%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU442+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:49:06 PM UTC 2026
% Result : Theorem 10.40s 2.35s
% Output : Refutation 11.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 31
% Syntax : Number of formulae : 223 ( 34 unt; 11 def)
% Number of atoms : 837 ( 80 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1079 ( 465 ~; 492 |; 73 &)
% ( 26 <=>; 22 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 8 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 8 con; 0-5 aty)
% Number of variables : 467 ( 1 sgn 424 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> ( r1_tarski(X2,k1_funct_5(X3))
<=> r1_tarski(X2,k10_relset_1(X0,X0,k9_relset_2(X0,X1,X0,X3,k6_relset_1(X0,X1,X3)),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> ( r1_tarski(X2,k1_funct_5(X3))
<=> r1_tarski(X2,k10_relset_1(X0,X0,k9_relset_2(X0,X1,X0,X3,k6_relset_1(X0,X1,X3)),X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( X1 = k1_funct_5(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> ? [X3] : r2_hidden(k4_tarski(X2,X3),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_5) ).
fof(f10,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f11,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f12,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ( X1 = k4_relat_1(X0)
<=> ! [X2,X3] :
( r2_hidden(k4_tarski(X2,X3),X1)
<=> r2_hidden(k4_tarski(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f13,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ( X2 = k5_relat_1(X0,X1)
<=> ! [X3,X4] :
( r2_hidden(k4_tarski(X3,X4),X2)
<=> ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f22,axiom,
! [X0] :
( v1_relat_1(X0)
=> v1_relat_1(k4_relat_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f24,axiom,
! [X0,X1] :
( ( v1_relat_1(X0)
& v1_relat_1(X1) )
=> v1_relat_1(k5_relat_1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f25,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_1) ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
=> m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_2) ).
fof(f30,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f51,axiom,
! [X0,X1,X2,X3] :
( m1_relset_1(X2,X0,X1)
=> k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
fof(f52,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> k6_relset_1(X0,X1,X2) = k4_relat_1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_relset_1) ).
fof(f53,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
=> k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
fof(f54,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f55,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f57,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_relat_1) ).
fof(f67,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f55]) ).
fof(f70,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( r1_tarski(X2,k1_funct_5(X3))
<~> r1_tarski(X2,k10_relset_1(X0,X0,k9_relset_2(X0,X1,X0,X3,k6_relset_1(X0,X1,X3)),X2)) )
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f73,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f74,plain,
! [X0] :
( ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) ) ) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f75,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( X1 = k4_relat_1(X0)
<=> ! [X2,X3] :
( r2_hidden(k4_tarski(X2,X3),X1)
<=> r2_hidden(k4_tarski(X3,X2),X0) ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k5_relat_1(X0,X1)
<=> ! [X3,X4] :
( r2_hidden(k4_tarski(X3,X4),X2)
<=> ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) ) ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f79,plain,
! [X0] :
( v1_relat_1(k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f80,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f81,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f84,plain,
! [X0,X1,X2,X3,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f97,plain,
! [X0,X1,X2] :
( k6_relset_1(X0,X1,X2) = k4_relat_1(X2)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4] :
( k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4] :
( k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0))
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f113,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( ~ r1_tarski(X2,k10_relset_1(X0,X0,k9_relset_2(X0,X1,X0,X3,k6_relset_1(X0,X1,X3)),X2))
| ~ r1_tarski(X2,k1_funct_5(X3)) )
& ( r1_tarski(X2,k10_relset_1(X0,X0,k9_relset_2(X0,X1,X0,X3,k6_relset_1(X0,X1,X3)),X2))
| r1_tarski(X2,k1_funct_5(X3)) )
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(nnf_transformation,[],[f70]) ).
fof(f114,plain,
? [X0,X1,X2] :
( ? [X3] :
( ( ~ r1_tarski(X2,k10_relset_1(X0,X0,k9_relset_2(X0,X1,X0,X3,k6_relset_1(X0,X1,X3)),X2))
| ~ r1_tarski(X2,k1_funct_5(X3)) )
& ( r1_tarski(X2,k10_relset_1(X0,X0,k9_relset_2(X0,X1,X0,X3,k6_relset_1(X0,X1,X3)),X2))
| r1_tarski(X2,k1_funct_5(X3)) )
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
( ( ~ r1_tarski(sK2,k10_relset_1(sK0,sK0,k9_relset_2(sK0,sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK3)),sK2))
| ~ r1_tarski(sK2,k1_funct_5(sK3)) )
& ( r1_tarski(sK2,k10_relset_1(sK0,sK0,k9_relset_2(sK0,sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK3)),sK2))
| r1_tarski(sK2,k1_funct_5(sK3)) )
& m2_relset_1(sK3,sK0,sK1)
& m1_subset_1(sK2,k1_zfmisc_1(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f114]) ).
fof(f116,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = k9_relat_1(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ r2_hidden(k4_tarski(X4,X3),X0)
| ~ r2_hidden(X4,X1) )
| ~ r2_hidden(X3,X2) )
& ( ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ! [X4] :
( ~ r2_hidden(k4_tarski(X4,X3),X0)
| ~ r2_hidden(X4,X1) ) )
& ( ? [X4] :
( r2_hidden(k4_tarski(X4,X3),X0)
& r2_hidden(X4,X1) )
| ~ r2_hidden(X3,X2) ) )
| k9_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X0) ),
inference(nnf_transformation,[],[f74]) ).
fof(f117,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = k9_relat_1(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ r2_hidden(k4_tarski(X4,X3),X0)
| ~ r2_hidden(X4,X1) )
| ~ r2_hidden(X3,X2) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X5,X3),X0)
& r2_hidden(X5,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X6] :
( ( r2_hidden(X6,X2)
| ! [X7] :
( ~ r2_hidden(k4_tarski(X7,X6),X0)
| ~ r2_hidden(X7,X1) ) )
& ( ? [X8] :
( r2_hidden(k4_tarski(X8,X6),X0)
& r2_hidden(X8,X1) )
| ~ r2_hidden(X6,X2) ) )
| k9_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X0) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = k9_relat_1(X0,X1)
| ( ( ! [X4] :
( ~ r2_hidden(k4_tarski(X4,sK4(X0,X1,X2)),X0)
| ~ r2_hidden(X4,X1) )
| ~ r2_hidden(sK4(X0,X1,X2),X2) )
& ( ( r2_hidden(k4_tarski(sK5(X0,X1,X2),sK4(X0,X1,X2)),X0)
& r2_hidden(sK5(X0,X1,X2),X1) )
| r2_hidden(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( r2_hidden(X6,X2)
| ! [X7] :
( ~ r2_hidden(k4_tarski(X7,X6),X0)
| ~ r2_hidden(X7,X1) ) )
& ( ( r2_hidden(k4_tarski(sK6(X0,X1,X6),X6),X0)
& r2_hidden(sK6(X0,X1,X6),X1) )
| ~ r2_hidden(X6,X2) ) )
| k9_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X5,sK5(X0,X1,X2)),skolemize(X8,sK6(X0,X1,X6))],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ( X1 = k1_funct_5(X0)
| ? [X2] :
( ( ! [X3] : ~ r2_hidden(k4_tarski(X2,X3),X0)
| ~ r2_hidden(X2,X1) )
& ( ? [X3] : r2_hidden(k4_tarski(X2,X3),X0)
| r2_hidden(X2,X1) ) ) )
& ( ! [X2] :
( ( r2_hidden(X2,X1)
| ! [X3] : ~ r2_hidden(k4_tarski(X2,X3),X0) )
& ( ? [X3] : r2_hidden(k4_tarski(X2,X3),X0)
| ~ r2_hidden(X2,X1) ) )
| k1_funct_5(X0) != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f120,plain,
! [X0,X1] :
( ( X1 = k1_funct_5(X0)
| ? [X2] :
( ( ! [X3] : ~ r2_hidden(k4_tarski(X2,X3),X0)
| ~ r2_hidden(X2,X1) )
& ( ? [X4] : r2_hidden(k4_tarski(X2,X4),X0)
| r2_hidden(X2,X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] : ~ r2_hidden(k4_tarski(X5,X6),X0) )
& ( ? [X7] : r2_hidden(k4_tarski(X5,X7),X0)
| ~ r2_hidden(X5,X1) ) )
| k1_funct_5(X0) != X1 ) ),
inference(rectify,[],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ( X1 = k1_funct_5(X0)
| ( ( ! [X3] : ~ r2_hidden(k4_tarski(sK7(X0,X1),X3),X0)
| ~ r2_hidden(sK7(X0,X1),X1) )
& ( r2_hidden(k4_tarski(sK7(X0,X1),sK8(X0,X1)),X0)
| r2_hidden(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] : ~ r2_hidden(k4_tarski(X5,X6),X0) )
& ( r2_hidden(k4_tarski(X5,sK9(X0,X5)),X0)
| ~ r2_hidden(X5,X1) ) )
| k1_funct_5(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f120]) ).
fof(f125,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f126,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK11(X0,X1),X1)
& r2_hidden(sK11(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f126]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k4_relat_1(X0)
| ? [X2,X3] :
( ( ~ r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(k4_tarski(X2,X3),X1) )
& ( r2_hidden(k4_tarski(X3,X2),X0)
| r2_hidden(k4_tarski(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( r2_hidden(k4_tarski(X2,X3),X1)
| ~ r2_hidden(k4_tarski(X3,X2),X0) )
& ( r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(k4_tarski(X2,X3),X1) ) )
| k4_relat_1(X0) != X1 ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k4_relat_1(X0)
| ? [X2,X3] :
( ( ~ r2_hidden(k4_tarski(X3,X2),X0)
| ~ r2_hidden(k4_tarski(X2,X3),X1) )
& ( r2_hidden(k4_tarski(X3,X2),X0)
| r2_hidden(k4_tarski(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( r2_hidden(k4_tarski(X4,X5),X1)
| ~ r2_hidden(k4_tarski(X5,X4),X0) )
& ( r2_hidden(k4_tarski(X5,X4),X0)
| ~ r2_hidden(k4_tarski(X4,X5),X1) ) )
| k4_relat_1(X0) != X1 ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k4_relat_1(X0)
| ( ( ~ r2_hidden(k4_tarski(sK13(X0,X1),sK12(X0,X1)),X0)
| ~ r2_hidden(k4_tarski(sK12(X0,X1),sK13(X0,X1)),X1) )
& ( r2_hidden(k4_tarski(sK13(X0,X1),sK12(X0,X1)),X0)
| r2_hidden(k4_tarski(sK12(X0,X1),sK13(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( r2_hidden(k4_tarski(X4,X5),X1)
| ~ r2_hidden(k4_tarski(X5,X4),X0) )
& ( r2_hidden(k4_tarski(X5,X4),X0)
| ~ r2_hidden(k4_tarski(X4,X5),X1) ) )
| k4_relat_1(X0) != X1 ) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f129]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) )
| r2_hidden(k4_tarski(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( r2_hidden(k4_tarski(X3,X4),X2)
| ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) ) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) )
& ( ? [X6] :
( r2_hidden(k4_tarski(X3,X6),X0)
& r2_hidden(k4_tarski(X6,X4),X1) )
| r2_hidden(k4_tarski(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( r2_hidden(k4_tarski(X7,X8),X2)
| ! [X9] :
( ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1) ) )
& ( ? [X10] :
( r2_hidden(k4_tarski(X7,X10),X0)
& r2_hidden(k4_tarski(X10,X8),X1) )
| ~ r2_hidden(k4_tarski(X7,X8),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(rectify,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ( ( ! [X5] :
( ~ r2_hidden(k4_tarski(sK14(X0,X1,X2),X5),X0)
| ~ r2_hidden(k4_tarski(X5,sK15(X0,X1,X2)),X1) )
| ~ r2_hidden(k4_tarski(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2) )
& ( ( r2_hidden(k4_tarski(sK14(X0,X1,X2),sK16(X0,X1,X2)),X0)
& r2_hidden(k4_tarski(sK16(X0,X1,X2),sK15(X0,X1,X2)),X1) )
| r2_hidden(k4_tarski(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( r2_hidden(k4_tarski(X7,X8),X2)
| ! [X9] :
( ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1) ) )
& ( ( r2_hidden(k4_tarski(X7,sK17(X0,X1,X7,X8)),X0)
& r2_hidden(k4_tarski(sK17(X0,X1,X7,X8),X8),X1) )
| ~ r2_hidden(k4_tarski(X7,X8),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X3,sK14(X0,X1,X2)),skolemize(X4,sK15(X0,X1,X2)),skolemize(X6,sK16(X0,X1,X2)),skolemize(X10,sK17(X0,X1,X7,X8))],[f132]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f145,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f115]) ).
fof(f146,plain,
( r1_tarski(sK2,k10_relset_1(sK0,sK0,k9_relset_2(sK0,sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK3)),sK2))
| r1_tarski(sK2,k1_funct_5(sK3)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f147,plain,
( ~ r1_tarski(sK2,k10_relset_1(sK0,sK0,k9_relset_2(sK0,sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK3)),sK2))
| ~ r1_tarski(sK2,k1_funct_5(sK3)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f151,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f153,plain,
! [X2,X0,X1,X6] :
( r2_hidden(k4_tarski(sK6(X0,X1,X6),X6),X0)
| ~ r2_hidden(X6,X2)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f154,plain,
! [X2,X0,X1,X6,X7] :
( r2_hidden(X6,X2)
| ~ r2_hidden(k4_tarski(X7,X6),X0)
| ~ r2_hidden(X7,X1)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f158,plain,
! [X0,X1,X5] :
( r2_hidden(k4_tarski(X5,sK9(X0,X5)),X0)
| ~ r2_hidden(X5,X1)
| k1_funct_5(X0) != X1 ),
inference(cnf_transformation,[],[f121]) ).
fof(f159,plain,
! [X0,X1,X6,X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(k4_tarski(X5,X6),X0)
| k1_funct_5(X0) != X1 ),
inference(cnf_transformation,[],[f121]) ).
fof(f166,plain,
! [X3,X0,X1] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f167,plain,
! [X0,X1] :
( r2_hidden(sK11(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f168,plain,
! [X0,X1] :
( ~ r2_hidden(sK11(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f169,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f170,plain,
! [X0,X1,X4,X5] :
( r2_hidden(k4_tarski(X5,X4),X0)
| ~ r2_hidden(k4_tarski(X4,X5),X1)
| k4_relat_1(X0) != X1
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f171,plain,
! [X0,X1,X4,X5] :
( r2_hidden(k4_tarski(X4,X5),X1)
| ~ r2_hidden(k4_tarski(X5,X4),X0)
| k4_relat_1(X0) != X1
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f176,plain,
! [X2,X0,X1,X8,X9,X7] :
( r2_hidden(k4_tarski(X7,X8),X2)
| ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f181,plain,
! [X0] :
( v1_relat_1(k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f182,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f183,plain,
! [X2,X0,X1] :
( m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f184,plain,
! [X2,X3,X0,X1,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f185,plain,
! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f96]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| k6_relset_1(X0,X1,X2) = k4_relat_1(X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f217,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
inference(cnf_transformation,[],[f99]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f220,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f67]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f236,plain,
! [X2,X0,X1,X6,X7] :
( r2_hidden(X6,X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| ~ r2_hidden(X7,X1)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f154,f169]) ).
fof(f237,plain,
! [X2,X0,X1,X6] :
( r2_hidden(k2_tarski(k2_tarski(sK6(X0,X1,X6),X6),k1_tarski(sK6(X0,X1,X6))),X0)
| ~ r2_hidden(X6,X2)
| k9_relat_1(X0,X1) != X2
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f153,f169]) ).
fof(f240,plain,
! [X0,X1,X6,X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X5,X6),k1_tarski(X5)),X0)
| k1_funct_5(X0) != X1 ),
inference(definition_unfolding,[],[f159,f169]) ).
fof(f241,plain,
! [X0,X1,X5] :
( r2_hidden(k2_tarski(k2_tarski(X5,sK9(X0,X5)),k1_tarski(X5)),X0)
| ~ r2_hidden(X5,X1)
| k1_funct_5(X0) != X1 ),
inference(definition_unfolding,[],[f158,f169]) ).
fof(f244,plain,
! [X0,X1,X4,X5] :
( r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| k4_relat_1(X0) != X1
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f171,f169,f169]) ).
fof(f245,plain,
! [X0,X1,X4,X5] :
( r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),X1)
| k4_relat_1(X0) != X1
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f170,f169,f169]) ).
fof(f249,plain,
! [X2,X0,X1,X8,X9,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f176,f169,f169,f169]) ).
fof(f252,plain,
! [X0,X1,X6,X7] :
( ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| r2_hidden(X6,k9_relat_1(X0,X1))
| ~ r2_hidden(X7,X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f236]) ).
fof(f253,plain,
! [X0,X1,X6] :
( r2_hidden(k2_tarski(k2_tarski(sK6(X0,X1,X6),X6),k1_tarski(sK6(X0,X1,X6))),X0)
| ~ r2_hidden(X6,k9_relat_1(X0,X1))
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f237]) ).
fof(f255,plain,
! [X0,X6,X5] :
( ~ r2_hidden(k2_tarski(k2_tarski(X5,X6),k1_tarski(X5)),X0)
| r2_hidden(X5,k1_funct_5(X0)) ),
inference(equality_resolution,[],[f240]) ).
fof(f256,plain,
! [X0,X5] :
( r2_hidden(k2_tarski(k2_tarski(X5,sK9(X0,X5)),k1_tarski(X5)),X0)
| ~ r2_hidden(X5,k1_funct_5(X0)) ),
inference(equality_resolution,[],[f241]) ).
fof(f260,plain,
! [X0,X4,X5] :
( r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),k4_relat_1(X0))
| ~ r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| ~ v1_relat_1(k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f244]) ).
fof(f261,plain,
! [X0,X4,X5] :
( r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),k4_relat_1(X0))
| ~ v1_relat_1(k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f245]) ).
fof(f262,plain,
! [X0,X1,X8,X9,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| ~ v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f249]) ).
fof(f265,definition,
sF26 = k6_relset_1(sK0,sK1,sK3),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f266,plain,
k6_relset_1(sK0,sK1,sK3) = sF26,
inference(reorient_equations,[],[f265]) ).
fof(f267,definition,
sF27 = k9_relset_2(sK0,sK1,sK0,sK3,sF26),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f268,plain,
k9_relset_2(sK0,sK1,sK0,sK3,sF26) = sF27,
inference(reorient_equations,[],[f267]) ).
fof(f269,definition,
sF28 = k10_relset_1(sK0,sK0,sF27,sK2),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f270,plain,
k10_relset_1(sK0,sK0,sF27,sK2) = sF28,
inference(reorient_equations,[],[f269]) ).
fof(f271,definition,
sF29 = k1_funct_5(sK3),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f272,plain,
k1_funct_5(sK3) = sF29,
inference(reorient_equations,[],[f271]) ).
fof(f273,plain,
( ~ r1_tarski(sK2,sF28)
| ~ r1_tarski(sK2,sF29) ),
inference(definition_folding,[],[f147,f272,f270,f268,f266]) ).
fof(f274,plain,
( r1_tarski(sK2,sF28)
| r1_tarski(sK2,sF29) ),
inference(definition_folding,[],[f146,f272,f270,f268,f266]) ).
fof(f280,plain,
! [X0,X1,X8,X9,X7] :
( ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f262,f182]) ).
fof(f281,plain,
! [X0,X4,X5] :
( ~ r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),k4_relat_1(X0))
| r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f261,f181]) ).
fof(f282,plain,
! [X0,X4,X5] :
( ~ r2_hidden(k2_tarski(k2_tarski(X5,X4),k1_tarski(X5)),X0)
| r2_hidden(k2_tarski(k2_tarski(X4,X5),k1_tarski(X4)),k4_relat_1(X0))
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f260,f181]) ).
fof(f284,definition,
( spl31_1
<=> r1_tarski(sK2,sF29) ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
fof(f285,plain,
( ~ r1_tarski(sK2,sF29)
| spl31_1 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f286,plain,
( r1_tarski(sK2,sF29)
| ~ spl31_1 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f288,definition,
( spl31_2
<=> r1_tarski(sK2,sF28) ),
introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
fof(f289,plain,
( ~ r1_tarski(sK2,sF28)
| spl31_2 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( r1_tarski(sK2,sF28)
| ~ spl31_2 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f291,plain,
( spl31_1
| spl31_2 ),
inference(avatar_split_clause,[],[f274,f288,f284]) ).
fof(f292,plain,
( ~ spl31_1
| ~ spl31_2 ),
inference(avatar_split_clause,[],[f273,f288,f284]) ).
fof(f295,plain,
! [X2,X0,X1] :
( r2_hidden(sK11(X0,X1),X2)
| ~ r1_tarski(X0,X2)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f166,f167]) ).
fof(f300,plain,
! [X2,X3,X0,X1] :
( ~ r1_tarski(X1,X3)
| r1_tarski(X0,X2)
| r2_hidden(sK11(X0,X2),X3)
| ~ r1_tarski(X0,X1) ),
inference(resolution,[],[f295,f166]) ).
fof(f305,plain,
m1_relset_1(sK3,sK0,sK1),
inference(resolution,[],[f218,f145]) ).
fof(f306,plain,
k6_relset_1(sK0,sK1,sK3) = k4_relat_1(sK3),
inference(resolution,[],[f216,f305]) ).
fof(f307,plain,
sF26 = k4_relat_1(sK3),
inference(forward_demodulation,[],[f306,f266]) ).
fof(f319,definition,
( spl31_3
<=> m1_relset_1(sF27,sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl31_3])],[avatar_definition]) ).
fof(f320,plain,
( m1_relset_1(sF27,sK0,sK0)
| ~ spl31_3 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f321,plain,
( ~ m1_relset_1(sF27,sK0,sK0)
| spl31_3 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f346,plain,
( ! [X0,X1] :
( r2_hidden(sK11(X0,X1),sF28)
| r1_tarski(X0,X1)
| ~ r1_tarski(X0,sK2) )
| ~ spl31_2 ),
inference(resolution,[],[f300,f290]) ).
fof(f358,definition,
( spl31_7
<=> v1_relat_1(sK3) ),
introduced(definition,[new_symbols(definition,[spl31_7])],[avatar_definition]) ).
fof(f359,plain,
( v1_relat_1(sK3)
| ~ spl31_7 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f360,plain,
( ~ v1_relat_1(sK3)
| spl31_7 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f372,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(resolution,[],[f185,f150]) ).
fof(f374,plain,
v1_relat_1(sK3),
inference(resolution,[],[f372,f145]) ).
fof(f375,plain,
( $false
| spl31_7 ),
inference(forward_subsumption_resolution,[],[f374,f360]) ).
fof(f376,plain,
spl31_7,
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f381,plain,
( m2_relset_1(sF27,sK0,sK0)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(superposition,[],[f184,f268]) ).
fof(f383,definition,
( spl31_10
<=> m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl31_10])],[avatar_definition]) ).
fof(f384,plain,
( m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ spl31_10 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f385,plain,
( ~ m1_subset_1(sF26,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| spl31_10 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f387,definition,
( spl31_11
<=> m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl31_11])],[avatar_definition]) ).
fof(f388,plain,
( m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ spl31_11 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f389,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| spl31_11 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f391,definition,
( spl31_12
<=> m2_relset_1(sF27,sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl31_12])],[avatar_definition]) ).
fof(f393,plain,
( m2_relset_1(sF27,sK0,sK0)
| ~ spl31_12 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f394,plain,
( ~ spl31_10
| ~ spl31_11
| spl31_12 ),
inference(avatar_split_clause,[],[f381,f391,f387,f383]) ).
fof(f395,plain,
( ~ m2_relset_1(sF26,sK1,sK0)
| spl31_10 ),
inference(resolution,[],[f385,f185]) ).
fof(f398,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2_hidden(k2_tarski(k2_tarski(X3,X1),k1_tarski(X3)),X4)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X1)),X2)
| r2_hidden(k2_tarski(k2_tarski(X3,X0),k1_tarski(X3)),k5_relat_1(X4,X2))
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X4) ),
inference(superposition,[],[f280,f151]) ).
fof(f412,plain,
( m2_relset_1(sF26,sK1,sK0)
| ~ m1_relset_1(sK3,sK0,sK1) ),
inference(superposition,[],[f183,f266]) ).
fof(f423,plain,
( ~ m1_relset_1(sK3,sK0,sK1)
| spl31_10 ),
inference(forward_subsumption_resolution,[],[f412,f395]) ).
fof(f424,plain,
( $false
| spl31_10 ),
inference(forward_subsumption_resolution,[],[f423,f305]) ).
fof(f425,plain,
spl31_10,
inference(avatar_contradiction_clause,[],[f424]) ).
fof(f426,plain,
m2_relset_1(sF26,sK1,sK0),
inference(forward_subsumption_resolution,[],[f412,f305]) ).
fof(f427,plain,
v1_relat_1(sF26),
inference(resolution,[],[f426,f372]) ).
fof(f448,plain,
( ~ m2_relset_1(sK3,sK0,sK1)
| spl31_11 ),
inference(resolution,[],[f389,f185]) ).
fof(f450,plain,
( $false
| spl31_11 ),
inference(forward_subsumption_resolution,[],[f448,f145]) ).
fof(f451,plain,
spl31_11,
inference(avatar_contradiction_clause,[],[f450]) ).
fof(f452,plain,
( v1_relat_1(sF27)
| ~ spl31_12 ),
inference(resolution,[],[f393,f372]) ).
fof(f454,plain,
( m1_relset_1(sF27,sK0,sK0)
| ~ spl31_12 ),
inference(resolution,[],[f393,f218]) ).
fof(f456,plain,
( $false
| spl31_3
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f454,f321]) ).
fof(f457,plain,
( spl31_3
| ~ spl31_12 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f463,plain,
( ! [X0] : k10_relset_1(sK0,sK0,sF27,X0) = k9_relat_1(sF27,X0)
| ~ spl31_3 ),
inference(resolution,[],[f320,f215]) ).
fof(f467,plain,
( sF28 = k9_relat_1(sF27,sK2)
| ~ spl31_3 ),
inference(superposition,[],[f270,f463]) ).
fof(f475,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,sK1)))
| k9_relset_2(X1,sK1,sK0,X0,sF26) = k5_relat_1(X0,sF26) )
| ~ spl31_10 ),
inference(resolution,[],[f384,f217]) ).
fof(f493,plain,
! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF26)
| r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),sK3)
| ~ v1_relat_1(sK3) ),
inference(superposition,[],[f281,f307]) ).
fof(f494,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF26)
| r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),sK3) )
| ~ spl31_7 ),
inference(forward_subsumption_resolution,[],[f493,f359]) ).
fof(f516,plain,
! [X0,X1] :
( r2_hidden(k2_tarski(k2_tarski(sK9(X0,X1),X1),k1_tarski(sK9(X0,X1))),k4_relat_1(X0))
| ~ v1_relat_1(X0)
| ~ r2_hidden(X1,k1_funct_5(X0)) ),
inference(resolution,[],[f282,f256]) ).
fof(f530,plain,
! [X0] :
( r2_hidden(k2_tarski(k2_tarski(sK9(sK3,X0),X0),k1_tarski(sK9(sK3,X0))),sF26)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k1_funct_5(sK3)) ),
inference(superposition,[],[f516,f307]) ).
fof(f532,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(sK9(sK3,X0),X0),k1_tarski(sK9(sK3,X0))),sF26)
| ~ r2_hidden(X0,k1_funct_5(sK3)) )
| ~ spl31_7 ),
inference(forward_subsumption_resolution,[],[f530,f359]) ).
fof(f535,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(sK9(sK3,X0),X0),k1_tarski(sK9(sK3,X0))),sF26)
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7 ),
inference(forward_demodulation,[],[f532,f272]) ).
fof(f542,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,sK9(sK3,X0)),k1_tarski(sK9(sK3,X0))),sF26)
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7 ),
inference(superposition,[],[f535,f151]) ).
fof(f611,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X1)),X2)
| r2_hidden(X0,k9_relat_1(X2,X3))
| ~ r2_hidden(X1,X3)
| ~ v1_relat_1(X2) ),
inference(superposition,[],[f252,f151]) ).
fof(f690,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,k9_relat_1(sF26,X1))
| ~ v1_relat_1(sF26)
| r2_hidden(k2_tarski(k2_tarski(X0,sK6(sF26,X1,X0)),k1_tarski(X0)),sK3) )
| ~ spl31_7 ),
inference(resolution,[],[f253,f494]) ).
fof(f698,plain,
( ! [X0,X1] :
( r2_hidden(k2_tarski(k2_tarski(X0,sK6(sF26,X1,X0)),k1_tarski(X0)),sK3)
| ~ r2_hidden(X0,k9_relat_1(sF26,X1)) )
| ~ spl31_7 ),
inference(forward_subsumption_resolution,[],[f690,f427]) ).
fof(f705,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,k9_relat_1(sF26,X1))
| r2_hidden(X0,k1_funct_5(sK3)) )
| ~ spl31_7 ),
inference(resolution,[],[f698,f255]) ).
fof(f708,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,k9_relat_1(sF26,X1))
| r2_hidden(X0,sF29) )
| ~ spl31_7 ),
inference(forward_demodulation,[],[f705,f272]) ).
fof(f748,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,sK9(X1,X2)),k1_tarski(sK9(X1,X2))),X3)
| r2_hidden(k2_tarski(k2_tarski(X2,X0),k1_tarski(X2)),k5_relat_1(X1,X3))
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X2,k1_funct_5(X1)) ),
inference(resolution,[],[f398,f256]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ v1_relat_1(X0)
| k9_relat_1(k5_relat_1(X0,sF26),X1) = k9_relat_1(sF26,k9_relat_1(X0,X1)) ),
inference(resolution,[],[f222,f427]) ).
fof(f1055,plain,
( ! [X0] : k9_relat_1(k5_relat_1(sK3,sF26),X0) = k9_relat_1(sF26,k9_relat_1(sK3,X0))
| ~ spl31_7 ),
inference(resolution,[],[f1027,f359]) ).
fof(f1877,plain,
( k9_relset_2(sK0,sK1,sK0,sK3,sF26) = k5_relat_1(sK3,sF26)
| ~ spl31_10
| ~ spl31_11 ),
inference(resolution,[],[f475,f388]) ).
fof(f1878,plain,
( sF27 = k5_relat_1(sK3,sF26)
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_demodulation,[],[f1877,f268]) ).
fof(f1880,plain,
( ! [X0] : k9_relat_1(sF27,X0) = k9_relat_1(sF26,k9_relat_1(sK3,X0))
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(superposition,[],[f1055,f1878]) ).
fof(f2125,plain,
( ! [X0,X1] :
( ~ r2_hidden(X1,k9_relat_1(sF27,X0))
| r2_hidden(X1,sF29) )
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(superposition,[],[f708,f1880]) ).
fof(f2201,plain,
( ! [X0] :
( ~ r2_hidden(X0,sF28)
| r2_hidden(X0,sF29) )
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(superposition,[],[f2125,f467]) ).
fof(f2226,plain,
( ! [X0,X1] :
( r2_hidden(sK11(X0,X1),sF29)
| r1_tarski(X0,X1)
| ~ r1_tarski(X0,sK2) )
| ~ spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(resolution,[],[f2201,f346]) ).
fof(f2396,plain,
( ! [X0] :
( r1_tarski(X0,sF29)
| ~ r1_tarski(X0,sK2)
| r1_tarski(X0,sF29) )
| ~ spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(resolution,[],[f2226,f168]) ).
fof(f2399,plain,
( ! [X0] :
( ~ r1_tarski(X0,sK2)
| r1_tarski(X0,sF29) )
| ~ spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(duplicate_literal_removal,[],[f2396]) ).
fof(f2400,plain,
( r1_tarski(sK2,sF29)
| ~ spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(resolution,[],[f2399,f220]) ).
fof(f2401,plain,
( $false
| spl31_1
| ~ spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_subsumption_resolution,[],[f2400,f285]) ).
fof(f2402,plain,
( spl31_1
| ~ spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(avatar_contradiction_clause,[],[f2401]) ).
fof(f2404,plain,
( ! [X0,X1] :
( r2_hidden(sK11(X0,X1),sF29)
| r1_tarski(X0,X1)
| ~ r1_tarski(X0,sK2) )
| ~ spl31_1 ),
inference(resolution,[],[f286,f300]) ).
fof(f3077,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sK3,sF26))
| ~ v1_relat_1(sF26)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k1_funct_5(sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7 ),
inference(resolution,[],[f748,f542]) ).
fof(f3092,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sK3,sF26))
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k1_funct_5(sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7 ),
inference(forward_subsumption_resolution,[],[f3077,f427]) ).
fof(f3098,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),k5_relat_1(sK3,sF26))
| ~ r2_hidden(X0,k1_funct_5(sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7 ),
inference(forward_subsumption_resolution,[],[f3092,f359]) ).
fof(f3102,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),sF27)
| ~ r2_hidden(X0,k1_funct_5(sK3))
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_demodulation,[],[f3098,f1878]) ).
fof(f3105,plain,
( ! [X0] :
( ~ r2_hidden(X0,sF29)
| r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),sF27)
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_demodulation,[],[f3102,f272]) ).
fof(f3106,plain,
( ! [X0] :
( r2_hidden(k2_tarski(k2_tarski(X0,X0),k1_tarski(X0)),sF27)
| ~ r2_hidden(X0,sF29) )
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(duplicate_literal_removal,[],[f3105]) ).
fof(f3122,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,sF29)
| r2_hidden(X0,k9_relat_1(sF27,X1))
| ~ r2_hidden(X0,X1)
| ~ v1_relat_1(sF27) )
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(resolution,[],[f3106,f611]) ).
fof(f3128,plain,
( ! [X0,X1] :
( r2_hidden(X0,k9_relat_1(sF27,X1))
| ~ r2_hidden(X0,sF29)
| ~ r2_hidden(X0,X1) )
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f3122,f452]) ).
fof(f3171,plain,
( ! [X0] :
( ~ r2_hidden(X0,sF29)
| r2_hidden(X0,sF28)
| ~ r2_hidden(X0,sK2) )
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(superposition,[],[f3128,f467]) ).
fof(f3206,plain,
( ! [X0,X1] :
( r2_hidden(sK11(X0,X1),sF28)
| ~ r2_hidden(sK11(X0,X1),sK2)
| r1_tarski(X0,X1)
| ~ r1_tarski(X0,sK2) )
| ~ spl31_1
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(resolution,[],[f3171,f2404]) ).
fof(f3212,plain,
( ! [X0,X1] :
( r2_hidden(sK11(X0,X1),sF28)
| r1_tarski(X0,X1)
| ~ r1_tarski(X0,sK2) )
| ~ spl31_1
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f3206,f295]) ).
fof(f3249,plain,
( ! [X0] :
( r1_tarski(X0,sF28)
| ~ r1_tarski(X0,sK2)
| r1_tarski(X0,sF28) )
| ~ spl31_1
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(resolution,[],[f3212,f168]) ).
fof(f3253,plain,
( ! [X0] :
( ~ r1_tarski(X0,sK2)
| r1_tarski(X0,sF28) )
| ~ spl31_1
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(duplicate_literal_removal,[],[f3249]) ).
fof(f3254,plain,
( r1_tarski(sK2,sF28)
| ~ spl31_1
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(resolution,[],[f3253,f220]) ).
fof(f3255,plain,
( $false
| ~ spl31_1
| spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f3254,f289]) ).
fof(f3256,plain,
( ~ spl31_1
| spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(avatar_contradiction_clause,[],[f3255]) ).
cnf(s1,plain,
( spl31_1
| spl31_2 ),
inference(sat_conversion,[],[f291]) ).
cnf(s2,plain,
( ~ spl31_1
| ~ spl31_2 ),
inference(sat_conversion,[],[f292]) ).
cnf(s7,plain,
spl31_7,
inference(sat_conversion,[],[f376]) ).
cnf(s8,plain,
( ~ spl31_10
| ~ spl31_11
| spl31_12 ),
inference(sat_conversion,[],[f394]) ).
cnf(s10,plain,
spl31_10,
inference(sat_conversion,[],[f425]) ).
cnf(s12,plain,
spl31_11,
inference(sat_conversion,[],[f451]) ).
cnf(s13,plain,
( spl31_3
| ~ spl31_12 ),
inference(sat_conversion,[],[f457]) ).
cnf(s90,plain,
( spl31_1
| ~ spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11 ),
inference(sat_conversion,[],[f2402]) ).
cnf(s133,plain,
( ~ spl31_1
| spl31_2
| ~ spl31_3
| ~ spl31_7
| ~ spl31_10
| ~ spl31_11
| ~ spl31_12 ),
inference(sat_conversion,[],[f3256]) ).
cnf(s136,plain,
spl31_12,
inference(rat,[],[s8,s12,s10]) ).
cnf(s137,plain,
spl31_3,
inference(rat,[],[s13,s136]) ).
cnf(s148,plain,
spl31_1,
inference(rat,[],[s1,s90,s137,s7,s10,s12]) ).
cnf(s149,plain,
spl31_2,
inference(rat,[],[s133,s136,s12,s10,s7,s137,s148]) ).
cnf(s150,plain,
$false,
inference(rat,[],[s2,s149,s148]) ).
fof(f3257,plain,
$false,
inference(avatar_sat_refutation,[],[s150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU442+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 05:33:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 10.40/2.35 % (3056249)Detected formulas, will run a generic FOF schedule.
% 10.40/2.35 % (3056372)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3384066224:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.40/2.35 % (3056364)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=1957295303:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.40/2.35 % (3056369)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=481536163:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.40/2.35 % (3056368)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=3587288466:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.40/2.35 % (3056369)Refutation not found, incomplete strategy
% 10.40/2.35 % (3056369)------------------------------
% 10.40/2.35 % (3056369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056369)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056369)Termination reason: Refutation not found, incomplete strategy
% 10.40/2.35 % (3056369)Time elapsed: 0.004 s
% 10.40/2.35 % (3056369)Peak memory usage: 88 MB
% 10.40/2.35 % (3056369)Instructions burned: 3 (million)
% 10.40/2.35 % (3056366)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=1462129854:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.40/2.35 % (3056373)dis-21_1_sil=8000:lcm=predicate:random_seed=75293834: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)
% 10.40/2.35 % (3056371)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1674887104:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.40/2.35 % (3056372)Instruction limit reached!
% 10.40/2.35 % (3056372)------------------------------
% 10.40/2.35 % (3056372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056372)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056372)Termination reason: Instruction limit
% 10.40/2.35 % (3056372)Termination phase: Saturation
% 10.40/2.35 % (3056372)Time elapsed: 0.060 s
% 10.40/2.35 % (3056372)Peak memory usage: 90 MB
% 10.40/2.35 % (3056372)Instructions burned: 141 (million)
% 10.40/2.35 % (3056371)Instruction limit reached!
% 10.40/2.35 % (3056371)------------------------------
% 10.40/2.35 % (3056371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056373)Instruction limit reached!
% 10.40/2.35 % (3056373)------------------------------
% 10.40/2.35 % (3056373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056373)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056371)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056373)Termination reason: Instruction limit
% 10.40/2.35 % (3056373)Termination phase: Saturation
% 10.40/2.35 % (3056371)Termination reason: Instruction limit
% 10.40/2.35 % (3056371)Termination phase: Saturation
% 10.40/2.35 % (3056373)Time elapsed: 0.080 s
% 10.40/2.35 % (3056371)Time elapsed: 0.080 s
% 10.40/2.35 % (3056373)Peak memory usage: 90 MB
% 10.40/2.35 % (3056371)Peak memory usage: 89 MB
% 10.40/2.35 % (3056371)Instructions burned: 121 (million)
% 10.40/2.35 % (3056373)Instructions burned: 129 (million)
% 10.40/2.35 % (3056420)lrs+10_1_sil=8000:sp=occurrence:random_seed=3571818331:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.40/2.35 % (3056369)------------------------------
% 10.40/2.35 % (3056369)------------------------------
% 10.40/2.35 % (3056420)Instruction limit reached!
% 10.40/2.35 % (3056420)------------------------------
% 10.40/2.35 % (3056420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056420)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056420)Termination reason: Instruction limit
% 10.40/2.35 % (3056420)Termination phase: Saturation
% 10.40/2.35 % (3056420)Time elapsed: 0.100 s
% 10.40/2.35 % (3056420)Peak memory usage: 92 MB
% 10.40/2.35 % (3056420)Instructions burned: 285 (million)
% 10.40/2.35 % (3056421)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2815116119:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.40/2.35 % (3056422)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3734744276:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.40/2.35 % (3056421)Instruction limit reached!
% 10.40/2.35 % (3056421)------------------------------
% 10.40/2.35 % (3056421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056421)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056421)Termination reason: Instruction limit
% 10.40/2.35 % (3056421)Termination phase: Saturation
% 10.40/2.35 % (3056421)Time elapsed: 0.102 s
% 10.40/2.35 % (3056421)Peak memory usage: 90 MB
% 10.40/2.35 % (3056421)Instructions burned: 158 (million)
% 10.40/2.35 % (3056425)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2710963456:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.40/2.35 % (3056424)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=3115514741:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 10.40/2.35 % (3056425)Instruction limit reached!
% 10.40/2.35 % (3056425)------------------------------
% 10.40/2.35 % (3056425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056425)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056425)Termination reason: Instruction limit
% 10.40/2.35 % (3056425)Termination phase: Saturation
% 10.40/2.35 % (3056425)Time elapsed: 0.083 s
% 10.40/2.35 % (3056425)Peak memory usage: 89 MB
% 10.40/2.35 % (3056425)Instructions burned: 298 (million)
% 10.40/2.35 % (3056422)Instruction limit reached!
% 10.40/2.35 % (3056422)------------------------------
% 10.40/2.35 % (3056422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056422)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056422)Termination reason: Instruction limit
% 10.40/2.35 % (3056422)Termination phase: Saturation
% 10.40/2.35 % (3056422)Time elapsed: 0.237 s
% 10.40/2.35 % (3056422)Peak memory usage: 91 MB
% 10.40/2.35 % (3056422)Instructions burned: 326 (million)
% 10.40/2.35 % (3056428)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1102729002:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.40/2.35 % (3056424)Instruction limit reached!
% 10.40/2.35 % (3056424)------------------------------
% 10.40/2.35 % (3056424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056424)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056424)Termination reason: Instruction limit
% 10.40/2.35 % (3056424)Termination phase: Saturation
% 10.40/2.35 % (3056424)Time elapsed: 0.145 s
% 10.40/2.35 % (3056424)Peak memory usage: 92 MB
% 10.40/2.35 % (3056424)Instructions burned: 249 (million)
% 10.40/2.35 % (3056431)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=990135358:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 10.40/2.35 % (3056431)Instruction limit reached!
% 10.40/2.35 % (3056431)------------------------------
% 10.40/2.35 % (3056431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056431)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056431)Termination reason: Instruction limit
% 10.40/2.35 % (3056431)Termination phase: Saturation
% 10.40/2.35 % (3056431)Time elapsed: 0.045 s
% 10.40/2.35 % (3056431)Peak memory usage: 90 MB
% 10.40/2.35 % (3056431)Instructions burned: 114 (million)
% 10.40/2.35 % (3056432)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=41908077:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.40/2.35 % (3056432)Instruction limit reached!
% 10.40/2.35 % (3056432)------------------------------
% 10.40/2.35 % (3056432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056432)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056432)Termination reason: Instruction limit
% 10.40/2.35 % (3056432)Termination phase: Saturation
% 10.40/2.35 % (3056432)Time elapsed: 0.064 s
% 10.40/2.35 % (3056432)Peak memory usage: 89 MB
% 10.40/2.35 % (3056432)Instructions burned: 129 (million)
% 10.40/2.35 % (3056434)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1901298318:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 10.40/2.35 % (3056436)lrs+10_1_sil=8000:sp=occurrence:random_seed=1587762842:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.40/2.35 % (3056434)Instruction limit reached!
% 10.40/2.35 % (3056434)------------------------------
% 10.40/2.35 % (3056434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056434)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056434)Termination reason: Instruction limit
% 10.40/2.35 % (3056434)Termination phase: Saturation
% 10.40/2.35 % (3056434)Time elapsed: 0.073 s
% 10.40/2.35 % (3056434)Peak memory usage: 89 MB
% 10.40/2.35 % (3056434)Instructions burned: 114 (million)
% 10.40/2.35 % (3056438)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1422348607:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 10.40/2.35 % (3056438)Refutation not found, incomplete strategy
% 10.40/2.35 % (3056438)------------------------------
% 10.40/2.35 % (3056438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056438)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056438)Termination reason: Refutation not found, incomplete strategy
% 10.40/2.35 % (3056438)Time elapsed: 0.008 s
% 10.40/2.35 % (3056438)Peak memory usage: 88 MB
% 10.40/2.35 % (3056438)Instructions burned: 11 (million)
% 10.40/2.35 % (3056441)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=801171705:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 10.40/2.35 % (3056436)Instruction limit reached!
% 10.40/2.35 % (3056436)------------------------------
% 10.40/2.35 % (3056436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056436)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056436)Termination reason: Instruction limit
% 10.40/2.35 % (3056436)Termination phase: Saturation
% 10.40/2.35 % (3056436)Time elapsed: 0.298 s
% 10.40/2.35 % (3056436)Peak memory usage: 99 MB
% 10.40/2.35 % (3056436)Instructions burned: 910 (million)
% 10.40/2.35 % (3056364)First to succeed.
% 10.40/2.35 % (3056364)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3056249"
% 10.40/2.35 % (3056438)------------------------------
% 10.40/2.35 % (3056438)------------------------------
% 10.40/2.35 % (3056444)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2519904084:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 10.40/2.35 % (3056444)Instruction limit reached!
% 10.40/2.35 % (3056444)------------------------------
% 10.40/2.35 % (3056444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.40/2.35 % (3056444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.40/2.35 % (3056444)CaDiCaL version: 2.1.3
% 10.40/2.35 % (3056444)Termination reason: Instruction limit
% 10.40/2.35 % (3056444)Termination phase: Saturation
% 10.40/2.35 % (3056444)Time elapsed: 0.041 s
% 10.40/2.35 % (3056444)Peak memory usage: 91 MB
% 10.40/2.35 % (3056444)Instructions burned: 135 (million)
% 10.40/2.35 % (3056445)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1455688447:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 10.40/2.35 % (3056447)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2914581812:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 10.40/2.35 % (3056364)Refutation found. Thanks to Tanya!
% 10.40/2.35 % SZS status Theorem for theBenchmark
% 10.40/2.35 % SZS output start Proof for theBenchmark
% See solution above
% 11.16/2.45 % (3056364)------------------------------
% 11.16/2.45 % (3056364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.16/2.45 % (3056364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.16/2.45 % (3056364)CaDiCaL version: 2.1.3
% 11.16/2.45 % (3056364)Termination reason: Refutation
% 11.16/2.45 % (3056364)Time elapsed: 1.105 s
% 11.16/2.45 % (3056364)Peak memory usage: 135 MB
% 11.16/2.45 % (3056364)Instructions burned: 1631 (million)
% 11.16/2.45 % (3056364)------------------------------
% 11.16/2.45 % (3056364)------------------------------
% 11.16/2.45 % (3056249)Success in time 1.521 s
% 11.16/2.45 % Vampire exiting
%------------------------------------------------------------------------------