%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG225+2 : 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 09:19:27 AM UTC 2026
% Result : Theorem 28.01s 4.45s
% Output : Refutation 28.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 31
% Syntax : Number of formulae : 198 ( 36 unt; 8 def)
% Number of atoms : 690 ( 111 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 882 ( 390 ~; 396 |; 51 &)
% ( 18 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 9 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 311 ( 2 sgn 300 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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(f18,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f24,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f55,axiom,
! [X0,X1] : k2_xboole_0(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f68,axiom,
! [X0,X1] :
~ ( r2_hidden(X0,X1)
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f538,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f667,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ( r1_tarski(k1_relat_1(X1),X0)
=> k7_relat_1(X1,X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_relat_1) ).
fof(f762,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ! [X2,X3] :
( ( r1_tarski(X2,X3)
& k7_relat_1(X0,X3) = k7_relat_1(X1,X3) )
=> k7_relat_1(X0,X2) = k7_relat_1(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t188_relat_1) ).
fof(f773,axiom,
! [X0,X1] :
( v1_relat_1(X0)
=> v1_relat_1(k7_relat_1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f785,axiom,
! [X0,X1] :
( ( v1_relat_1(X0)
& v1_funct_1(X0) )
=> ( v1_relat_1(k7_relat_1(X0,X1))
& v1_funct_1(k7_relat_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f1597,axiom,
! [X0,X1] : k2_funcop_1(X0,X1) = k2_zfmisc_1(X0,k1_tarski(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funcop_1) ).
fof(f1770,axiom,
! [X0] :
( ( v1_relat_1(X0)
& v1_funct_1(X0) )
=> ! [X1,X2] :
( r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X2))
=> k1_funct_4(k7_relat_1(X0,X1),k7_relat_1(X0,X2)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_4) ).
fof(f1771,axiom,
! [X0] :
( ( v1_relat_1(X0)
& v1_funct_1(X0) )
=> ! [X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ! [X2] : k7_relat_1(k1_funct_4(X0,X1),X2) = k1_funct_4(k7_relat_1(X0,X2),k7_relat_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_4) ).
fof(f1776,axiom,
! [X0] :
( ( v1_relat_1(X0)
& v1_funct_1(X0) )
=> ! [X1] : k1_funct_4(X0,k7_relat_1(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funct_4) ).
fof(f2945,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X0)
& v2_relat_1(X1)
& m1_pboole(X1,X0)
& m1_subset_1(X2,X0) )
=> ~ v1_xboole_0(k1_funct_1(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pboole) ).
fof(f2952,axiom,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pboole) ).
fof(f2956,axiom,
! [X0] : k1_pboole(X0) = k2_funcop_1(X0,k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pboole) ).
fof(f3131,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( v1_relat_1(X1)
& v1_funct_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pboole) ).
fof(f3150,axiom,
! [X0] : m1_pboole(k1_pboole(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pboole) ).
fof(f4703,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_pboole(X2,X1) )
=> ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f4722,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_pboole(X2,X0)
=> k1_funct_4(X1,X2) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_closure3) ).
fof(f4729,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
fof(f4730,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( v2_relat_1(X1)
& m1_pboole(X1,X0) )
=> X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_closure3) ).
fof(f4731,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( v2_relat_1(X1)
& m1_pboole(X1,X0) )
=> X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) ) ),
inference(negated_conjecture,[status(cth)],[f4730]) ).
fof(f4733,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f18]) ).
fof(f4736,plain,
! [X0] : k2_xboole_0(X0,X0) = X0,
inference(rectify,[],[f55]) ).
fof(f4743,plain,
? [X0] :
( ? [X1] :
( k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) != X1
& v2_relat_1(X1)
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f4731]) ).
fof(f4744,plain,
? [X0] :
( ? [X1] :
( k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) != X1
& v2_relat_1(X1)
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(flattening,[],[f4743]) ).
fof(f4751,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f4763,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| v1_xboole_0(X0)
| ~ v2_relat_1(X1)
| ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,X0) ),
inference(ennf_transformation,[],[f2945]) ).
fof(f4764,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| v1_xboole_0(X0)
| ~ v2_relat_1(X1)
| ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,X0) ),
inference(flattening,[],[f4763]) ).
fof(f4784,plain,
! [X0,X1] :
( ( v1_relat_1(k7_relat_1(X0,X1))
& v1_funct_1(k7_relat_1(X0,X1)) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(ennf_transformation,[],[f785]) ).
fof(f4785,plain,
! [X0,X1] :
( ( v1_relat_1(k7_relat_1(X0,X1))
& v1_funct_1(k7_relat_1(X0,X1)) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(flattening,[],[f4784]) ).
fof(f4786,plain,
! [X0,X1] :
( v1_relat_1(k7_relat_1(X0,X1))
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f773]) ).
fof(f4788,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( k7_relat_1(X0,X2) = k7_relat_1(X1,X2)
| ~ r1_tarski(X2,X3)
| k7_relat_1(X0,X3) != k7_relat_1(X1,X3) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f762]) ).
fof(f4789,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( k7_relat_1(X0,X2) = k7_relat_1(X1,X2)
| ~ r1_tarski(X2,X3)
| k7_relat_1(X0,X3) != k7_relat_1(X1,X3) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(flattening,[],[f4788]) ).
fof(f4813,plain,
! [X0,X1] :
( k7_relat_1(X1,X0) = X1
| ~ r1_tarski(k1_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f667]) ).
fof(f4814,plain,
! [X0,X1] :
( k7_relat_1(X1,X0) = X1
| ~ r1_tarski(k1_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f4813]) ).
fof(f4826,plain,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f3131]) ).
fof(f4827,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k1_funct_4(X1,X2) = X2
| ~ m1_pboole(X2,X0) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f4722]) ).
fof(f4842,plain,
! [X0] :
( ! [X1] : k1_funct_4(X0,k7_relat_1(X0,X1)) = X0
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(ennf_transformation,[],[f1776]) ).
fof(f4843,plain,
! [X0] :
( ! [X1] : k1_funct_4(X0,k7_relat_1(X0,X1)) = X0
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(flattening,[],[f4842]) ).
fof(f4852,plain,
! [X0] :
( ! [X1] :
( ! [X2] : k7_relat_1(k1_funct_4(X0,X1),X2) = k1_funct_4(k7_relat_1(X0,X2),k7_relat_1(X1,X2))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(ennf_transformation,[],[f1771]) ).
fof(f4853,plain,
! [X0] :
( ! [X1] :
( ! [X2] : k7_relat_1(k1_funct_4(X0,X1),X2) = k1_funct_4(k7_relat_1(X0,X2),k7_relat_1(X1,X2))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(flattening,[],[f4852]) ).
fof(f4854,plain,
! [X0] :
( ! [X1,X2] :
( k1_funct_4(k7_relat_1(X0,X1),k7_relat_1(X0,X2)) = X0
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X2)) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(ennf_transformation,[],[f1770]) ).
fof(f4855,plain,
! [X0] :
( ! [X1,X2] :
( k1_funct_4(k7_relat_1(X0,X1),k7_relat_1(X0,X2)) = X0
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X2)) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(flattening,[],[f4854]) ).
fof(f4931,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f4729]) ).
fof(f4936,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f538]) ).
fof(f5085,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(ennf_transformation,[],[f2952]) ).
fof(f5086,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(flattening,[],[f5085]) ).
fof(f5117,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f5437,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(ennf_transformation,[],[f4703]) ).
fof(f5438,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(flattening,[],[f5437]) ).
fof(f5566,plain,
( sK5 != k1_funct_4(k1_pboole(sK4),k7_relat_1(sK5,k1_closure3(sK4,sK5)))
& v2_relat_1(sK5)
& m1_pboole(sK5,sK4)
& ~ v1_xboole_0(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f4744]) ).
fof(f5603,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k1_closure3(X0,X1)
| a_2_0_closure3(X0,X1) != X2 )
& ( X2 = a_2_0_closure3(X0,X1)
| k1_closure3(X0,X1) != X2 ) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(nnf_transformation,[],[f4931]) ).
fof(f5641,plain,
! [X0,X1] :
( ( ( m1_pboole(X1,X0)
| k1_relat_1(X1) != X0 )
& ( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0) ) )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(nnf_transformation,[],[f5086]) ).
fof(f5646,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,[],[f5117]) ).
fof(f5647,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,[],[f5646]) ).
fof(f5648,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK50(X0,X1),X1)
& r2_hidden(sK50(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(X2,sK50(X0,X1))],[f5647]) ).
fof(f5757,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(nnf_transformation,[],[f5438]) ).
fof(f5758,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ? [X4] :
( m1_subset_1(X4,X1)
& X0 = X4
& k1_xboole_0 != k1_funct_1(X2,X4) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(rectify,[],[f5757]) ).
fof(f5759,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ( m1_subset_1(sK130(X0,X1,X2),X1)
& sK130(X0,X1,X2) = X0
& k1_xboole_0 != k1_funct_1(X2,sK130(X0,X1,X2)) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(X4,sK130(X0,X1,X2))],[f5758]) ).
fof(f5824,plain,
~ v1_xboole_0(sK4),
inference(cnf_transformation,[],[f5566]) ).
fof(f5825,plain,
m1_pboole(sK5,sK4),
inference(cnf_transformation,[],[f5566]) ).
fof(f5826,plain,
v2_relat_1(sK5),
inference(cnf_transformation,[],[f5566]) ).
fof(f5827,plain,
sK5 != k1_funct_4(k1_pboole(sK4),k7_relat_1(sK5,k1_closure3(sK4,sK5))),
inference(cnf_transformation,[],[f5566]) ).
fof(f5843,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f4751]) ).
fof(f5861,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| v1_xboole_0(X0)
| ~ v2_relat_1(X1)
| ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,X0) ),
inference(cnf_transformation,[],[f4764]) ).
fof(f5887,plain,
! [X0,X1] :
( v1_funct_1(k7_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f4785]) ).
fof(f5889,plain,
! [X0,X1] :
( v1_relat_1(k7_relat_1(X0,X1))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f4786]) ).
fof(f5891,plain,
! [X2,X3,X0,X1] :
( k7_relat_1(X0,X2) = k7_relat_1(X1,X2)
| ~ r1_tarski(X2,X3)
| k7_relat_1(X0,X3) != k7_relat_1(X1,X3)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f4789]) ).
fof(f5909,plain,
! [X0,X1] :
( k7_relat_1(X1,X0) = X1
| ~ r1_tarski(k1_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f4814]) ).
fof(f5928,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_funct_1(X1) ),
inference(cnf_transformation,[],[f4826]) ).
fof(f5929,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_relat_1(X1) ),
inference(cnf_transformation,[],[f4826]) ).
fof(f5930,plain,
! [X2,X0,X1] :
( k1_funct_4(X1,X2) = X2
| ~ m1_pboole(X2,X0)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f4827]) ).
fof(f5940,plain,
! [X0,X1] :
( k1_funct_4(X0,k7_relat_1(X0,X1)) = X0
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f4843]) ).
fof(f5946,plain,
! [X2,X0,X1] :
( k7_relat_1(k1_funct_4(X0,X1),X2) = k1_funct_4(k7_relat_1(X0,X2),k7_relat_1(X1,X2))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f4853]) ).
fof(f5947,plain,
! [X2,X0,X1] :
( k1_funct_4(k7_relat_1(X0,X1),k7_relat_1(X0,X2)) = X0
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X2))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f4855]) ).
fof(f5985,plain,
! [X0] : m1_pboole(k1_pboole(X0),X0),
inference(cnf_transformation,[],[f3150]) ).
fof(f6013,plain,
! [X0] : k1_pboole(X0) = k2_funcop_1(X0,k1_xboole_0),
inference(cnf_transformation,[],[f2956]) ).
fof(f6014,plain,
! [X2,X0,X1] :
( a_2_0_closure3(X0,X1) = X2
| k1_closure3(X0,X1) != X2
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f5603]) ).
fof(f6022,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f4936]) ).
fof(f6113,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f24]) ).
fof(f6201,plain,
! [X0,X1] :
( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(cnf_transformation,[],[f5641]) ).
fof(f6233,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f4733]) ).
fof(f6235,plain,
! [X0,X1] :
( r2_hidden(sK50(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f5648]) ).
fof(f6236,plain,
! [X0,X1] :
( ~ r2_hidden(sK50(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f5648]) ).
fof(f6346,plain,
! [X0] : k2_xboole_0(X0,X0) = X0,
inference(cnf_transformation,[],[f4736]) ).
fof(f6744,plain,
! [X0,X1] : k2_zfmisc_1(X0,k1_tarski(X1)) = k2_funcop_1(X0,X1),
inference(cnf_transformation,[],[f1597]) ).
fof(f6761,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(cnf_transformation,[],[f5759]) ).
fof(f6985,plain,
! [X0] : k1_pboole(X0) = k2_zfmisc_1(X0,k1_tarski(k1_xboole_0)),
inference(definition_unfolding,[],[f6013,f6744]) ).
fof(f6986,plain,
sK5 != k1_funct_4(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),k7_relat_1(sK5,k1_closure3(sK4,sK5))),
inference(definition_unfolding,[],[f5827,f6985]) ).
fof(f6996,plain,
! [X0] : m1_pboole(k2_zfmisc_1(X0,k1_tarski(k1_xboole_0)),X0),
inference(definition_unfolding,[],[f5985,f6985]) ).
fof(f7146,plain,
! [X0,X1] :
( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(equality_resolution,[],[f6014]) ).
fof(f7221,plain,
! [X2,X3,X1] :
( r2_hidden(X3,a_2_0_closure3(X1,X2))
| ~ m1_subset_1(X3,X1)
| k1_xboole_0 = k1_funct_1(X2,X3)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(equality_resolution,[],[f6761]) ).
fof(f7315,plain,
( sK5 != k1_funct_4(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),k7_relat_1(sK5,a_2_0_closure3(sK4,sK5)))
| ~ m1_pboole(sK5,sK4)
| v1_xboole_0(sK4) ),
inference(superposition,[],[f6986,f7146]) ).
fof(f7316,plain,
( sK5 != k1_funct_4(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),k7_relat_1(sK5,a_2_0_closure3(sK4,sK5)))
| v1_xboole_0(sK4) ),
inference(forward_subsumption_resolution,[],[f7315,f5825]) ).
fof(f7317,plain,
sK5 != k1_funct_4(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),k7_relat_1(sK5,a_2_0_closure3(sK4,sK5))),
inference(forward_subsumption_resolution,[],[f7316,f5824]) ).
fof(f7318,plain,
! [X0] :
( sK5 != k7_relat_1(sK5,a_2_0_closure3(sK4,sK5))
| ~ m1_pboole(k7_relat_1(sK5,a_2_0_closure3(sK4,sK5)),X0)
| ~ m1_pboole(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),X0)
| v1_xboole_0(X0) ),
inference(superposition,[],[f7317,f5930]) ).
fof(f7320,definition,
( spl169_5
<=> ! [X0] :
( ~ m1_pboole(k7_relat_1(sK5,a_2_0_closure3(sK4,sK5)),X0)
| v1_xboole_0(X0)
| ~ m1_pboole(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl169_5])],[avatar_definition]) ).
fof(f7321,plain,
( ! [X0] :
( ~ m1_pboole(k7_relat_1(sK5,a_2_0_closure3(sK4,sK5)),X0)
| v1_xboole_0(X0)
| ~ m1_pboole(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),X0) )
| ~ spl169_5 ),
inference(avatar_component_clause,[],[f7320]) ).
fof(f7323,definition,
( spl169_6
<=> sK5 = k7_relat_1(sK5,a_2_0_closure3(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl169_6])],[avatar_definition]) ).
fof(f7325,plain,
( sK5 != k7_relat_1(sK5,a_2_0_closure3(sK4,sK5))
| spl169_6 ),
inference(avatar_component_clause,[],[f7323]) ).
fof(f7326,plain,
( spl169_5
| ~ spl169_6 ),
inference(avatar_split_clause,[],[f7318,f7323,f7320]) ).
fof(f7329,plain,
! [X2,X0,X1] :
( k7_relat_1(X0,X1) = X0
| ~ m1_pboole(k7_relat_1(X0,X1),X2)
| ~ m1_pboole(X0,X2)
| v1_xboole_0(X2)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(superposition,[],[f5930,f5940]) ).
fof(f7330,plain,
! [X2,X0,X1] :
( k7_relat_1(X0,X1) = X0
| ~ m1_pboole(k7_relat_1(X0,X1),X2)
| ~ m1_pboole(X0,X2)
| v1_xboole_0(X2)
| ~ v1_funct_1(X0) ),
inference(forward_subsumption_resolution,[],[f7329,f5929]) ).
fof(f7332,plain,
! [X2,X0,X1] :
( ~ m1_pboole(k7_relat_1(X0,X1),X2)
| k7_relat_1(X0,X1) = X0
| ~ m1_pboole(X0,X2)
| v1_xboole_0(X2) ),
inference(forward_subsumption_resolution,[],[f7330,f5928]) ).
fof(f7357,definition,
( spl169_7
<=> v1_relat_1(sK5) ),
introduced(definition,[new_symbols(definition,[spl169_7])],[avatar_definition]) ).
fof(f7358,plain,
( v1_relat_1(sK5)
| ~ spl169_7 ),
inference(avatar_component_clause,[],[f7357]) ).
fof(f7359,plain,
( ~ v1_relat_1(sK5)
| spl169_7 ),
inference(avatar_component_clause,[],[f7357]) ).
fof(f7428,plain,
v1_funct_1(sK5),
inference(resolution,[],[f5928,f5825]) ).
fof(f7430,plain,
v1_relat_1(sK5),
inference(resolution,[],[f5929,f5825]) ).
fof(f7431,plain,
( $false
| spl169_7 ),
inference(forward_subsumption_resolution,[],[f7430,f7359]) ).
fof(f7432,plain,
spl169_7,
inference(avatar_contradiction_clause,[],[f7431]) ).
fof(f7776,plain,
! [X2,X0,X1] :
( k1_xboole_0 = k1_funct_1(X2,sK50(X0,a_2_0_closure3(X1,X2)))
| ~ m1_subset_1(sK50(X0,a_2_0_closure3(X1,X2)),X1)
| r1_tarski(X0,a_2_0_closure3(X1,X2))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(resolution,[],[f6236,f7221]) ).
fof(f8580,plain,
! [X2,X3,X0,X1,X4] :
( k1_funct_4(k7_relat_1(X2,X3),k7_relat_1(X0,X1)) = X2
| ~ r1_tarski(k1_relat_1(X2),k2_xboole_0(X3,X1))
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2)
| ~ r1_tarski(X1,X4)
| k7_relat_1(X2,X4) != k7_relat_1(X0,X4)
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X2) ),
inference(superposition,[],[f5947,f5891]) ).
fof(f8605,plain,
! [X2,X3,X0,X1,X4] :
( k1_funct_4(k7_relat_1(X2,X3),k7_relat_1(X0,X1)) = X2
| ~ r1_tarski(k1_relat_1(X2),k2_xboole_0(X3,X1))
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2)
| ~ r1_tarski(X1,X4)
| k7_relat_1(X2,X4) != k7_relat_1(X0,X4)
| ~ v1_relat_1(X0) ),
inference(duplicate_literal_removal,[],[f8580]) ).
fof(f8673,definition,
( spl169_17
<=> ! [X1] : ~ r1_tarski(k1_relat_1(sK5),X1) ),
introduced(definition,[new_symbols(definition,[spl169_17])],[avatar_definition]) ).
fof(f8674,plain,
( ! [X1] : ~ r1_tarski(k1_relat_1(sK5),X1)
| ~ spl169_17 ),
inference(avatar_component_clause,[],[f8673]) ).
fof(f8881,definition,
( spl169_20
<=> m1_pboole(k7_relat_1(sK5,k1_relat_1(sK5)),sK4) ),
introduced(definition,[new_symbols(definition,[spl169_20])],[avatar_definition]) ).
fof(f8882,plain,
( m1_pboole(k7_relat_1(sK5,k1_relat_1(sK5)),sK4)
| ~ spl169_20 ),
inference(avatar_component_clause,[],[f8881]) ).
fof(f8883,plain,
( ~ m1_pboole(k7_relat_1(sK5,k1_relat_1(sK5)),sK4)
| spl169_20 ),
inference(avatar_component_clause,[],[f8881]) ).
fof(f8962,plain,
( $false
| ~ spl169_17 ),
inference(resolution,[],[f8674,f6233]) ).
fof(f8968,plain,
~ spl169_17,
inference(avatar_contradiction_clause,[],[f8962]) ).
fof(f8973,definition,
( spl169_21
<=> r1_tarski(k1_relat_1(sK5),a_2_0_closure3(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl169_21])],[avatar_definition]) ).
fof(f8974,plain,
( r1_tarski(k1_relat_1(sK5),a_2_0_closure3(sK4,sK5))
| ~ spl169_21 ),
inference(avatar_component_clause,[],[f8973]) ).
fof(f8975,plain,
( ~ r1_tarski(k1_relat_1(sK5),a_2_0_closure3(sK4,sK5))
| spl169_21 ),
inference(avatar_component_clause,[],[f8973]) ).
fof(f9029,plain,
( ! [X0] :
( ~ r1_tarski(X0,a_2_0_closure3(sK4,sK5))
| ~ m1_pboole(sK5,X0)
| ~ v1_relat_1(sK5)
| ~ v1_funct_1(sK5) )
| spl169_21 ),
inference(superposition,[],[f8975,f6201]) ).
fof(f9084,plain,
( ~ m1_pboole(sK5,sK4)
| ~ r1_tarski(k1_relat_1(sK5),k1_relat_1(sK5))
| ~ v1_relat_1(sK5)
| spl169_20 ),
inference(superposition,[],[f8883,f5909]) ).
fof(f9089,plain,
( ~ r1_tarski(k1_relat_1(sK5),k1_relat_1(sK5))
| ~ v1_relat_1(sK5)
| spl169_20 ),
inference(forward_subsumption_resolution,[],[f9084,f5825]) ).
fof(f9091,plain,
( ~ v1_relat_1(sK5)
| spl169_20 ),
inference(forward_subsumption_resolution,[],[f9089,f6233]) ).
fof(f9093,plain,
( $false
| ~ spl169_7
| spl169_20 ),
inference(forward_subsumption_resolution,[],[f9091,f7358]) ).
fof(f9094,plain,
( ~ spl169_7
| spl169_20 ),
inference(avatar_contradiction_clause,[],[f9093]) ).
fof(f9268,plain,
( ! [X0] :
( ~ r1_tarski(X0,a_2_0_closure3(sK4,sK5))
| ~ m1_pboole(sK5,X0)
| ~ v1_funct_1(sK5) )
| ~ spl169_7
| spl169_21 ),
inference(forward_subsumption_resolution,[],[f9029,f7358]) ).
fof(f9302,plain,
( ! [X0] :
( ~ r1_tarski(X0,a_2_0_closure3(sK4,sK5))
| ~ m1_pboole(sK5,X0) )
| ~ spl169_7
| spl169_21 ),
inference(forward_subsumption_resolution,[],[f9268,f7428]) ).
fof(f12629,plain,
( sK5 = k7_relat_1(sK5,k1_relat_1(sK5))
| ~ m1_pboole(sK5,sK4)
| v1_xboole_0(sK4)
| ~ spl169_20 ),
inference(resolution,[],[f8882,f7332]) ).
fof(f12649,plain,
( sK5 = k7_relat_1(sK5,k1_relat_1(sK5))
| v1_xboole_0(sK4)
| ~ spl169_20 ),
inference(forward_subsumption_resolution,[],[f12629,f5825]) ).
fof(f12653,definition,
( spl169_65
<=> sK5 = k7_relat_1(sK5,k1_relat_1(sK5)) ),
introduced(definition,[new_symbols(definition,[spl169_65])],[avatar_definition]) ).
fof(f12655,plain,
( sK5 = k7_relat_1(sK5,k1_relat_1(sK5))
| ~ spl169_65 ),
inference(avatar_component_clause,[],[f12653]) ).
fof(f12660,plain,
( sK5 = k7_relat_1(sK5,k1_relat_1(sK5))
| ~ spl169_20 ),
inference(forward_subsumption_resolution,[],[f12649,f5824]) ).
fof(f12662,plain,
( spl169_65
| ~ spl169_20 ),
inference(avatar_split_clause,[],[f12660,f8881,f12653]) ).
fof(f14164,plain,
! [X0,X1] :
( k7_relat_1(k1_funct_4(X0,X0),X1) = X0
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(superposition,[],[f5947,f5946]) ).
fof(f14200,plain,
! [X0,X1] :
( k7_relat_1(k1_funct_4(X0,X0),X1) = X0
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(duplicate_literal_removal,[],[f14164]) ).
fof(f14247,plain,
! [X0,X1] :
( k7_relat_1(k1_funct_4(X0,X0),X1) = X0
| ~ r1_tarski(k1_relat_1(X0),X1)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(forward_demodulation,[],[f14200,f6346]) ).
fof(f14329,plain,
! [X2,X3,X0,X1] :
( k7_relat_1(X0,X1) = k7_relat_1(X0,X2)
| ~ r1_tarski(k1_relat_1(k7_relat_1(X0,X1)),X2)
| ~ v1_relat_1(k7_relat_1(X0,X1))
| ~ v1_funct_1(k7_relat_1(X0,X1))
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ r1_tarski(X1,X3)
| k7_relat_1(X0,X3) != k7_relat_1(X0,X3)
| ~ v1_relat_1(X0) ),
inference(superposition,[],[f14247,f8605]) ).
fof(f14415,plain,
! [X2,X3,X0,X1] :
( k7_relat_1(X0,X1) = k7_relat_1(X0,X2)
| ~ r1_tarski(k1_relat_1(k7_relat_1(X0,X1)),X2)
| ~ v1_relat_1(k7_relat_1(X0,X1))
| ~ v1_funct_1(k7_relat_1(X0,X1))
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ r1_tarski(X1,X3)
| k7_relat_1(X0,X3) != k7_relat_1(X0,X3) ),
inference(duplicate_literal_removal,[],[f14329]) ).
fof(f14416,plain,
! [X2,X3,X0,X1] :
( k7_relat_1(X0,X1) = k7_relat_1(X0,X2)
| ~ r1_tarski(k1_relat_1(k7_relat_1(X0,X1)),X2)
| ~ v1_relat_1(k7_relat_1(X0,X1))
| ~ v1_funct_1(k7_relat_1(X0,X1))
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ r1_tarski(X1,X3) ),
inference(trivial_inequality_removal,[],[f14415]) ).
fof(f14442,plain,
! [X2,X3,X0,X1] :
( k7_relat_1(X0,X1) = k7_relat_1(X0,X2)
| ~ r1_tarski(k1_relat_1(k7_relat_1(X0,X1)),X2)
| ~ v1_relat_1(k7_relat_1(X0,X1))
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ r1_tarski(X1,X3) ),
inference(forward_subsumption_resolution,[],[f14416,f5887]) ).
fof(f14456,plain,
! [X2,X3,X0,X1] :
( k7_relat_1(X0,X1) = k7_relat_1(X0,X2)
| ~ r1_tarski(k1_relat_1(k7_relat_1(X0,X1)),X2)
| ~ r1_tarski(k1_relat_1(X0),k2_xboole_0(X1,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ r1_tarski(X1,X3) ),
inference(forward_subsumption_resolution,[],[f14442,f5889]) ).
fof(f14461,plain,
! [X2,X3,X0,X1] :
( k7_relat_1(X0,X1) = k7_relat_1(X0,X2)
| ~ r1_tarski(k1_relat_1(X0),X1)
| ~ r1_tarski(k1_relat_1(k7_relat_1(X0,X1)),X2)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ r1_tarski(X1,X3) ),
inference(forward_demodulation,[],[f14456,f6346]) ).
fof(f14589,plain,
( ! [X0,X1] :
( m1_pboole(k7_relat_1(sK5,X0),sK4)
| ~ r1_tarski(k1_relat_1(sK5),k1_relat_1(sK5))
| ~ r1_tarski(k1_relat_1(k7_relat_1(sK5,k1_relat_1(sK5))),X0)
| ~ v1_relat_1(sK5)
| ~ v1_funct_1(sK5)
| ~ r1_tarski(k1_relat_1(sK5),X1) )
| ~ spl169_20 ),
inference(superposition,[],[f8882,f14461]) ).
fof(f14877,plain,
( ! [X0,X1] :
( m1_pboole(k7_relat_1(sK5,X0),sK4)
| ~ r1_tarski(k1_relat_1(k7_relat_1(sK5,k1_relat_1(sK5))),X0)
| ~ v1_relat_1(sK5)
| ~ v1_funct_1(sK5)
| ~ r1_tarski(k1_relat_1(sK5),X1) )
| ~ spl169_20 ),
inference(forward_subsumption_resolution,[],[f14589,f6233]) ).
fof(f14955,plain,
( ! [X0,X1] :
( m1_pboole(k7_relat_1(sK5,X0),sK4)
| ~ r1_tarski(k1_relat_1(k7_relat_1(sK5,k1_relat_1(sK5))),X0)
| ~ v1_funct_1(sK5)
| ~ r1_tarski(k1_relat_1(sK5),X1) )
| ~ spl169_7
| ~ spl169_20 ),
inference(forward_subsumption_resolution,[],[f14877,f7358]) ).
fof(f14977,plain,
( ! [X0,X1] :
( m1_pboole(k7_relat_1(sK5,X0),sK4)
| ~ r1_tarski(k1_relat_1(k7_relat_1(sK5,k1_relat_1(sK5))),X0)
| ~ r1_tarski(k1_relat_1(sK5),X1) )
| ~ spl169_7
| ~ spl169_20 ),
inference(forward_subsumption_resolution,[],[f14955,f7428]) ).
fof(f15001,plain,
( ! [X0,X1] :
( ~ r1_tarski(k1_relat_1(sK5),X0)
| m1_pboole(k7_relat_1(sK5,X0),sK4)
| ~ r1_tarski(k1_relat_1(sK5),X1) )
| ~ spl169_7
| ~ spl169_20
| ~ spl169_65 ),
inference(forward_demodulation,[],[f14977,f12655]) ).
fof(f15009,definition,
( spl169_85
<=> ! [X0] :
( ~ r1_tarski(k1_relat_1(sK5),X0)
| m1_pboole(k7_relat_1(sK5,X0),sK4) ) ),
introduced(definition,[new_symbols(definition,[spl169_85])],[avatar_definition]) ).
fof(f15010,plain,
( ! [X0] :
( m1_pboole(k7_relat_1(sK5,X0),sK4)
| ~ r1_tarski(k1_relat_1(sK5),X0) )
| ~ spl169_85 ),
inference(avatar_component_clause,[],[f15009]) ).
fof(f15011,plain,
( spl169_17
| spl169_85
| ~ spl169_7
| ~ spl169_20
| ~ spl169_65 ),
inference(avatar_split_clause,[],[f15001,f12653,f8881,f7357,f15009,f8673]) ).
fof(f15152,plain,
( sK5 != sK5
| ~ r1_tarski(k1_relat_1(sK5),a_2_0_closure3(sK4,sK5))
| ~ v1_relat_1(sK5)
| spl169_6 ),
inference(superposition,[],[f7325,f5909]) ).
fof(f15159,plain,
( ~ r1_tarski(k1_relat_1(sK5),a_2_0_closure3(sK4,sK5))
| ~ v1_relat_1(sK5)
| spl169_6 ),
inference(trivial_inequality_removal,[],[f15152]) ).
fof(f16697,plain,
( ~ r1_tarski(k1_relat_1(sK5),a_2_0_closure3(sK4,sK5))
| v1_xboole_0(sK4)
| ~ m1_pboole(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),sK4)
| ~ spl169_5
| ~ spl169_85 ),
inference(resolution,[],[f15010,f7321]) ).
fof(f20233,plain,
! [X2,X3,X0,X1] :
( ~ v1_xboole_0(k1_xboole_0)
| v1_xboole_0(X3)
| ~ v2_relat_1(X0)
| ~ m1_pboole(X0,X3)
| ~ m1_subset_1(sK50(X1,a_2_0_closure3(X2,X0)),X3)
| ~ m1_subset_1(sK50(X1,a_2_0_closure3(X2,X0)),X2)
| r1_tarski(X1,a_2_0_closure3(X2,X0))
| v1_xboole_0(X2)
| ~ m1_pboole(X0,X2) ),
inference(superposition,[],[f5861,f7776]) ).
fof(f20235,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(sK50(X1,a_2_0_closure3(X2,X0)),X3)
| ~ v2_relat_1(X0)
| ~ m1_pboole(X0,X3)
| v1_xboole_0(X3)
| ~ m1_subset_1(sK50(X1,a_2_0_closure3(X2,X0)),X2)
| r1_tarski(X1,a_2_0_closure3(X2,X0))
| v1_xboole_0(X2)
| ~ m1_pboole(X0,X2) ),
inference(forward_subsumption_resolution,[],[f20233,f6113]) ).
fof(f20237,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(sK50(X0,a_2_0_closure3(X1,X2)),X1)
| ~ v2_relat_1(X2)
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| r1_tarski(X0,a_2_0_closure3(X1,X2))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(factoring,[],[f20235]) ).
fof(f20240,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(sK50(X0,a_2_0_closure3(X1,X2)),X1)
| ~ v2_relat_1(X2)
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| r1_tarski(X0,a_2_0_closure3(X1,X2)) ),
inference(duplicate_literal_removal,[],[f20237]) ).
fof(f20241,plain,
! [X2,X0,X1] :
( ~ v2_relat_1(X0)
| ~ m1_pboole(X0,X1)
| v1_xboole_0(X1)
| r1_tarski(X2,a_2_0_closure3(X1,X0))
| ~ r2_hidden(sK50(X2,a_2_0_closure3(X1,X0)),X1) ),
inference(resolution,[],[f20240,f6022]) ).
fof(f20244,plain,
! [X2,X0,X1] :
( ~ r2_hidden(sK50(X2,a_2_0_closure3(X1,X0)),X1)
| ~ m1_pboole(X0,X1)
| r1_tarski(X2,a_2_0_closure3(X1,X0))
| ~ v2_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f20241,f5843]) ).
fof(f20840,plain,
! [X0,X1] :
( ~ m1_pboole(X0,X1)
| r1_tarski(X1,a_2_0_closure3(X1,X0))
| ~ v2_relat_1(X0)
| r1_tarski(X1,a_2_0_closure3(X1,X0)) ),
inference(resolution,[],[f20244,f6235]) ).
fof(f20848,plain,
! [X0,X1] :
( r1_tarski(X1,a_2_0_closure3(X1,X0))
| ~ m1_pboole(X0,X1)
| ~ v2_relat_1(X0) ),
inference(duplicate_literal_removal,[],[f20840]) ).
fof(f20849,plain,
( ~ m1_pboole(sK5,sK4)
| ~ v2_relat_1(sK5)
| ~ m1_pboole(sK5,sK4)
| ~ spl169_7
| spl169_21 ),
inference(resolution,[],[f20848,f9302]) ).
fof(f20859,plain,
( ~ m1_pboole(sK5,sK4)
| ~ v2_relat_1(sK5)
| ~ spl169_7
| spl169_21 ),
inference(duplicate_literal_removal,[],[f20849]) ).
fof(f20860,plain,
( ~ v2_relat_1(sK5)
| ~ spl169_7
| spl169_21 ),
inference(forward_subsumption_resolution,[],[f20859,f5825]) ).
fof(f20861,plain,
( $false
| ~ spl169_7
| spl169_21 ),
inference(forward_subsumption_resolution,[],[f20860,f5826]) ).
fof(f20862,plain,
( ~ spl169_7
| spl169_21 ),
inference(avatar_contradiction_clause,[],[f20861]) ).
fof(f20872,plain,
( ~ v1_relat_1(sK5)
| spl169_6
| ~ spl169_21 ),
inference(forward_subsumption_resolution,[],[f15159,f8974]) ).
fof(f20896,plain,
( $false
| spl169_6
| ~ spl169_7
| ~ spl169_21 ),
inference(forward_subsumption_resolution,[],[f20872,f7358]) ).
fof(f20897,plain,
( spl169_6
| ~ spl169_7
| ~ spl169_21 ),
inference(avatar_contradiction_clause,[],[f20896]) ).
fof(f20948,plain,
( v1_xboole_0(sK4)
| ~ m1_pboole(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),sK4)
| ~ spl169_5
| ~ spl169_21
| ~ spl169_85 ),
inference(forward_subsumption_resolution,[],[f16697,f8974]) ).
fof(f21013,plain,
( ~ m1_pboole(k2_zfmisc_1(sK4,k1_tarski(k1_xboole_0)),sK4)
| ~ spl169_5
| ~ spl169_21
| ~ spl169_85 ),
inference(forward_subsumption_resolution,[],[f20948,f5824]) ).
fof(f21067,plain,
( $false
| ~ spl169_5
| ~ spl169_21
| ~ spl169_85 ),
inference(forward_subsumption_resolution,[],[f21013,f6996]) ).
fof(f21068,plain,
( ~ spl169_5
| ~ spl169_21
| ~ spl169_85 ),
inference(avatar_contradiction_clause,[],[f21067]) ).
cnf(s3,plain,
( spl169_5
| ~ spl169_6 ),
inference(sat_conversion,[],[f7326]) ).
cnf(s12,plain,
spl169_7,
inference(sat_conversion,[],[f7432]) ).
cnf(s22,plain,
~ spl169_17,
inference(sat_conversion,[],[f8968]) ).
cnf(s26,plain,
( ~ spl169_7
| spl169_20 ),
inference(sat_conversion,[],[f9094]) ).
cnf(s83,plain,
( ~ spl169_20
| spl169_65 ),
inference(sat_conversion,[],[f12662]) ).
cnf(s102,plain,
( ~ spl169_7
| spl169_17
| ~ spl169_20
| ~ spl169_65
| spl169_85 ),
inference(sat_conversion,[],[f15011]) ).
cnf(s183,plain,
( ~ spl169_7
| spl169_21 ),
inference(sat_conversion,[],[f20862]) ).
cnf(s185,plain,
( spl169_6
| ~ spl169_7
| ~ spl169_21 ),
inference(sat_conversion,[],[f20897]) ).
cnf(s204,plain,
( ~ spl169_5
| ~ spl169_21
| ~ spl169_85 ),
inference(sat_conversion,[],[f21068]) ).
cnf(s248,plain,
spl169_21,
inference(rat,[],[s183,s12]) ).
cnf(s251,plain,
spl169_20,
inference(rat,[],[s26,s12]) ).
cnf(s258,plain,
spl169_6,
inference(rat,[],[s185,s12,s248]) ).
cnf(s260,plain,
spl169_65,
inference(rat,[],[s83,s251]) ).
cnf(s268,plain,
spl169_85,
inference(rat,[],[s102,s251,s12,s22,s260]) ).
cnf(s277,plain,
~ spl169_5,
inference(rat,[],[s204,s248,s268]) ).
cnf(s302,plain,
$false,
inference(rat,[],[s3,s258,s277]) ).
fof(f21193,plain,
$false,
inference(avatar_sat_refutation,[],[s302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG225+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 19:52:41 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 13.32/2.43 % (3702564)Detected formulas, will run a generic FOF schedule.
% 13.32/2.43 % (3702575)dis-21_1_sil=8000:lcm=predicate:random_seed=717229980: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)
% 13.32/2.43 % (3702573)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=663142561:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.32/2.43 % (3702569)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=1963681109:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.32/2.43 % (3702574)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=720939837:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.32/2.43 % (3702572)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4265253030:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.32/2.43 % (3702571)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=120588944:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.32/2.43 % (3702570)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=3859464172:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.32/2.43 % (3702572)Refutation not found, incomplete strategy
% 13.32/2.43 % (3702572)------------------------------
% 13.32/2.43 % (3702572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.32/2.43 % (3702572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.43 % (3702572)CaDiCaL version: 2.1.3
% 13.32/2.43 % (3702572)Termination reason: Refutation not found, incomplete strategy
% 13.32/2.43 % (3702572)Time elapsed: 0.030 s
% 13.32/2.43 % (3702572)Peak memory usage: 94 MB
% 13.32/2.43 % (3702572)Instructions burned: 42 (million)
% 13.32/2.43 % (3702575)Instruction limit reached!
% 13.32/2.43 % (3702575)------------------------------
% 13.32/2.43 % (3702575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.32/2.43 % (3702575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.43 % (3702575)CaDiCaL version: 2.1.3
% 13.32/2.43 % (3702575)Termination reason: Instruction limit
% 13.32/2.43 % (3702575)Termination phase: Preprocessing 3
% 13.32/2.43 % (3702575)Time elapsed: 0.053 s
% 13.32/2.43 % (3702575)Peak memory usage: 95 MB
% 13.32/2.43 % (3702575)Instructions burned: 130 (million)
% 13.32/2.43 % (3702573)Instruction limit reached!
% 13.32/2.43 % (3702573)------------------------------
% 13.32/2.43 % (3702573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.32/2.43 % (3702573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.43 % (3702573)CaDiCaL version: 2.1.3
% 13.32/2.43 % (3702573)Termination reason: Instruction limit
% 13.32/2.43 % (3702573)Termination phase: Saturation
% 13.32/2.43 % (3702573)Time elapsed: 0.080 s
% 13.32/2.43 % (3702573)Peak memory usage: 94 MB
% 13.32/2.43 % (3702573)Instructions burned: 119 (million)
% 13.32/2.43 % (3702574)Instruction limit reached!
% 13.32/2.43 % (3702574)------------------------------
% 13.32/2.43 % (3702574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.32/2.43 % (3702574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.43 % (3702574)CaDiCaL version: 2.1.3
% 13.32/2.43 % (3702574)Termination reason: Instruction limit
% 13.32/2.43 % (3702574)Termination phase: Naming
% 13.32/2.43 % (3702574)Time elapsed: 0.092 s
% 13.32/2.43 % (3702574)Peak memory usage: 94 MB
% 13.32/2.43 % (3702574)Instructions burned: 140 (million)
% 13.32/2.43 % (3702583)lrs+10_1_sil=8000:sp=occurrence:random_seed=3133877322:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 13.32/2.43 % (3702585)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2059306650:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 13.32/2.43 % (3702584)lrs+10_1_sil=32000:urr=on:br=off:random_seed=875122207:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 13.32/2.43 % (3702572)------------------------------
% 13.32/2.43 % (3702572)------------------------------
% 13.32/2.43 % (3702583)Instruction limit reached!
% 13.32/2.43 % (3702583)------------------------------
% 13.32/2.43 % (3702583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.68/3.46 % (3702583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.68/3.46 % (3702583)CaDiCaL version: 2.1.3
% 20.68/3.46 % (3702583)Termination reason: Instruction limit
% 20.68/3.46 % (3702583)Termination phase: Saturation
% 20.68/3.46 % (3702583)Time elapsed: 0.106 s
% 20.68/3.46 % (3702583)Peak memory usage: 98 MB
% 20.68/3.46 % (3702583)Instructions burned: 285 (million)
% 20.68/3.46 % (3702584)Instruction limit reached!
% 20.68/3.46 % (3702584)------------------------------
% 20.68/3.46 % (3702584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.68/3.46 % (3702584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.68/3.46 % (3702584)CaDiCaL version: 2.1.3
% 20.68/3.46 % (3702584)Termination reason: Instruction limit
% 20.68/3.46 % (3702584)Termination phase: Saturation
% 20.68/3.46 % (3702584)Time elapsed: 0.089 s
% 20.68/3.46 % (3702584)Peak memory usage: 95 MB
% 20.68/3.46 % (3702584)Instructions burned: 158 (million)
% 20.68/3.46 % (3702590)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1224714201:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 20.68/3.46 % (3702589)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=1179966385:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 20.68/3.46 % (3702585)Instruction limit reached!
% 20.68/3.46 % (3702585)------------------------------
% 20.68/3.46 % (3702585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.68/3.46 % (3702585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.68/3.46 % (3702585)CaDiCaL version: 2.1.3
% 20.68/3.46 % (3702585)Termination reason: Instruction limit
% 20.68/3.46 % (3702585)Termination phase: Saturation
% 20.68/3.46 % (3702585)Time elapsed: 0.228 s
% 20.68/3.46 % (3702585)Peak memory usage: 98 MB
% 20.68/3.46 % (3702585)Instructions burned: 326 (million)
% 20.68/3.46 % (3702590)Instruction limit reached!
% 20.68/3.46 % (3702590)------------------------------
% 20.68/3.46 % (3702590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.68/3.46 % (3702590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.68/3.46 % (3702590)CaDiCaL version: 2.1.3
% 20.68/3.46 % (3702590)Termination reason: Instruction limit
% 20.68/3.46 % (3702590)Termination phase: Saturation
% 20.68/3.46 % (3702590)Time elapsed: 0.098 s
% 20.68/3.46 % (3702590)Peak memory usage: 99 MB
% 20.68/3.46 % (3702590)Instructions burned: 295 (million)
% 20.68/3.46 % (3702591)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2116057734:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 20.68/3.46 % (3702589)Instruction limit reached!
% 20.68/3.46 % (3702589)------------------------------
% 20.68/3.46 % (3702589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.68/3.46 % (3702589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.68/3.46 % (3702589)CaDiCaL version: 2.1.3
% 20.68/3.46 % (3702589)Termination reason: Instruction limit
% 20.68/3.46 % (3702589)Termination phase: Property scanning
% 20.68/3.46 % (3702589)Time elapsed: 0.158 s
% 20.68/3.46 % (3702589)Peak memory usage: 100 MB
% 20.68/3.46 % (3702589)Instructions burned: 250 (million)
% 20.68/3.46 % (3702595)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2302649604:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 20.68/3.46 % (3702594)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=673865245:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 20.68/3.46 % (3702595)Instruction limit reached!
% 20.68/3.46 % (3702595)------------------------------
% 20.68/3.46 % (3702595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.68/3.46 % (3702595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.68/3.46 % (3702595)CaDiCaL version: 2.1.3
% 20.68/3.46 % (3702595)Termination reason: Instruction limit
% 20.68/3.46 % (3702595)Termination phase: Preprocessing 3
% 20.68/3.46 % (3702595)Time elapsed: 0.051 s
% 20.68/3.46 % (3702595)Peak memory usage: 97 MB
% 20.68/3.46 % (3702595)Instructions burned: 129 (million)
% 20.68/3.46 % (3702594)Instruction limit reached!
% 20.68/3.46 % (3702594)------------------------------
% 20.68/3.46 % (3702594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.68/3.46 % (3702594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702594)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702594)Termination reason: Instruction limit
% 28.01/4.45 % (3702594)Termination phase: Property scanning
% 28.01/4.45 % (3702594)Time elapsed: 0.072 s
% 28.01/4.45 % (3702594)Peak memory usage: 94 MB
% 28.01/4.45 % (3702594)Instructions burned: 115 (million)
% 28.01/4.45 % (3702597)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1783927858:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 28.01/4.45 % (3702600)lrs+10_1_sil=8000:sp=occurrence:random_seed=79146116:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 28.01/4.45 % (3702597)Instruction limit reached!
% 28.01/4.45 % (3702597)------------------------------
% 28.01/4.45 % (3702597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702597)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702597)Termination reason: Instruction limit
% 28.01/4.45 % (3702597)Termination phase: SInE selection
% 28.01/4.45 % (3702597)Time elapsed: 0.051 s
% 28.01/4.45 % (3702597)Peak memory usage: 90 MB
% 28.01/4.45 % (3702597)Instructions burned: 114 (million)
% 28.01/4.45 % (3702601)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=916741568:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 28.01/4.45 % (3702604)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4052637878:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 28.01/4.45 % (3702600)Instruction limit reached!
% 28.01/4.45 % (3702600)------------------------------
% 28.01/4.45 % (3702600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702600)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702600)Termination reason: Instruction limit
% 28.01/4.45 % (3702600)Termination phase: Saturation
% 28.01/4.45 % (3702600)Time elapsed: 0.339 s
% 28.01/4.45 % (3702600)Peak memory usage: 109 MB
% 28.01/4.45 % (3702600)Instructions burned: 909 (million)
% 28.01/4.45 % (3702601)Instruction limit reached!
% 28.01/4.45 % (3702601)------------------------------
% 28.01/4.45 % (3702601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702601)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702601)Termination reason: Instruction limit
% 28.01/4.45 % (3702601)Termination phase: Saturation
% 28.01/4.45 % (3702601)Time elapsed: 0.284 s
% 28.01/4.45 % (3702601)Peak memory usage: 97 MB
% 28.01/4.45 % (3702601)Instructions burned: 437 (million)
% 28.01/4.45 % (3702607)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=367634535:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 28.01/4.45 % (3702608)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4134093083:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 28.01/4.45 % (3702607)Instruction limit reached!
% 28.01/4.45 % (3702607)------------------------------
% 28.01/4.45 % (3702607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702607)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702607)Termination reason: Instruction limit
% 28.01/4.45 % (3702607)Termination phase: Saturation
% 28.01/4.45 % (3702607)Time elapsed: 0.089 s
% 28.01/4.45 % (3702607)Peak memory usage: 97 MB
% 28.01/4.45 % (3702607)Instructions burned: 135 (million)
% 28.01/4.45 % (3702611)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=184807322:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 28.01/4.45 % (3702608)Instruction limit reached!
% 28.01/4.45 % (3702608)------------------------------
% 28.01/4.45 % (3702608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702608)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702608)Termination reason: Instruction limit
% 28.01/4.45 % (3702608)Termination phase: Saturation
% 28.01/4.45 % (3702608)Time elapsed: 0.325 s
% 28.01/4.45 % (3702608)Peak memory usage: 107 MB
% 28.01/4.45 % (3702608)Instructions burned: 592 (million)
% 28.01/4.45 % (3702613)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2954694142:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/125Mi)
% 28.01/4.45 % (3702613)Instruction limit reached!
% 28.01/4.45 % (3702613)------------------------------
% 28.01/4.45 % (3702613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702613)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702613)Termination reason: Instruction limit
% 28.01/4.45 % (3702613)Termination phase: General splitting
% 28.01/4.45 % (3702613)Time elapsed: 0.074 s
% 28.01/4.45 % (3702613)Peak memory usage: 92 MB
% 28.01/4.45 % (3702613)Instructions burned: 126 (million)
% 28.01/4.45 % (3702591)Instruction limit reached!
% 28.01/4.45 % (3702591)------------------------------
% 28.01/4.45 % (3702591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702591)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702591)Termination reason: Instruction limit
% 28.01/4.45 % (3702591)Termination phase: Saturation
% 28.01/4.45 % (3702591)Time elapsed: 1.509 s
% 28.01/4.45 % (3702591)Peak memory usage: 235 MB
% 28.01/4.45 % (3702591)Instructions burned: 2352 (million)
% 28.01/4.45 % (3702615)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2135734860:i=134:gtgl=5:slsql=off:gtg=exists_sym_2978 on theBenchmark for (2978ds/134Mi)
% 28.01/4.45 % (3702615)Instruction limit reached!
% 28.01/4.45 % (3702615)------------------------------
% 28.01/4.45 % (3702615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702615)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702615)Termination reason: Instruction limit
% 28.01/4.45 % (3702615)Termination phase: SInE selection
% 28.01/4.45 % (3702615)Time elapsed: 0.069 s
% 28.01/4.45 % (3702615)Peak memory usage: 90 MB
% 28.01/4.45 % (3702615)Instructions burned: 134 (million)
% 28.01/4.45 % (3702617)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3270531313:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2977 on theBenchmark for (2977ds/141Mi)
% 28.01/4.45 % (3702618)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1868252965:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2976 on theBenchmark for (2976ds/431Mi)
% 28.01/4.45 % (3702617)Instruction limit reached!
% 28.01/4.45 % (3702617)------------------------------
% 28.01/4.45 % (3702617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702617)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702617)Termination reason: Instruction limit
% 28.01/4.45 % (3702617)Termination phase: Saturation
% 28.01/4.45 % (3702617)Time elapsed: 0.091 s
% 28.01/4.45 % (3702617)Peak memory usage: 96 MB
% 28.01/4.45 % (3702617)Instructions burned: 142 (million)
% 28.01/4.45 % (3702618)Refutation not found, incomplete strategy
% 28.01/4.45 % (3702618)------------------------------
% 28.01/4.45 % (3702618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702618)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702618)Termination reason: Refutation not found, incomplete strategy
% 28.01/4.45 % (3702618)Time elapsed: 0.029 s
% 28.01/4.45 % (3702618)Peak memory usage: 94 MB
% 28.01/4.45 % (3702618)Instructions burned: 36 (million)
% 28.01/4.45 % (3702621)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2801220804:i=6060:aac=none:ins=25_2974 on theBenchmark for (2974ds/6060Mi)
% 28.01/4.45 % (3702618)------------------------------
% 28.01/4.45 % (3702618)------------------------------
% 28.01/4.45 % (3702623)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=2945105892:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2972 on theBenchmark for (2972ds/150Mi)
% 28.01/4.45 % (3702623)Instruction limit reached!
% 28.01/4.45 % (3702623)------------------------------
% 28.01/4.45 % (3702623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.01/4.45 % (3702623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.01/4.45 % (3702623)CaDiCaL version: 2.1.3
% 28.01/4.45 % (3702623)Termination reason: Instruction limit
% 28.01/4.45 % (3702623)Termination phase: Preprocessing 3
% 28.01/4.45 % (3702623)Time elapsed: 0.102 s
% 28.01/4.45 % (3702623)Peak memory usage: 97 MB
% 28.01/4.45 % (3702623)Instructions burned: 151 (million)
% 28.01/4.45 % (3702625)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=129172266:i=14155:bd=all_2969 on theBenchmark for (2969ds/14155Mi)
% 28.01/4.45 % (3702604)First to succeed.
% 28.01/4.45 % (3702604)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3702564"
% 28.01/4.45 % (3702604)Refutation found. Thanks to Tanya!
% 28.01/4.45 % SZS status Theorem for theBenchmark
% 28.01/4.45 % SZS output start Proof for theBenchmark
% See solution above
% 28.53/4.65 % (3702604)------------------------------
% 28.53/4.65 % (3702604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.53/4.65 % (3702604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.53/4.65 % (3702604)CaDiCaL version: 2.1.3
% 28.53/4.65 % (3702604)Termination reason: Refutation
% 28.53/4.65 % (3702604)Time elapsed: 2.540 s
% 28.53/4.65 % (3702604)Peak memory usage: 161 MB
% 28.53/4.65 % (3702604)Instructions burned: 4043 (million)
% 28.53/4.65 % (3702604)------------------------------
% 28.53/4.65 % (3702604)------------------------------
% 28.53/4.65 % (3702564)Success in time 4.044 s
% 28.53/4.65 % Vampire exiting
%------------------------------------------------------------------------------