached!
% 16.97/3.24 % (3177424)------------------------------
% 16.97/3.24 % (3177424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177424)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177424)Termination reason: Instruction limit
% 16.97/3.24 % (3177424)Termination phase: Saturation
% 16.97/3.24 % (3177424)Time elapsed: 0.073 s
% 16.97/3.24 % (3177424)Peak memory usage: 91 MB
% 16.97/3.24 % (3177424)Instructions burned: 134 (million)
% 16.97/3.24 % (3177417)Instruction limit reached!
% 16.97/3.24 % (3177417)------------------------------
% 16.97/3.24 % (3177417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177417)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177417)Termination reason: Instruction limit
% 16.97/3.24 % (3177417)Termination phase: Saturation
% 16.97/3.24 % (3177417)Time elapsed: 0.497 s
% 16.97/3.24 % (3177417)Peak memory usage: 96 MB
% 16.97/3.24 % (3177417)Instructions burned: 907 (million)
% 16.97/3.24 % (3177426)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4273302431:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 16.97/3.24 % (3177427)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2229374243:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 16.97/3.24 % (3177408)Instruction limit reached!
% 16.97/3.24 % (3177408)------------------------------
% 16.97/3.24 % (3177408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177408)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177408)Termination reason: Instruction limit
% 16.97/3.24 % (3177408)Termination phase: Saturation
% 16.97/3.24 % (3177408)Time elapsed: 1.248 s
% 16.97/3.24 % (3177408)Peak memory usage: 140 MB
% 16.97/3.24 % (3177408)Instructions burned: 2350 (million)
% 16.97/3.24 % (3177426)Instruction limit reached!
% 16.97/3.24 % (3177426)------------------------------
% 16.97/3.24 % (3177426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177426)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177426)Termination reason: Instruction limit
% 16.97/3.24 % (3177426)Termination phase: Saturation
% 16.97/3.24 % (3177426)Time elapsed: 0.286 s
% 16.97/3.24 % (3177426)Peak memory usage: 91 MB
% 16.97/3.24 % (3177426)Instructions burned: 592 (million)
% 16.97/3.24 % (3177430)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=3075842610:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/125Mi)
% 16.97/3.24 % (3177431)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=70927434:i=134:gtgl=5:slsql=off:gtg=exists_sym_2981 on theBenchmark for (2981ds/134Mi)
% 16.97/3.24 % (3177430)Instruction limit reached!
% 16.97/3.24 % (3177430)------------------------------
% 16.97/3.24 % (3177430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177430)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177430)Termination reason: Instruction limit
% 16.97/3.24 % (3177430)Termination phase: Saturation
% 16.97/3.24 % (3177430)Time elapsed: 0.074 s
% 16.97/3.24 % (3177430)Peak memory usage: 90 MB
% 16.97/3.24 % (3177430)Instructions burned: 125 (million)
% 16.97/3.24 % (3177431)Instruction limit reached!
% 16.97/3.24 % (3177431)------------------------------
% 16.97/3.24 % (3177431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177431)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177431)Termination reason: Instruction limit
% 16.97/3.24 % (3177431)Termination phase: Saturation
% 16.97/3.24 % (3177431)Time elapsed: 0.071 s
% 16.97/3.24 % (3177431)Peak memory usage: 90 MB
% 16.97/3.24 % (3177431)Instructions burned: 136 (million)
% 16.97/3.24 % (3177434)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3877483876:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2979 on theBenchmark for (2979ds/141Mi)
% 16.97/3.24 % (3177435)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1090789509:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2979 on theBenchmark for (2979ds/431Mi)
% 16.97/3.24 % (3177435)Refutation not found, incomplete strategy
% 16.97/3.24 % (3177435)------------------------------
% 16.97/3.24 % (3177435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177435)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177435)Termination reason: Refutation not found, incomplete strategy
% 16.97/3.24 % (3177435)Time elapsed: 0.003 s
% 16.97/3.24 % (3177435)Peak memory usage: 88 MB
% 16.97/3.24 % (3177435)Instructions burned: 3 (million)
% 16.97/3.24 % (3177386)First to succeed.
% 16.97/3.24 % (3177386)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3177381"
% 16.97/3.24 % (3177434)Instruction limit reached!
% 16.97/3.24 % (3177434)------------------------------
% 16.97/3.24 % (3177434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.97/3.24 % (3177434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.97/3.24 % (3177434)CaDiCaL version: 2.1.3
% 16.97/3.24 % (3177434)Termination reason: Instruction limit
% 16.97/3.24 % (3177434)Termination phase: Saturation
% 16.97/3.24 % (3177434)Time elapsed: 0.082 s
% 16.97/3.24 % (3177434)Peak memory usage: 91 MB
% 16.97/3.24 % (3177434)Instructions burned: 142 (million)
% 16.97/3.24 % (3177438)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=4240841748:i=6060:aac=none:ins=25_2977 on theBenchmark for (2977ds/6060Mi)
% 16.97/3.24 % (3177386)Refutation found. Thanks to Tanya!
% 16.97/3.24 % SZS status Theorem for theBenchmark
% 16.97/3.24 % SZS output start Proof for theBenchmark
% See solution above
% 17.56/3.45 % (3177386)------------------------------
% 17.56/3.45 % (3177386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.56/3.45 % (3177386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.56/3.45 % (3177386)CaDiCaL version: 2.1.3
% 17.56/3.45 % (3177386)Termination reason: Refutation
% 17.56/3.45 % (3177386)Time elapsed: 2.079 s
% 17.56/3.45 % (3177386)Peak memory usage: 164 MB
% 17.56/3.45 % (3177386)Instructions burned: 5098 (million)
% 17.56/3.45 % (3177386)------------------------------
% 17.56/3.45 % (3177386)------------------------------
% 17.56/3.45 % (3177381)Success in time 2.398 s
% 17.56/3.45 % Vampire exiting
%------------------------------------------------------------------------------