%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG225+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 09:29:51 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 103 ( 21 unt; 2 def)
% Number of atoms : 329 ( 74 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 373 ( 147 ~; 150 |; 45 &)
% ( 14 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 161 ( 0 sgn 148 !; 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/sandbox2/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(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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f17,axiom,
! [X0] : k1_pboole(X0) = k2_funcop_1(X0,k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pboole) ).
fof(f21,axiom,
! [X0] : m1_pboole(k1_pboole(X0),X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
fof(f33,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t1_closure3) ).
fof(f58,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
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/sandbox2/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(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(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(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(f186,plain,
! [X0] : k1_pboole(X0) = k2_funcop_1(X0,k1_xboole_0),
inference(cnf_transformation,[],[f17]) ).
fof(f189,plain,
! [X0] : m1_pboole(k1_pboole(X0),X0),
inference(cnf_transformation,[],[f21]) ).
fof(f191,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_funct_1(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f192,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_relat_1(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f199,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f33]) ).
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] :
( ~ m1_pboole(X2,X0)
| k1_funct_4(X1,X2) = X2
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f259,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
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,
sK1 != k1_funct_4(k2_funcop_1(sK0,k1_xboole_0),k7_relat_1(sK1,k1_closure3(sK0,sK1))),
inference(definition_unfolding,[],[f164,f186]) ).
fof(f272,plain,
! [X0] : m1_pboole(k2_funcop_1(X0,k1_xboole_0),X0),
inference(definition_unfolding,[],[f189,f186]) ).
fof(f281,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| v1_xboole_0(X0) ),
inference(equality_resolution,[],[f180]) ).
fof(f284,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,[],[f209]) ).
fof(f307,plain,
v1_relat_1(sK1),
inference(resolution,[],[f192,f162]) ).
fof(f357,plain,
! [X0,X1] :
( m1_subset_1(sK3(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f184,f259]) ).
fof(f478,plain,
! [X0,X1] :
( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0)
| ~ v1_funct_1(X1) ),
inference(forward_subsumption_resolution,[],[f181,f192]) ).
fof(f479,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 ),
inference(forward_subsumption_resolution,[],[f478,f191]) ).
fof(f482,plain,
sK0 = k1_relat_1(sK1),
inference(resolution,[],[f479,f162]) ).
fof(f489,plain,
! [X0] :
( ~ r1_tarski(sK0,X0)
| sK1 = k7_relat_1(sK1,X0)
| ~ v1_relat_1(sK1) ),
inference(superposition,[],[f270,f482]) ).
fof(f490,plain,
! [X0] :
( ~ r1_tarski(sK0,X0)
| sK1 = k7_relat_1(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f489,f307]) ).
fof(f524,plain,
( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
| v1_xboole_0(sK0) ),
inference(resolution,[],[f281,f162]) ).
fof(f528,plain,
k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1),
inference(forward_subsumption_resolution,[],[f524,f161]) ).
fof(f535,plain,
! [X0] :
( sK1 = k1_funct_4(X0,sK1)
| ~ m1_pboole(X0,sK0)
| v1_xboole_0(sK0) ),
inference(resolution,[],[f258,f162]) ).
fof(f539,plain,
! [X0] :
( ~ m1_pboole(X0,sK0)
| sK1 = k1_funct_4(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f535,f161]) ).
fof(f540,plain,
sK1 = k1_funct_4(k2_funcop_1(sK0,k1_xboole_0),sK1),
inference(resolution,[],[f539,f272]) ).
fof(f659,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(sK3(X0,a_2_0_closure3(X1,X2)),X1)
| k1_xboole_0 = k1_funct_1(X2,sK3(X0,a_2_0_closure3(X1,X2)))
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1)
| r1_tarski(X0,a_2_0_closure3(X1,X2)) ),
inference(resolution,[],[f284,f185]) ).
fof(f1711,plain,
! [X0] :
( ~ m1_subset_1(sK3(X0,k1_closure3(sK0,sK1)),sK0)
| k1_xboole_0 = k1_funct_1(sK1,sK3(X0,k1_closure3(sK0,sK1)))
| v1_xboole_0(sK0)
| ~ m1_pboole(sK1,sK0)
| r1_tarski(X0,k1_closure3(sK0,sK1)) ),
inference(superposition,[],[f659,f528]) ).
fof(f1719,plain,
! [X0] :
( ~ m1_subset_1(sK3(X0,k1_closure3(sK0,sK1)),sK0)
| k1_xboole_0 = k1_funct_1(sK1,sK3(X0,k1_closure3(sK0,sK1)))
| ~ m1_pboole(sK1,sK0)
| r1_tarski(X0,k1_closure3(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f1711,f161]) ).
fof(f1729,plain,
! [X0] :
( ~ m1_subset_1(sK3(X0,k1_closure3(sK0,sK1)),sK0)
| k1_xboole_0 = k1_funct_1(sK1,sK3(X0,k1_closure3(sK0,sK1)))
| r1_tarski(X0,k1_closure3(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f1719,f162]) ).
fof(f1982,plain,
( k1_xboole_0 = k1_funct_1(sK1,sK3(sK0,k1_closure3(sK0,sK1)))
| r1_tarski(sK0,k1_closure3(sK0,sK1))
| r1_tarski(sK0,k1_closure3(sK0,sK1)) ),
inference(resolution,[],[f1729,f357]) ).
fof(f1983,plain,
( k1_xboole_0 = k1_funct_1(sK1,sK3(sK0,k1_closure3(sK0,sK1)))
| r1_tarski(sK0,k1_closure3(sK0,sK1)) ),
inference(duplicate_literal_removal,[],[f1982]) ).
fof(f1985,definition,
( spl25_46
<=> r1_tarski(sK0,k1_closure3(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl25_46])],[avatar_definition]) ).
fof(f1986,plain,
( ~ r1_tarski(sK0,k1_closure3(sK0,sK1))
| spl25_46 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f1987,plain,
( r1_tarski(sK0,k1_closure3(sK0,sK1))
| ~ spl25_46 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f1989,definition,
( spl25_47
<=> k1_xboole_0 = k1_funct_1(sK1,sK3(sK0,k1_closure3(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl25_47])],[avatar_definition]) ).
fof(f1991,plain,
( k1_xboole_0 = k1_funct_1(sK1,sK3(sK0,k1_closure3(sK0,sK1)))
| ~ spl25_47 ),
inference(avatar_component_clause,[],[f1989]) ).
fof(f1992,plain,
( spl25_46
| spl25_47 ),
inference(avatar_split_clause,[],[f1983,f1989,f1985]) ).
fof(f1998,plain,
( sK1 = k7_relat_1(sK1,k1_closure3(sK0,sK1))
| ~ spl25_46 ),
inference(resolution,[],[f1987,f490]) ).
fof(f2184,plain,
( sK1 != k1_funct_4(k2_funcop_1(sK0,k1_xboole_0),sK1)
| ~ spl25_46 ),
inference(superposition,[],[f271,f1998]) ).
fof(f2188,plain,
( $false
| ~ spl25_46 ),
inference(forward_subsumption_resolution,[],[f2184,f540]) ).
fof(f2189,plain,
~ spl25_46,
inference(avatar_contradiction_clause,[],[f2188]) ).
fof(f2216,plain,
( ! [X0] :
( ~ v1_xboole_0(k1_xboole_0)
| ~ r2_hidden(sK3(sK0,k1_closure3(sK0,sK1)),X0)
| ~ v2_relat_1(sK1)
| ~ m1_pboole(sK1,X0) )
| ~ spl25_47 ),
inference(superposition,[],[f176,f1991]) ).
fof(f2217,plain,
( ! [X0] :
( ~ r2_hidden(sK3(sK0,k1_closure3(sK0,sK1)),X0)
| ~ v2_relat_1(sK1)
| ~ m1_pboole(sK1,X0) )
| ~ spl25_47 ),
inference(forward_subsumption_resolution,[],[f2216,f199]) ).
fof(f2219,plain,
( ! [X0] :
( ~ r2_hidden(sK3(sK0,k1_closure3(sK0,sK1)),X0)
| ~ m1_pboole(sK1,X0) )
| ~ spl25_47 ),
inference(forward_subsumption_resolution,[],[f2217,f163]) ).
fof(f2224,plain,
( ~ m1_pboole(sK1,sK0)
| r1_tarski(sK0,k1_closure3(sK0,sK1))
| ~ spl25_47 ),
inference(resolution,[],[f2219,f184]) ).
fof(f2229,plain,
( r1_tarski(sK0,k1_closure3(sK0,sK1))
| ~ spl25_47 ),
inference(forward_subsumption_resolution,[],[f2224,f162]) ).
fof(f2230,plain,
( $false
| spl25_46
| ~ spl25_47 ),
inference(forward_subsumption_resolution,[],[f2229,f1986]) ).
fof(f2231,plain,
( spl25_46
| ~ spl25_47 ),
inference(avatar_contradiction_clause,[],[f2230]) ).
cnf(s38,plain,
( spl25_46
| spl25_47 ),
inference(sat_conversion,[],[f1992]) ).
cnf(s53,plain,
~ spl25_46,
inference(sat_conversion,[],[f2189]) ).
cnf(s54,plain,
( spl25_46
| ~ spl25_47 ),
inference(sat_conversion,[],[f2231]) ).
cnf(s55,plain,
~ spl25_47,
inference(rat,[],[s54,s53]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s38,s55,s53]) ).
fof(f2232,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG225+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 19:50:30 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.28 % (3382959)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (3382967)dis+10_1_sil=32000:sp=arity:random_seed=3883381743:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (3382965)% WARNING: option uhcvi not known.
% 0.19/0.28 % (3382964)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1175154052_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (3382965)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=665250028:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (3382966)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=277721432:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (3382968)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2363343075:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (3382969)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1807106494:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (3382970)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3296665385:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % TRYING [1]
% 0.19/0.28 % TRYING [2]
% 0.19/0.28 % TRYING [3]
% 0.19/0.28 % TRYING [4]
% 0.19/0.28 % (3382967) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3382959-3382967"...
% 0.19/0.28 % TRYING [5]
% 0.19/0.28 % (3382967)...printing done.
% 0.19/0.28 % (3382967)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3382967)------------------------------
% 0.19/0.28 % (3382967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3382967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3382967)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3382967)Termination reason: Refutation
% 0.19/0.28 % (3382967)Time elapsed: 0.032 s
% 0.19/0.28 % (3382967)Peak memory usage: 13 MB
% 0.19/0.28 % (3382967)Instructions burned: 90 (million)
% 0.19/0.28 % (3382959)Success in time 0.058 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------