%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU078+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:47:12 PM UTC 2026
% Result : Theorem 5.08s 1.65s
% Output : Refutation 6.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of formulae : 196 ( 22 unt; 18 def)
% Number of atoms : 721 ( 118 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 917 ( 392 ~; 388 |; 86 &)
% ( 40 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 19 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 243 ( 0 sgn 207 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f24,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f29,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f30,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1] :
~ ( in(X1,relation_rng(X0))
& ! [X2] : relation_inverse_image(X0,singleton(X1)) != singleton(X2) )
<=> one_to_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
fof(f31,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0,X1] :
( relation(X1)
=> ( relation_inverse_image(X1,X0) = empty_set
<=> disjoint(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
fof(f36,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f37,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f40,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
fof(f42,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f43,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f53,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f53]) ).
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(ennf_transformation,[],[f7]) ).
fof(f56,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,[],[f55]) ).
fof(f64,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0] :
( ( ! [X1] :
( ~ in(X1,relation_rng(X0))
| ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2) )
<=> one_to_one(X0) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f66,plain,
! [X0] :
( ( ! [X1] :
( ~ in(X1,relation_rng(X0))
| ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2) )
<=> one_to_one(X0) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
? [X0] :
( ( one_to_one(X0)
<~> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f68,plain,
? [X0] :
( ( one_to_one(X0)
<~> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( relation_inverse_image(X1,X0) = empty_set
<=> disjoint(relation_rng(X1),X0) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f75,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f77,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f78,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f80,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f54]) ).
fof(f81,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK0(X0,X1,X2)),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f82]) ).
fof(f84,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,[],[f6]) ).
fof(f85,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,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK1(X0,X1) != X0
| ~ in(sK1(X0,X1),X1) )
& ( sK1(X0,X1) = X0
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f85]) ).
fof(f87,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,[],[f56]) ).
fof(f88,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,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK2(X0,X1) )
| ~ in(sK2(X0,X1),X1) )
& ( ( in(sK3(X0,X1),relation_dom(X0))
& sK2(X0,X1) = apply(X0,sK3(X0,X1)) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK4(X0,X5),relation_dom(X0))
& apply(X0,sK4(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f88]) ).
fof(f97,plain,
! [X0] :
( element(sK12(X0),powerset(X0))
& empty(sK12(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f24]) ).
fof(f101,plain,
! [X0] :
( ( ( ! [X1] :
( ~ in(X1,relation_rng(X0))
| ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2) )
| ~ one_to_one(X0) )
& ( one_to_one(X0)
| ? [X1] :
( in(X1,relation_rng(X0))
& ! [X2] : relation_inverse_image(X0,singleton(X1)) != singleton(X2) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f66]) ).
fof(f102,plain,
! [X0] :
( ( ( ! [X1] :
( ~ in(X1,relation_rng(X0))
| ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2) )
| ~ one_to_one(X0) )
& ( one_to_one(X0)
| ? [X3] :
( in(X3,relation_rng(X0))
& ! [X4] : relation_inverse_image(X0,singleton(X3)) != singleton(X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ( ( ! [X1] :
( ~ in(X1,relation_rng(X0))
| relation_inverse_image(X0,singleton(X1)) = singleton(sK16(X0,X1)) )
| ~ one_to_one(X0) )
& ( one_to_one(X0)
| ( in(sK17(X0),relation_rng(X0))
& ! [X4] : singleton(X4) != relation_inverse_image(X0,singleton(sK17(X0))) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X2,sK16(X0,X1)),skolemize(X3,sK17(X0))],[f102]) ).
fof(f104,plain,
? [X0] :
( ( ? [X1] :
! [X2] : ~ subset(relation_inverse_image(X0,singleton(X1)),singleton(X2))
| ~ one_to_one(X0) )
& ( ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2))
| one_to_one(X0) )
& relation(X0)
& function(X0) ),
inference(nnf_transformation,[],[f68]) ).
fof(f105,plain,
? [X0] :
( ( ? [X1] :
! [X2] : ~ subset(relation_inverse_image(X0,singleton(X1)),singleton(X2))
| ~ one_to_one(X0) )
& ( ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2))
| one_to_one(X0) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
? [X0] :
( ( ? [X1] :
! [X2] : ~ subset(relation_inverse_image(X0,singleton(X1)),singleton(X2))
| ~ one_to_one(X0) )
& ( ! [X3] :
? [X4] : subset(relation_inverse_image(X0,singleton(X3)),singleton(X4))
| one_to_one(X0) )
& relation(X0)
& function(X0) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
( ( ! [X2] : ~ subset(relation_inverse_image(sK18,singleton(sK19)),singleton(X2))
| ~ one_to_one(sK18) )
& ( ! [X3] : subset(relation_inverse_image(sK18,singleton(X3)),singleton(sK20(X3)))
| one_to_one(sK18) )
& relation(sK18)
& function(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X4,sK20(X3))],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ( ( relation_inverse_image(X1,X0) = empty_set
| ~ disjoint(relation_rng(X1),X0) )
& ( disjoint(relation_rng(X1),X0)
| empty_set != relation_inverse_image(X1,X0) ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f69]) ).
fof(f109,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f110,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f109]) ).
fof(f120,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f125,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f86]) ).
fof(f128,plain,
! [X0,X1,X5] :
( apply(X0,sK4(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f129,plain,
! [X0,X1,X5] :
( in(sK4(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f160,plain,
! [X0] : empty(sK12(X0)),
inference(cnf_transformation,[],[f97]) ).
fof(f168,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f169,plain,
! [X0,X4] :
( one_to_one(X0)
| singleton(X4) != relation_inverse_image(X0,singleton(sK17(X0)))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f170,plain,
! [X0] :
( one_to_one(X0)
| in(sK17(X0),relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f171,plain,
! [X0,X1] :
( ~ in(X1,relation_rng(X0))
| relation_inverse_image(X0,singleton(X1)) = singleton(sK16(X0,X1))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f172,plain,
function(sK18),
inference(cnf_transformation,[],[f107]) ).
fof(f173,plain,
relation(sK18),
inference(cnf_transformation,[],[f107]) ).
fof(f174,plain,
! [X3] :
( subset(relation_inverse_image(sK18,singleton(X3)),singleton(sK20(X3)))
| one_to_one(sK18) ),
inference(cnf_transformation,[],[f107]) ).
fof(f175,plain,
! [X2] :
( ~ subset(relation_inverse_image(sK18,singleton(sK19)),singleton(X2))
| ~ one_to_one(sK18) ),
inference(cnf_transformation,[],[f107]) ).
fof(f177,plain,
! [X0,X1] :
( empty_set = relation_inverse_image(X1,X0)
| ~ disjoint(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f180,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f181,plain,
! [X0,X1] :
( empty_set = X0
| singleton(X1) = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f182,plain,
! [X0,X1] :
( subset(X0,singleton(X1))
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f110]) ).
fof(f187,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f189,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f190,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f192,plain,
! [X0,X1,X4] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f120]) ).
fof(f195,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f125]) ).
fof(f196,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f195]) ).
fof(f200,plain,
! [X0,X5] :
( in(sK4(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f129]) ).
fof(f201,plain,
! [X0,X5] :
( apply(X0,sK4(X0,X5)) = X5
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f203,plain,
! [X1] : subset(singleton(X1),singleton(X1)),
inference(equality_resolution,[],[f182]) ).
fof(f207,definition,
( spl22_1
<=> one_to_one(sK18) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f208,plain,
( one_to_one(sK18)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( ~ one_to_one(sK18)
| spl22_1 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,definition,
( spl22_2
<=> ! [X2] : ~ subset(relation_inverse_image(sK18,singleton(sK19)),singleton(X2)) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f212,plain,
( ! [X2] : ~ subset(relation_inverse_image(sK18,singleton(sK19)),singleton(X2))
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( ~ spl22_1
| spl22_2 ),
inference(avatar_split_clause,[],[f175,f211,f207]) ).
fof(f214,plain,
( ! [X3] : subset(relation_inverse_image(sK18,singleton(X3)),singleton(sK20(X3)))
| spl22_1 ),
inference(backward_subsumption_resolution,[],[f174,f209]) ).
fof(f216,definition,
( spl22_3
<=> relation(sK18) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f218,plain,
( relation(sK18)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f219,plain,
spl22_3,
inference(avatar_split_clause,[],[f173,f216]) ).
fof(f229,plain,
( ! [X0] :
( one_to_one(sK18)
| singleton(X0) != relation_inverse_image(sK18,singleton(sK17(sK18)))
| ~ function(sK18) )
| ~ spl22_3 ),
inference(resolution,[],[f218,f169]) ).
fof(f230,plain,
( one_to_one(sK18)
| in(sK17(sK18),relation_rng(sK18))
| ~ function(sK18)
| ~ spl22_3 ),
inference(resolution,[],[f218,f170]) ).
fof(f233,plain,
( ! [X0] :
( empty_set = relation_inverse_image(sK18,X0)
| ~ disjoint(relation_rng(sK18),X0) )
| ~ spl22_3 ),
inference(resolution,[],[f218,f177]) ).
fof(f246,plain,
( in(sK17(sK18),relation_rng(sK18))
| ~ function(sK18)
| spl22_1
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f230,f209]) ).
fof(f247,plain,
( ! [X0] :
( singleton(X0) != relation_inverse_image(sK18,singleton(sK17(sK18)))
| ~ function(sK18) )
| spl22_1
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f229,f209]) ).
fof(f255,plain,
( in(sK17(sK18),relation_rng(sK18))
| spl22_1
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f246,f172]) ).
fof(f256,plain,
( ! [X0] : singleton(X0) != relation_inverse_image(sK18,singleton(sK17(sK18)))
| spl22_1
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f247,f172]) ).
fof(f261,definition,
( spl22_4
<=> function(sK18) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f263,plain,
( function(sK18)
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f264,plain,
spl22_4,
inference(avatar_split_clause,[],[f172,f261]) ).
fof(f282,definition,
( spl22_5
<=> in(sK17(sK18),relation_rng(sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_5])],[avatar_definition]) ).
fof(f284,plain,
( in(sK17(sK18),relation_rng(sK18))
| ~ spl22_5 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,plain,
( spl22_5
| spl22_1
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f255,f216,f207,f282]) ).
fof(f287,plain,
( sK17(sK18) = apply(sK18,sK4(sK18,sK17(sK18)))
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl22_5 ),
inference(resolution,[],[f284,f201]) ).
fof(f288,plain,
( in(sK4(sK18,sK17(sK18)),relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl22_5 ),
inference(resolution,[],[f284,f200]) ).
fof(f301,plain,
( in(sK4(sK18,sK17(sK18)),relation_dom(sK18))
| ~ function(sK18)
| ~ spl22_3
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f288,f218]) ).
fof(f302,plain,
( sK17(sK18) = apply(sK18,sK4(sK18,sK17(sK18)))
| ~ function(sK18)
| ~ spl22_3
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f287,f218]) ).
fof(f306,plain,
( in(sK4(sK18,sK17(sK18)),relation_dom(sK18))
| ~ spl22_3
| ~ spl22_4
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f301,f263]) ).
fof(f307,plain,
( sK17(sK18) = apply(sK18,sK4(sK18,sK17(sK18)))
| ~ spl22_3
| ~ spl22_4
| ~ spl22_5 ),
inference(forward_subsumption_resolution,[],[f302,f263]) ).
fof(f312,definition,
( spl22_6
<=> in(sK4(sK18,sK17(sK18)),relation_dom(sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f314,plain,
( in(sK4(sK18,sK17(sK18)),relation_dom(sK18))
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f315,plain,
( spl22_6
| ~ spl22_3
| ~ spl22_4
| ~ spl22_5 ),
inference(avatar_split_clause,[],[f306,f282,f261,f216,f312]) ).
fof(f335,definition,
( spl22_7
<=> ! [X3] : subset(relation_inverse_image(sK18,singleton(X3)),singleton(sK20(X3))) ),
introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition]) ).
fof(f336,plain,
( ! [X3] : subset(relation_inverse_image(sK18,singleton(X3)),singleton(sK20(X3)))
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f337,plain,
( spl22_7
| spl22_1 ),
inference(avatar_split_clause,[],[f214,f207,f335]) ).
fof(f393,definition,
( spl22_10
<=> ! [X0] : singleton(X0) != relation_inverse_image(sK18,singleton(sK17(sK18))) ),
introduced(definition,[new_symbols(definition,[spl22_10])],[avatar_definition]) ).
fof(f394,plain,
( ! [X0] : singleton(X0) != relation_inverse_image(sK18,singleton(sK17(sK18)))
| ~ spl22_10 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f395,plain,
( spl22_10
| spl22_1
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f256,f216,f207,f393]) ).
fof(f654,definition,
( spl22_19
<=> sK17(sK18) = apply(sK18,sK4(sK18,sK17(sK18))) ),
introduced(definition,[new_symbols(definition,[spl22_19])],[avatar_definition]) ).
fof(f656,plain,
( sK17(sK18) = apply(sK18,sK4(sK18,sK17(sK18)))
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f657,plain,
( spl22_19
| ~ spl22_3
| ~ spl22_4
| ~ spl22_5 ),
inference(avatar_split_clause,[],[f307,f282,f261,f216,f654]) ).
fof(f756,plain,
( ! [X0] :
( ~ in(sK17(sK18),X0)
| in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0))
| ~ in(sK4(sK18,sK17(sK18)),relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18) )
| ~ spl22_19 ),
inference(superposition,[],[f192,f656]) ).
fof(f757,plain,
( ! [X0] :
( ~ in(sK17(sK18),X0)
| in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0))
| ~ relation(sK18)
| ~ function(sK18) )
| ~ spl22_6
| ~ spl22_19 ),
inference(forward_subsumption_resolution,[],[f756,f314]) ).
fof(f760,plain,
( ! [X0] :
( ~ in(sK17(sK18),X0)
| in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0))
| ~ function(sK18) )
| ~ spl22_3
| ~ spl22_6
| ~ spl22_19 ),
inference(forward_subsumption_resolution,[],[f757,f218]) ).
fof(f763,plain,
( ! [X0] :
( ~ in(sK17(sK18),X0)
| in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0)) )
| ~ spl22_3
| ~ spl22_4
| ~ spl22_6
| ~ spl22_19 ),
inference(forward_subsumption_resolution,[],[f760,f263]) ).
fof(f790,plain,
( ! [X0,X1] :
( relation_inverse_image(sK18,singleton(sK17(sK18))) != X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) )
| ~ spl22_10 ),
inference(superposition,[],[f394,f181]) ).
fof(f843,definition,
( spl22_23
<=> ! [X0] :
( empty_set = relation_inverse_image(sK18,X0)
| ~ disjoint(relation_rng(sK18),X0) ) ),
introduced(definition,[new_symbols(definition,[spl22_23])],[avatar_definition]) ).
fof(f844,plain,
( ! [X0] :
( empty_set = relation_inverse_image(sK18,X0)
| ~ disjoint(relation_rng(sK18),X0) )
| ~ spl22_23 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f845,plain,
( spl22_23
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f233,f216,f843]) ).
fof(f1063,definition,
( spl22_33
<=> empty_set = relation_inverse_image(sK18,singleton(sK17(sK18))) ),
introduced(definition,[new_symbols(definition,[spl22_33])],[avatar_definition]) ).
fof(f1064,plain,
( empty_set = relation_inverse_image(sK18,singleton(sK17(sK18)))
| ~ spl22_33 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f1065,plain,
( empty_set != relation_inverse_image(sK18,singleton(sK17(sK18)))
| spl22_33 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f1385,definition,
( spl22_46
<=> ! [X0] :
( ~ in(sK17(sK18),X0)
| in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl22_46])],[avatar_definition]) ).
fof(f1386,plain,
( ! [X0] :
( in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0))
| ~ in(sK17(sK18),X0) )
| ~ spl22_46 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f1387,plain,
( spl22_46
| ~ spl22_3
| ~ spl22_4
| ~ spl22_6
| ~ spl22_19 ),
inference(avatar_split_clause,[],[f763,f654,f312,f261,f216,f1385]) ).
fof(f1485,definition,
( spl22_51
<=> ! [X0,X1] :
( relation_inverse_image(sK18,singleton(sK17(sK18))) != X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl22_51])],[avatar_definition]) ).
fof(f1486,plain,
( ! [X0,X1] :
( relation_inverse_image(sK18,singleton(sK17(sK18))) != X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) )
| ~ spl22_51 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f1487,plain,
( spl22_51
| ~ spl22_10 ),
inference(avatar_split_clause,[],[f790,f393,f1485]) ).
fof(f1497,plain,
( ! [X0] :
( empty_set = relation_inverse_image(sK18,singleton(sK17(sK18)))
| ~ subset(relation_inverse_image(sK18,singleton(sK17(sK18))),singleton(X0)) )
| ~ spl22_51 ),
inference(equality_resolution,[],[f1486]) ).
fof(f1498,plain,
( ! [X0] : ~ subset(relation_inverse_image(sK18,singleton(sK17(sK18))),singleton(X0))
| spl22_33
| ~ spl22_51 ),
inference(forward_subsumption_resolution,[],[f1497,f1065]) ).
fof(f1506,definition,
( spl22_52
<=> ! [X0] : ~ subset(relation_inverse_image(sK18,singleton(sK17(sK18))),singleton(X0)) ),
introduced(definition,[new_symbols(definition,[spl22_52])],[avatar_definition]) ).
fof(f1507,plain,
( ! [X0] : ~ subset(relation_inverse_image(sK18,singleton(sK17(sK18))),singleton(X0))
| ~ spl22_52 ),
inference(avatar_component_clause,[],[f1506]) ).
fof(f1508,plain,
( spl22_52
| spl22_33
| ~ spl22_51 ),
inference(avatar_split_clause,[],[f1498,f1485,f1063,f1506]) ).
fof(f1509,plain,
( $false
| ~ spl22_7
| ~ spl22_52 ),
inference(resolution,[],[f1507,f336]) ).
fof(f1523,plain,
( ~ spl22_7
| ~ spl22_52 ),
inference(avatar_contradiction_clause,[],[f1509]) ).
fof(f1568,plain,
( in(sK4(sK18,sK17(sK18)),empty_set)
| ~ in(sK17(sK18),singleton(sK17(sK18)))
| ~ spl22_33
| ~ spl22_46 ),
inference(superposition,[],[f1386,f1064]) ).
fof(f1585,plain,
( in(sK4(sK18,sK17(sK18)),empty_set)
| ~ spl22_33
| ~ spl22_46 ),
inference(forward_subsumption_resolution,[],[f1568,f196]) ).
fof(f1741,definition,
( spl22_57
<=> in(sK4(sK18,sK17(sK18)),empty_set) ),
introduced(definition,[new_symbols(definition,[spl22_57])],[avatar_definition]) ).
fof(f1743,plain,
( in(sK4(sK18,sK17(sK18)),empty_set)
| ~ spl22_57 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f1744,plain,
( spl22_57
| ~ spl22_33
| ~ spl22_46 ),
inference(avatar_split_clause,[],[f1585,f1385,f1063,f1741]) ).
fof(f1751,plain,
( ! [X0] :
( in(sK4(sK18,sK17(sK18)),X0)
| ~ empty(X0) )
| ~ spl22_57 ),
inference(superposition,[],[f1743,f189]) ).
fof(f1753,plain,
( ! [X0] : ~ empty(X0)
| ~ spl22_57 ),
inference(forward_subsumption_resolution,[],[f1751,f190]) ).
fof(f1772,plain,
( $false
| ~ spl22_57 ),
inference(backward_subsumption_resolution,[],[f160,f1753]) ).
fof(f1779,plain,
~ spl22_57,
inference(avatar_contradiction_clause,[],[f1772]) ).
fof(f1846,plain,
( ! [X0] :
( ~ subset(empty_set,singleton(X0))
| ~ disjoint(relation_rng(sK18),singleton(sK19)) )
| ~ spl22_2
| ~ spl22_23 ),
inference(superposition,[],[f212,f844]) ).
fof(f1847,plain,
( ! [X0] :
( ~ subset(singleton(sK16(sK18,sK19)),singleton(X0))
| ~ in(sK19,relation_rng(sK18))
| ~ one_to_one(sK18)
| ~ relation(sK18)
| ~ function(sK18) )
| ~ spl22_2 ),
inference(superposition,[],[f212,f171]) ).
fof(f1860,plain,
( ! [X0] :
( ~ subset(singleton(sK16(sK18,sK19)),singleton(X0))
| ~ in(sK19,relation_rng(sK18))
| ~ relation(sK18)
| ~ function(sK18) )
| ~ spl22_1
| ~ spl22_2 ),
inference(forward_subsumption_resolution,[],[f1847,f208]) ).
fof(f1861,plain,
( ~ disjoint(relation_rng(sK18),singleton(sK19))
| ~ spl22_2
| ~ spl22_23 ),
inference(forward_subsumption_resolution,[],[f1846,f180]) ).
fof(f1866,plain,
( ! [X0] :
( ~ subset(singleton(sK16(sK18,sK19)),singleton(X0))
| ~ in(sK19,relation_rng(sK18))
| ~ function(sK18) )
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f1860,f218]) ).
fof(f1867,plain,
( ! [X0] :
( ~ subset(singleton(sK16(sK18,sK19)),singleton(X0))
| ~ in(sK19,relation_rng(sK18)) )
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_4 ),
inference(forward_subsumption_resolution,[],[f1866,f263]) ).
fof(f1869,definition,
( spl22_58
<=> in(sK19,relation_rng(sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_58])],[avatar_definition]) ).
fof(f1871,plain,
( ~ in(sK19,relation_rng(sK18))
| spl22_58 ),
inference(avatar_component_clause,[],[f1869]) ).
fof(f1873,definition,
( spl22_59
<=> ! [X0] : ~ subset(singleton(sK16(sK18,sK19)),singleton(X0)) ),
introduced(definition,[new_symbols(definition,[spl22_59])],[avatar_definition]) ).
fof(f1874,plain,
( ! [X0] : ~ subset(singleton(sK16(sK18,sK19)),singleton(X0))
| ~ spl22_59 ),
inference(avatar_component_clause,[],[f1873]) ).
fof(f1875,plain,
( ~ spl22_58
| spl22_59
| ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f1867,f261,f216,f211,f207,f1873,f1869]) ).
fof(f1876,plain,
( disjoint(singleton(sK19),relation_rng(sK18))
| spl22_58 ),
inference(resolution,[],[f1871,f187]) ).
fof(f2397,definition,
( spl22_85
<=> disjoint(singleton(sK19),relation_rng(sK18)) ),
introduced(definition,[new_symbols(definition,[spl22_85])],[avatar_definition]) ).
fof(f2399,plain,
( disjoint(singleton(sK19),relation_rng(sK18))
| ~ spl22_85 ),
inference(avatar_component_clause,[],[f2397]) ).
fof(f2400,plain,
( spl22_85
| spl22_58 ),
inference(avatar_split_clause,[],[f1876,f1869,f2397]) ).
fof(f2401,plain,
( disjoint(relation_rng(sK18),singleton(sK19))
| ~ spl22_85 ),
inference(resolution,[],[f2399,f168]) ).
fof(f2411,plain,
( $false
| ~ spl22_2
| ~ spl22_23
| ~ spl22_85 ),
inference(forward_subsumption_resolution,[],[f2401,f1861]) ).
fof(f2412,plain,
( ~ spl22_2
| ~ spl22_23
| ~ spl22_85 ),
inference(avatar_contradiction_clause,[],[f2411]) ).
fof(f2437,plain,
( $false
| ~ spl22_59 ),
inference(resolution,[],[f1874,f203]) ).
fof(f2445,plain,
~ spl22_59,
inference(avatar_contradiction_clause,[],[f2437]) ).
cnf(s1,plain,
( ~ spl22_1
| spl22_2 ),
inference(sat_conversion,[],[f213]) ).
cnf(s2,plain,
spl22_3,
inference(sat_conversion,[],[f219]) ).
cnf(s3,plain,
spl22_4,
inference(sat_conversion,[],[f264]) ).
cnf(s4,plain,
( spl22_1
| ~ spl22_3
| spl22_5 ),
inference(sat_conversion,[],[f285]) ).
cnf(s5,plain,
( ~ spl22_3
| ~ spl22_4
| ~ spl22_5
| spl22_6 ),
inference(sat_conversion,[],[f315]) ).
cnf(s6,plain,
( spl22_1
| spl22_7 ),
inference(sat_conversion,[],[f337]) ).
cnf(s9,plain,
( spl22_1
| ~ spl22_3
| spl22_10 ),
inference(sat_conversion,[],[f395]) ).
cnf(s18,plain,
( ~ spl22_3
| ~ spl22_4
| ~ spl22_5
| spl22_19 ),
inference(sat_conversion,[],[f657]) ).
cnf(s24,plain,
( ~ spl22_3
| spl22_23 ),
inference(sat_conversion,[],[f845]) ).
cnf(s46,plain,
( ~ spl22_3
| ~ spl22_4
| ~ spl22_6
| ~ spl22_19
| spl22_46 ),
inference(sat_conversion,[],[f1387]) ).
cnf(s51,plain,
( ~ spl22_10
| spl22_51 ),
inference(sat_conversion,[],[f1487]) ).
cnf(s52,plain,
( spl22_33
| ~ spl22_51
| spl22_52 ),
inference(sat_conversion,[],[f1508]) ).
cnf(s53,plain,
( ~ spl22_7
| ~ spl22_52 ),
inference(sat_conversion,[],[f1523]) ).
cnf(s60,plain,
( ~ spl22_33
| ~ spl22_46
| spl22_57 ),
inference(sat_conversion,[],[f1744]) ).
cnf(s68,plain,
~ spl22_57,
inference(sat_conversion,[],[f1779]) ).
cnf(s70,plain,
( ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_4
| ~ spl22_58
| spl22_59 ),
inference(sat_conversion,[],[f1875]) ).
cnf(s96,plain,
( spl22_58
| spl22_85 ),
inference(sat_conversion,[],[f2400]) ).
cnf(s97,plain,
( ~ spl22_2
| ~ spl22_23
| ~ spl22_85 ),
inference(sat_conversion,[],[f2412]) ).
cnf(s101,plain,
~ spl22_59,
inference(sat_conversion,[],[f2445]) ).
cnf(s102,plain,
( ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_4
| ~ spl22_58 ),
inference(rat,[],[s70,s101]) ).
cnf(s103,plain,
( ~ spl22_33
| ~ spl22_46 ),
inference(rat,[],[s60,s68]) ).
cnf(s110,plain,
spl22_23,
inference(rat,[],[s24,s2]) ).
cnf(s128,plain,
spl22_1,
inference(rat,[],[s103,s46,s52,s5,s18,s53,s51,s4,s6,s9,s3,s2]) ).
cnf(s132,plain,
spl22_2,
inference(rat,[],[s1,s128]) ).
cnf(s134,plain,
~ spl22_85,
inference(rat,[],[s97,s110,s132]) ).
cnf(s140,plain,
~ spl22_58,
inference(rat,[],[s102,s128,s3,s2,s132]) ).
cnf(s142,plain,
$false,
inference(rat,[],[s96,s134,s140]) ).
fof(f2446,plain,
$false,
inference(avatar_sat_refutation,[],[s142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU078+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:32:39 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.08/1.65 % (1843530)Detected formulas, will run a generic FOF schedule.
% 5.08/1.65 % (1843537)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=3247750395:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.08/1.65 % (1843538)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3499494158:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.08/1.65 % (1843539)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2837666019:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.08/1.65 % (1843535)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=653025414:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.08/1.65 % (1843541)dis-21_1_sil=8000:lcm=predicate:random_seed=1404692418: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)
% 5.08/1.65 % (1843536)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=1100205793:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.08/1.65 % (1843540)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=863402969:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.08/1.65 % (1843538)Instruction limit reached!
% 5.08/1.65 % (1843538)------------------------------
% 5.08/1.65 % (1843538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843538)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843538)Termination reason: Instruction limit
% 5.08/1.65 % (1843538)Termination phase: Saturation
% 5.08/1.65 % (1843538)Time elapsed: 0.060 s
% 5.08/1.65 % (1843538)Peak memory usage: 89 MB
% 5.08/1.65 % (1843538)Instructions burned: 109 (million)
% 5.08/1.65 % (1843541)Instruction limit reached!
% 5.08/1.65 % (1843541)------------------------------
% 5.08/1.65 % (1843541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843541)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843541)Termination reason: Instruction limit
% 5.08/1.65 % (1843541)Termination phase: Saturation
% 5.08/1.65 % (1843541)Time elapsed: 0.072 s
% 5.08/1.65 % (1843541)Peak memory usage: 90 MB
% 5.08/1.65 % (1843541)Instructions burned: 130 (million)
% 5.08/1.65 % (1843539)Instruction limit reached!
% 5.08/1.65 % (1843539)------------------------------
% 5.08/1.65 % (1843539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843539)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843539)Termination reason: Instruction limit
% 5.08/1.65 % (1843539)Termination phase: Saturation
% 5.08/1.65 % (1843539)Time elapsed: 0.073 s
% 5.08/1.65 % (1843539)Peak memory usage: 88 MB
% 5.08/1.65 % (1843539)Instructions burned: 121 (million)
% 5.08/1.65 % (1843540)Instruction limit reached!
% 5.08/1.65 % (1843540)------------------------------
% 5.08/1.65 % (1843540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843540)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843540)Termination reason: Instruction limit
% 5.08/1.65 % (1843540)Termination phase: Saturation
% 5.08/1.65 % (1843540)Time elapsed: 0.094 s
% 5.08/1.65 % (1843540)Peak memory usage: 90 MB
% 5.08/1.65 % (1843540)Instructions burned: 139 (million)
% 5.08/1.65 % (1843549)lrs+10_1_sil=8000:sp=occurrence:random_seed=2856442970:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.08/1.65 % (1843550)lrs+10_1_sil=32000:urr=on:br=off:random_seed=750267487:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.08/1.65 % (1843551)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1732968984:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.08/1.65 % (1843550)Refutation not found, incomplete strategy
% 5.08/1.65 % (1843550)------------------------------
% 5.08/1.65 % (1843550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843550)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843550)Termination reason: Refutation not found, incomplete strategy
% 5.08/1.65 % (1843550)Time elapsed: 0.004 s
% 5.08/1.65 % (1843550)Peak memory usage: 88 MB
% 5.08/1.65 % (1843550)Instructions burned: 4 (million)
% 5.08/1.65 % (1843552)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=4246343969:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.08/1.65 % (1843549)Instruction limit reached!
% 5.08/1.65 % (1843549)------------------------------
% 5.08/1.65 % (1843549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843549)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843549)Termination reason: Instruction limit
% 5.08/1.65 % (1843549)Termination phase: Saturation
% 5.08/1.65 % (1843549)Time elapsed: 0.167 s
% 5.08/1.65 % (1843549)Peak memory usage: 91 MB
% 5.08/1.65 % (1843549)Instructions burned: 286 (million)
% 5.08/1.65 % (1843552)Instruction limit reached!
% 5.08/1.65 % (1843552)------------------------------
% 5.08/1.65 % (1843552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843552)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843552)Termination reason: Instruction limit
% 5.08/1.65 % (1843552)Termination phase: Saturation
% 5.08/1.65 % (1843552)Time elapsed: 0.130 s
% 5.08/1.65 % (1843552)Peak memory usage: 91 MB
% 5.08/1.65 % (1843552)Instructions burned: 249 (million)
% 5.08/1.65 % (1843551)Instruction limit reached!
% 5.08/1.65 % (1843551)------------------------------
% 5.08/1.65 % (1843551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.65 % (1843551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.65 % (1843551)CaDiCaL version: 2.1.3
% 5.08/1.65 % (1843551)Termination reason: Instruction limit
% 5.08/1.65 % (1843551)Termination phase: Saturation
% 5.08/1.65 % (1843551)Time elapsed: 0.189 s
% 5.08/1.65 % (1843551)Peak memory usage: 92 MB
% 5.08/1.65 % (1843551)Instructions burned: 327 (million)
% 5.08/1.65 % (1843550)------------------------------
% 5.08/1.65 % (1843550)------------------------------
% 5.08/1.65 % (1843537)First to succeed.
% 5.08/1.65 % (1843537)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1843530"
% 5.08/1.65 % (1843557)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2379804769:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.08/1.65 % (1843558)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=528907205:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.08/1.65 % (1843559)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1515260858:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.08/1.65 % (1843537)Refutation found. Thanks to Tanya!
% 5.08/1.65 % SZS status Theorem for theBenchmark
% 5.08/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 6.30/1.84 % (1843537)------------------------------
% 6.30/1.84 % (1843537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.30/1.84 % (1843537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.30/1.84 % (1843537)CaDiCaL version: 2.1.3
% 6.30/1.84 % (1843537)Termination reason: Refutation
% 6.30/1.84 % (1843537)Time elapsed: 0.517 s
% 6.30/1.84 % (1843537)Peak memory usage: 133 MB
% 6.30/1.84 % (1843537)Instructions burned: 1330 (million)
% 6.30/1.84 % (1843537)------------------------------
% 6.30/1.84 % (1843537)------------------------------
% 6.30/1.84 % (1843530)Success in time 0.807 s
% 6.30/1.84 % Vampire exiting
%------------------------------------------------------------------------------