%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG225+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 : n004.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 0.64s 1.03s
% Output : Refutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 143 ( 21 unt; 6 def)
% Number of atoms : 466 ( 77 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 539 ( 216 ~; 235 |; 51 &)
% ( 19 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 7 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 216 ( 0 sgn 203 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,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)],[f1]) ).
fof(f12,axiom,
! [X0,X1] :
( X0 = X1
<=> ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f13,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( v2_relat_1(X1)
<=> ! [X2] :
~ ( r2_hidden(X2,X0)
& v1_xboole_0(k1_funct_1(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_pboole) ).
fof(f14,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(f15,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(f16,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(f21,axiom,
! [X0] : m1_pboole(k1_pboole(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pboole) ).
fof(f27,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(f33,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f37,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(f57,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(f58,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f59,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f65,axiom,
! [X0,X1] :
~ ( r2_hidden(X0,X1)
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f67,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(f76,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,[],[f2]) ).
fof(f77,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,[],[f76]) ).
fof(f88,plain,
! [X0,X1] :
( ( v2_relat_1(X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| ~ v1_xboole_0(k1_funct_1(X1,X2)) ) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f89,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,[],[f14]) ).
fof(f90,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f91,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f101,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,[],[f37]) ).
fof(f102,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,[],[f101]) ).
fof(f110,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,[],[f57]) ).
fof(f111,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f112,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f113,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f112]) ).
fof(f119,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f121,plain,
! [X0,X1] :
( k7_relat_1(X1,X0) = X1
| ~ r1_tarski(k1_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f122,plain,
! [X0,X1] :
( k7_relat_1(X1,X0) = X1
| ~ r1_tarski(k1_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
( sK1 != k1_funct_4(k1_pboole(sK0),k7_relat_1(sK1,k1_closure3(sK0,sK1)))
& v2_relat_1(sK1)
& m1_pboole(sK1,sK0)
& ~ v1_xboole_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f77]) ).
fof(f124,plain,
! [X0,X1] :
( ( X0 = X1
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X0) )
& ( ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f125,plain,
! [X0,X1] :
( ( X0 = X1
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X0) )
& ( ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ( ( v2_relat_1(X1)
| ? [X2] :
( r2_hidden(X2,X0)
& v1_xboole_0(k1_funct_1(X1,X2)) ) )
& ( ! [X2] :
( ~ r2_hidden(X2,X0)
| ~ v1_xboole_0(k1_funct_1(X1,X2)) )
| ~ v2_relat_1(X1) ) )
| ~ m1_pboole(X1,X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f127,plain,
! [X0,X1] :
( ( ( v2_relat_1(X1)
| ? [X2] :
( r2_hidden(X2,X0)
& v1_xboole_0(k1_funct_1(X1,X2)) ) )
& ( ! [X3] :
( ~ r2_hidden(X3,X0)
| ~ v1_xboole_0(k1_funct_1(X1,X3)) )
| ~ v2_relat_1(X1) ) )
| ~ m1_pboole(X1,X0) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ( ( v2_relat_1(X1)
| ( r2_hidden(sK2(X0,X1),X0)
& v1_xboole_0(k1_funct_1(X1,sK2(X0,X1))) ) )
& ( ! [X3] :
( ~ r2_hidden(X3,X0)
| ~ v1_xboole_0(k1_funct_1(X1,X3)) )
| ~ v2_relat_1(X1) ) )
| ~ m1_pboole(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f127]) ).
fof(f129,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,[],[f89]) ).
fof(f130,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,[],[f91]) ).
fof(f131,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,[],[f92]) ).
fof(f132,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,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK3(X0,X1),X1)
& r2_hidden(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f132]) ).
fof(f136,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,[],[f102]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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(sK6(X0,X1,X2),X1)
& sK6(X0,X1,X2) = X0
& k1_xboole_0 != k1_funct_1(X2,sK6(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,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f137]) ).
fof(f161,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f123]) ).
fof(f162,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f123]) ).
fof(f163,plain,
v2_relat_1(sK1),
inference(cnf_transformation,[],[f123]) ).
fof(f164,plain,
sK1 != k1_funct_4(k1_pboole(sK0),k7_relat_1(sK1,k1_closure3(sK0,sK1))),
inference(cnf_transformation,[],[f123]) ).
fof(f174,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f125]) ).
fof(f175,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| X0 = X1
| ~ r1_tarski(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f176,plain,
! [X3,X0,X1] :
( ~ v1_xboole_0(k1_funct_1(X1,X3))
| ~ r2_hidden(X3,X0)
| ~ v2_relat_1(X1)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f180,plain,
! [X2,X0,X1] :
( k1_closure3(X0,X1) = X2
| a_2_0_closure3(X0,X1) != X2
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f181,plain,
! [X0,X1] :
( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f184,plain,
! [X0,X1] :
( r2_hidden(sK3(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f185,plain,
! [X0,X1] :
( ~ r2_hidden(sK3(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f189,plain,
! [X0] : m1_pboole(k1_pboole(X0),X0),
inference(cnf_transformation,[],[f21]) ).
fof(f191,plain,
! [X0,X1] :
( v1_funct_1(X1)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f192,plain,
! [X0,X1] :
( v1_relat_1(X1)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f199,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f33]) ).
fof(f207,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) = X0
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f208,plain,
! [X2,X0,X1] :
( m1_subset_1(sK6(X0,X1,X2),X1)
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f209,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,[],[f138]) ).
fof(f258,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,[],[f110]) ).
fof(f259,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f260,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f268,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f270,plain,
! [X0,X1] :
( ~ r1_tarski(k1_relat_1(X1),X0)
| k7_relat_1(X1,X0) = X1
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f271,plain,
! [X1] : r1_tarski(X1,X1),
inference(equality_resolution,[],[f174]) ).
fof(f273,plain,
! [X0,X1] :
( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(equality_resolution,[],[f180]) ).
fof(f276,plain,
! [X2,X3,X1] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| ~ m1_subset_1(X3,X1)
| r2_hidden(X3,a_2_0_closure3(X1,X2))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(equality_resolution,[],[f209]) ).
fof(f345,plain,
! [X0,X1] :
( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0)
| ~ v1_funct_1(X1) ),
inference(forward_subsumption_resolution,[],[f181,f192]) ).
fof(f346,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 ),
inference(forward_subsumption_resolution,[],[f345,f191]) ).
fof(f349,plain,
sK0 = k1_relat_1(sK1),
inference(resolution,[],[f346,f162]) ).
fof(f355,plain,
! [X0] :
( ~ r1_tarski(sK0,X0)
| sK1 = k7_relat_1(sK1,X0)
| ~ v1_relat_1(sK1) ),
inference(superposition,[],[f270,f349]) ).
fof(f358,definition,
( spl25_7
<=> v1_relat_1(sK1) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
fof(f360,plain,
( ~ v1_relat_1(sK1)
| spl25_7 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f362,definition,
( spl25_8
<=> ! [X0] :
( ~ r1_tarski(sK0,X0)
| sK1 = k7_relat_1(sK1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
fof(f363,plain,
( ! [X0] :
( ~ r1_tarski(sK0,X0)
| sK1 = k7_relat_1(sK1,X0) )
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f364,plain,
( ~ spl25_7
| spl25_8 ),
inference(avatar_split_clause,[],[f355,f362,f358]) ).
fof(f365,plain,
( ! [X0] : ~ m1_pboole(sK1,X0)
| spl25_7 ),
inference(resolution,[],[f360,f192]) ).
fof(f368,plain,
( $false
| spl25_7 ),
inference(resolution,[],[f365,f162]) ).
fof(f370,plain,
spl25_7,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f376,plain,
( sK1 = k7_relat_1(sK1,sK0)
| ~ spl25_8 ),
inference(resolution,[],[f363,f271]) ).
fof(f380,plain,
! [X0] :
( sK1 != k7_relat_1(sK1,k1_closure3(sK0,sK1))
| ~ m1_pboole(k7_relat_1(sK1,k1_closure3(sK0,sK1)),X0)
| ~ m1_pboole(k1_pboole(sK0),X0)
| v1_xboole_0(X0) ),
inference(superposition,[],[f164,f258]) ).
fof(f384,definition,
( spl25_9
<=> ! [X0] :
( ~ m1_pboole(k7_relat_1(sK1,k1_closure3(sK0,sK1)),X0)
| v1_xboole_0(X0)
| ~ m1_pboole(k1_pboole(sK0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl25_9])],[avatar_definition]) ).
fof(f385,plain,
( ! [X0] :
( ~ m1_pboole(k7_relat_1(sK1,k1_closure3(sK0,sK1)),X0)
| v1_xboole_0(X0)
| ~ m1_pboole(k1_pboole(sK0),X0) )
| ~ spl25_9 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,definition,
( spl25_10
<=> sK1 = k7_relat_1(sK1,k1_closure3(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl25_10])],[avatar_definition]) ).
fof(f388,plain,
( sK1 = k7_relat_1(sK1,k1_closure3(sK0,sK1))
| ~ spl25_10 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f389,plain,
( sK1 != k7_relat_1(sK1,k1_closure3(sK0,sK1))
| spl25_10 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f390,plain,
( spl25_9
| ~ spl25_10 ),
inference(avatar_split_clause,[],[f380,f387,f384]) ).
fof(f391,plain,
( sK1 != k7_relat_1(sK1,a_2_0_closure3(sK0,sK1))
| ~ m1_pboole(sK1,sK0)
| v1_xboole_0(sK0)
| spl25_10 ),
inference(superposition,[],[f389,f273]) ).
fof(f392,plain,
( sK1 != k7_relat_1(sK1,a_2_0_closure3(sK0,sK1))
| v1_xboole_0(sK0)
| spl25_10 ),
inference(forward_subsumption_resolution,[],[f391,f162]) ).
fof(f393,plain,
( sK1 != k7_relat_1(sK1,a_2_0_closure3(sK0,sK1))
| spl25_10 ),
inference(forward_subsumption_resolution,[],[f392,f161]) ).
fof(f405,plain,
! [X2,X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1)
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(superposition,[],[f208,f207]) ).
fof(f406,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| m1_subset_1(X0,X1)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(duplicate_literal_removal,[],[f405]) ).
fof(f423,plain,
! [X2,X3,X0,X1] :
( ~ v1_xboole_0(k1_xboole_0)
| ~ r2_hidden(X1,X2)
| ~ v2_relat_1(X0)
| ~ m1_pboole(X0,X2)
| ~ m1_subset_1(X1,X3)
| r2_hidden(X1,a_2_0_closure3(X3,X0))
| v1_xboole_0(X3)
| ~ m1_pboole(X0,X3) ),
inference(superposition,[],[f176,f276]) ).
fof(f426,plain,
! [X2,X3,X0,X1] :
( ~ v2_relat_1(X0)
| ~ r2_hidden(X1,X2)
| ~ m1_pboole(X0,X2)
| ~ m1_subset_1(X1,X3)
| r2_hidden(X1,a_2_0_closure3(X3,X0))
| v1_xboole_0(X3)
| ~ m1_pboole(X0,X3) ),
inference(forward_subsumption_resolution,[],[f423,f199]) ).
fof(f460,plain,
! [X0,X1] :
( ~ m1_subset_1(sK3(X0,X1),X1)
| v1_xboole_0(X1)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f185,f260]) ).
fof(f523,plain,
! [X2,X0,X1] :
( m1_subset_1(sK3(a_2_0_closure3(X0,X1),X2),X0)
| v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| r1_tarski(a_2_0_closure3(X0,X1),X2) ),
inference(resolution,[],[f406,f184]) ).
fof(f617,plain,
! [X2,X0,X1] :
( ~ m1_pboole(sK1,X1)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X2)
| r2_hidden(X0,a_2_0_closure3(X2,sK1))
| v1_xboole_0(X2)
| ~ m1_pboole(sK1,X2) ),
inference(resolution,[],[f426,f163]) ).
fof(f686,plain,
! [X0,X1] :
( ~ m1_pboole(sK1,X0)
| ~ r2_hidden(X1,X0)
| ~ m1_subset_1(X1,X0)
| r2_hidden(X1,a_2_0_closure3(X0,sK1))
| v1_xboole_0(X0) ),
inference(factoring,[],[f617]) ).
fof(f687,plain,
! [X0,X1] :
( ~ m1_pboole(sK1,X0)
| ~ r2_hidden(X1,X0)
| r2_hidden(X1,a_2_0_closure3(X0,sK1))
| v1_xboole_0(X0) ),
inference(forward_subsumption_resolution,[],[f686,f259]) ).
fof(f689,plain,
! [X0,X1] :
( ~ m1_pboole(sK1,X0)
| ~ r2_hidden(X1,X0)
| r2_hidden(X1,a_2_0_closure3(X0,sK1)) ),
inference(forward_subsumption_resolution,[],[f687,f268]) ).
fof(f707,plain,
! [X0] :
( ~ r2_hidden(X0,sK0)
| r2_hidden(X0,a_2_0_closure3(sK0,sK1)) ),
inference(resolution,[],[f689,f162]) ).
fof(f716,plain,
! [X0] :
( r1_tarski(sK0,X0)
| r2_hidden(sK3(sK0,X0),a_2_0_closure3(sK0,sK1)) ),
inference(resolution,[],[f707,f184]) ).
fof(f1035,plain,
! [X0,X1] :
( v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| r1_tarski(a_2_0_closure3(X0,X1),X0)
| v1_xboole_0(X0)
| r1_tarski(a_2_0_closure3(X0,X1),X0) ),
inference(resolution,[],[f523,f460]) ).
fof(f1041,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_xboole_0(X0)
| r1_tarski(a_2_0_closure3(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1035]) ).
fof(f2038,plain,
( v1_xboole_0(sK0)
| r1_tarski(a_2_0_closure3(sK0,sK1),sK0) ),
inference(resolution,[],[f1041,f162]) ).
fof(f2042,plain,
r1_tarski(a_2_0_closure3(sK0,sK1),sK0),
inference(forward_subsumption_resolution,[],[f2038,f161]) ).
fof(f2047,plain,
( sK0 = a_2_0_closure3(sK0,sK1)
| ~ r1_tarski(sK0,a_2_0_closure3(sK0,sK1)) ),
inference(resolution,[],[f2042,f175]) ).
fof(f2059,definition,
( spl25_78
<=> sK0 = a_2_0_closure3(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl25_78])],[avatar_definition]) ).
fof(f2061,plain,
( sK0 = a_2_0_closure3(sK0,sK1)
| ~ spl25_78 ),
inference(avatar_component_clause,[],[f2059]) ).
fof(f2064,definition,
( spl25_79
<=> r1_tarski(sK0,a_2_0_closure3(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl25_79])],[avatar_definition]) ).
fof(f2066,plain,
( ~ r1_tarski(sK0,a_2_0_closure3(sK0,sK1))
| spl25_79 ),
inference(avatar_component_clause,[],[f2064]) ).
fof(f2067,plain,
( ~ spl25_79
| spl25_78 ),
inference(avatar_split_clause,[],[f2047,f2059,f2064]) ).
fof(f2092,plain,
( r2_hidden(sK3(sK0,a_2_0_closure3(sK0,sK1)),a_2_0_closure3(sK0,sK1))
| spl25_79 ),
inference(resolution,[],[f2066,f716]) ).
fof(f2475,plain,
( r1_tarski(sK0,a_2_0_closure3(sK0,sK1))
| spl25_79 ),
inference(resolution,[],[f2092,f185]) ).
fof(f2497,plain,
( $false
| spl25_79 ),
inference(forward_subsumption_resolution,[],[f2475,f2066]) ).
fof(f2498,plain,
spl25_79,
inference(avatar_contradiction_clause,[],[f2497]) ).
fof(f2514,plain,
( sK1 != k7_relat_1(sK1,sK0)
| spl25_10
| ~ spl25_78 ),
inference(superposition,[],[f393,f2061]) ).
fof(f2567,plain,
( $false
| ~ spl25_8
| spl25_10
| ~ spl25_78 ),
inference(forward_subsumption_resolution,[],[f2514,f376]) ).
fof(f2568,plain,
( ~ spl25_8
| spl25_10
| ~ spl25_78 ),
inference(avatar_contradiction_clause,[],[f2567]) ).
fof(f2587,plain,
( ! [X0] :
( ~ m1_pboole(sK1,X0)
| v1_xboole_0(X0)
| ~ m1_pboole(k1_pboole(sK0),X0) )
| ~ spl25_9
| ~ spl25_10 ),
inference(forward_demodulation,[],[f385,f388]) ).
fof(f2590,plain,
( v1_xboole_0(sK0)
| ~ m1_pboole(k1_pboole(sK0),sK0)
| ~ spl25_9
| ~ spl25_10 ),
inference(resolution,[],[f2587,f162]) ).
fof(f2593,plain,
( ~ m1_pboole(k1_pboole(sK0),sK0)
| ~ spl25_9
| ~ spl25_10 ),
inference(forward_subsumption_resolution,[],[f2590,f161]) ).
fof(f2595,plain,
( $false
| ~ spl25_9
| ~ spl25_10 ),
inference(forward_subsumption_resolution,[],[f2593,f189]) ).
fof(f2596,plain,
( ~ spl25_9
| ~ spl25_10 ),
inference(avatar_contradiction_clause,[],[f2595]) ).
cnf(s4,plain,
( ~ spl25_7
| spl25_8 ),
inference(sat_conversion,[],[f364]) ).
cnf(s5,plain,
spl25_7,
inference(sat_conversion,[],[f370]) ).
cnf(s6,plain,
( spl25_9
| ~ spl25_10 ),
inference(sat_conversion,[],[f390]) ).
cnf(s78,plain,
( spl25_78
| ~ spl25_79 ),
inference(sat_conversion,[],[f2067]) ).
cnf(s87,plain,
spl25_79,
inference(sat_conversion,[],[f2498]) ).
cnf(s91,plain,
( ~ spl25_8
| spl25_10
| ~ spl25_78 ),
inference(sat_conversion,[],[f2568]) ).
cnf(s92,plain,
( ~ spl25_9
| ~ spl25_10 ),
inference(sat_conversion,[],[f2596]) ).
cnf(s95,plain,
spl25_78,
inference(rat,[],[s78,s87]) ).
cnf(s108,plain,
spl25_8,
inference(rat,[],[s4,s5]) ).
cnf(s109,plain,
spl25_10,
inference(rat,[],[s91,s95,s108]) ).
cnf(s110,plain,
~ spl25_9,
inference(rat,[],[s92,s109]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s6,s109,s110]) ).
fof(f2602,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG225+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 19:50:22 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 0.64/1.03 % (687714)Detected formulas, will run a generic FOF schedule.
% 0.64/1.03 % (687719)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=502968685:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.64/1.03 % (687724)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3243586851:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.64/1.03 % (687725)dis-21_1_sil=8000:lcm=predicate:random_seed=4054384261: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)
% 0.64/1.03 % (687723)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3285448517:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.64/1.03 % (687722)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1955406253:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.64/1.03 % (687720)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=3003284022:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.64/1.03 % (687721)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=3498479847:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.64/1.03 % (687722)Refutation not found, incomplete strategy
% 0.64/1.03 % (687722)------------------------------
% 0.64/1.03 % (687722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/1.03 % (687722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/1.03 % (687722)CaDiCaL version: 2.1.3
% 0.64/1.03 % (687722)Termination reason: Refutation not found, incomplete strategy
% 0.64/1.03 % (687722)Time elapsed: 0.002 s
% 0.64/1.03 % (687722)Peak memory usage: 88 MB
% 0.64/1.03 % (687722)Instructions burned: 2 (million)
% 0.64/1.03 % (687724)First to succeed.
% 0.64/1.03 % (687724)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-687714"
% 0.64/1.03 % (687723)Instruction limit reached!
% 0.64/1.03 % (687723)------------------------------
% 0.64/1.03 % (687723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/1.03 % (687723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/1.03 % (687723)CaDiCaL version: 2.1.3
% 0.64/1.03 % (687723)Termination reason: Instruction limit
% 0.64/1.03 % (687723)Termination phase: Saturation
% 0.64/1.03 % (687723)Time elapsed: 0.070 s
% 0.64/1.03 % (687723)Peak memory usage: 88 MB
% 0.64/1.03 % (687723)Instructions burned: 120 (million)
% 0.64/1.03 % (687725)Instruction limit reached!
% 0.64/1.03 % (687725)------------------------------
% 0.64/1.03 % (687725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/1.03 % (687725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/1.03 % (687725)CaDiCaL version: 2.1.3
% 0.64/1.03 % (687725)Termination reason: Instruction limit
% 0.64/1.03 % (687725)Termination phase: Saturation
% 0.64/1.03 % (687725)Time elapsed: 0.079 s
% 0.64/1.03 % (687725)Peak memory usage: 90 MB
% 0.64/1.03 % (687725)Instructions burned: 129 (million)
% 0.64/1.03 % (687724)Refutation found. Thanks to Tanya!
% 0.64/1.03 % SZS status Theorem for theBenchmark
% 0.64/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.20/1.23 % (687724)------------------------------
% 3.20/1.23 % (687724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.23 % (687724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.23 % (687724)CaDiCaL version: 2.1.3
% 3.20/1.23 % (687724)Termination reason: Refutation
% 3.20/1.23 % (687724)Time elapsed: 0.043 s
% 3.20/1.23 % (687724)Peak memory usage: 91 MB
% 3.20/1.23 % (687724)Instructions burned: 111 (million)
% 3.20/1.23 % (687724)------------------------------
% 3.20/1.23 % (687724)------------------------------
% 3.20/1.23 % (687714)Success in time 0.363 s
% 3.20/1.23 % Vampire exiting
%------------------------------------------------------------------------------