%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG231+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:19:30 AM UTC 2026
% Result : Theorem 16.88s 5.32s
% Output : Refutation 33.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of formulae : 221 ( 43 unt; 11 def)
% Number of atoms : 738 ( 79 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 900 ( 383 ~; 398 |; 71 &)
% ( 22 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 8 prp; 0-4 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-5 aty)
% Number of variables : 381 ( 1 sgn 355 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ( r1_tarski(X2,X3)
=> r2_pboole(X0,k2_closure3(X0,X1,X2),k2_closure3(X0,X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_closure3) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ( r1_tarski(X2,X3)
=> r2_pboole(X0,k2_closure3(X0,X1,X2),k2_closure3(X0,X1,X3)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f19,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(f20,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X3] :
( m4_pboole(X3,X0,X1)
=> ( X3 = k2_closure3(X0,X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X0)
=> k1_funct_1(X3,X4) = k3_tarski(a_4_0_closure3(X0,X1,X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_closure3) ).
fof(f21,axiom,
! [X0,X1] :
( X1 = k3_tarski(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> ? [X3] :
( r2_hidden(X2,X3)
& r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f22,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_pboole(X2,X0)
=> ( r2_pboole(X0,X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X0)
=> r1_tarski(k1_funct_1(X1,X3),k1_funct_1(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pboole) ).
fof(f27,axiom,
! [X0,X1,X2] :
( ( m1_pboole(X1,X0)
& m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
=> m4_pboole(k2_closure3(X0,X1,X2),X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_closure3) ).
fof(f34,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m4_pboole(X2,X0,X1)
=> m1_pboole(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m4_pboole) ).
fof(f42,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( ~ v1_xboole_0(k1_closure2(X0,X1))
& v1_fraenkel(k1_closure2(X0,X1))
& v1_pralg_2(k1_closure2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_closure2) ).
fof(f45,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_pboole(X2,X1)
& m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) )
=> ( r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
<=> ? [X5] :
( m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
& X0 = k1_funct_1(X5,X4)
& r2_hidden(X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_0_closure3) ).
fof(f68,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> k6_closure2(X0,X1) = k1_closure2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_closure2) ).
fof(f69,axiom,
! [X0,X1,X2] :
( ( m1_pboole(X1,X0)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
=> ! [X3] :
( m1_closure2(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_closure2) ).
fof(f71,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f76,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f77,axiom,
! [X0,X1,X2] :
( ( r2_hidden(X0,X1)
& m1_subset_1(X1,k1_zfmisc_1(X2)) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f82,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f71]) ).
fof(f85,plain,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( ~ v1_xboole_0(k1_closure2(X0,X1))
& v1_fraenkel(k1_closure2(X0,X1)) ) ),
inference(pure_predicate_removal,[],[f42]) ).
fof(f102,plain,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ~ v1_xboole_0(k1_closure2(X0,X1)) ),
inference(pure_predicate_removal,[],[f85]) ).
fof(f108,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_pboole(X0,k2_closure3(X0,X1,X2),k2_closure3(X0,X1,X3))
& r1_tarski(X2,X3)
& m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1))) )
& m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
& m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f109,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_pboole(X0,k2_closure3(X0,X1,X2),k2_closure3(X0,X1,X3))
& r1_tarski(X2,X3)
& m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1))) )
& m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
& m1_pboole(X1,X0) ),
inference(flattening,[],[f108]) ).
fof(f132,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f133,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ( X3 = k2_closure3(X0,X1,X2)
<=> ! [X4] :
( k1_funct_1(X3,X4) = k3_tarski(a_4_0_closure3(X0,X1,X2,X4))
| ~ r2_hidden(X4,X0) ) )
| ~ m4_pboole(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f134,plain,
! [X0,X1] :
( ! [X2] :
( ( r2_pboole(X0,X1,X2)
<=> ! [X3] :
( r1_tarski(k1_funct_1(X1,X3),k1_funct_1(X2,X3))
| ~ r2_hidden(X3,X0) ) )
| ~ m1_pboole(X2,X0) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f135,plain,
! [X0,X1,X2] :
( m4_pboole(k2_closure3(X0,X1,X2),X0,X1)
| ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f136,plain,
! [X0,X1,X2] :
( m4_pboole(k2_closure3(X0,X1,X2),X0,X1)
| ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) ),
inference(flattening,[],[f135]) ).
fof(f143,plain,
! [X0,X1] :
( ! [X2] :
( m1_pboole(X2,X0)
| ~ m4_pboole(X2,X0,X1) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f149,plain,
! [X0,X1] :
( ~ v1_xboole_0(k1_closure2(X0,X1))
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f102]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
<=> ? [X5] :
( m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
& X0 = k1_funct_1(X5,X4)
& r2_hidden(X5,X3) ) )
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(ennf_transformation,[],[f45]) ).
fof(f155,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
<=> ? [X5] :
( m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
& X0 = k1_funct_1(X5,X4)
& r2_hidden(X5,X3) ) )
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(flattening,[],[f154]) ).
fof(f167,plain,
! [X0,X1] :
( k6_closure2(X0,X1) = k1_closure2(X0,X1)
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f168,plain,
! [X0,X1,X2] :
( ! [X3] :
( m1_closure2(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) ),
inference(ennf_transformation,[],[f69]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ! [X3] :
( m1_closure2(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) ),
inference(flattening,[],[f168]) ).
fof(f178,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(ennf_transformation,[],[f77]) ).
fof(f179,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(flattening,[],[f178]) ).
fof(f184,plain,
( ~ r2_pboole(sK0,k2_closure3(sK0,sK1,sK2),k2_closure3(sK0,sK1,sK3))
& r1_tarski(sK2,sK3)
& m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1)))
& m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
& m1_pboole(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f109]) ).
fof(f185,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,[],[f132]) ).
fof(f186,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,[],[f185]) ).
fof(f187,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK4(X0,X1),X1)
& r2_hidden(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f186]) ).
fof(f188,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ( ( X3 = k2_closure3(X0,X1,X2)
| ? [X4] :
( k1_funct_1(X3,X4) != k3_tarski(a_4_0_closure3(X0,X1,X2,X4))
& r2_hidden(X4,X0) ) )
& ( ! [X4] :
( k1_funct_1(X3,X4) = k3_tarski(a_4_0_closure3(X0,X1,X2,X4))
| ~ r2_hidden(X4,X0) )
| k2_closure3(X0,X1,X2) != X3 ) )
| ~ m4_pboole(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
| ~ m1_pboole(X1,X0) ),
inference(nnf_transformation,[],[f133]) ).
fof(f189,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ( ( X3 = k2_closure3(X0,X1,X2)
| ? [X4] :
( k1_funct_1(X3,X4) != k3_tarski(a_4_0_closure3(X0,X1,X2,X4))
& r2_hidden(X4,X0) ) )
& ( ! [X5] :
( k1_funct_1(X3,X5) = k3_tarski(a_4_0_closure3(X0,X1,X2,X5))
| ~ r2_hidden(X5,X0) )
| k2_closure3(X0,X1,X2) != X3 ) )
| ~ m4_pboole(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
| ~ m1_pboole(X1,X0) ),
inference(rectify,[],[f188]) ).
fof(f190,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ( ( X3 = k2_closure3(X0,X1,X2)
| ( k1_funct_1(X3,sK5(X0,X1,X2,X3)) != k3_tarski(a_4_0_closure3(X0,X1,X2,sK5(X0,X1,X2,X3)))
& r2_hidden(sK5(X0,X1,X2,X3),X0) ) )
& ( ! [X5] :
( k1_funct_1(X3,X5) = k3_tarski(a_4_0_closure3(X0,X1,X2,X5))
| ~ r2_hidden(X5,X0) )
| k2_closure3(X0,X1,X2) != X3 ) )
| ~ m4_pboole(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) )
| ~ m1_pboole(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2,X3))],[f189]) ).
fof(f191,plain,
! [X0,X1] :
( ( X1 = k3_tarski(X0)
| ? [X2] :
( ( ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ r2_hidden(X3,X0) )
| ~ r2_hidden(X2,X1) )
& ( ? [X3] :
( r2_hidden(X2,X3)
& r2_hidden(X3,X0) )
| r2_hidden(X2,X1) ) ) )
& ( ! [X2] :
( ( r2_hidden(X2,X1)
| ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ r2_hidden(X3,X0) ) )
& ( ? [X3] :
( r2_hidden(X2,X3)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X2,X1) ) )
| k3_tarski(X0) != X1 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f192,plain,
! [X0,X1] :
( ( X1 = k3_tarski(X0)
| ? [X2] :
( ( ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ r2_hidden(X3,X0) )
| ~ r2_hidden(X2,X1) )
& ( ? [X4] :
( r2_hidden(X2,X4)
& r2_hidden(X4,X0) )
| r2_hidden(X2,X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] :
( ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X0) ) )
& ( ? [X7] :
( r2_hidden(X5,X7)
& r2_hidden(X7,X0) )
| ~ r2_hidden(X5,X1) ) )
| k3_tarski(X0) != X1 ) ),
inference(rectify,[],[f191]) ).
fof(f193,plain,
! [X0,X1] :
( ( X1 = k3_tarski(X0)
| ( ( ! [X3] :
( ~ r2_hidden(sK6(X0,X1),X3)
| ~ r2_hidden(X3,X0) )
| ~ r2_hidden(sK6(X0,X1),X1) )
& ( ( r2_hidden(sK6(X0,X1),sK7(X0,X1))
& r2_hidden(sK7(X0,X1),X0) )
| r2_hidden(sK6(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] :
( ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X0) ) )
& ( ( r2_hidden(X5,sK8(X0,X5))
& r2_hidden(sK8(X0,X5),X0) )
| ~ r2_hidden(X5,X1) ) )
| k3_tarski(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X2,sK6(X0,X1)),skolemize(X4,sK7(X0,X1)),skolemize(X7,sK8(X0,X5))],[f192]) ).
fof(f194,plain,
! [X0,X1] :
( ! [X2] :
( ( ( r2_pboole(X0,X1,X2)
| ? [X3] :
( ~ r1_tarski(k1_funct_1(X1,X3),k1_funct_1(X2,X3))
& r2_hidden(X3,X0) ) )
& ( ! [X3] :
( r1_tarski(k1_funct_1(X1,X3),k1_funct_1(X2,X3))
| ~ r2_hidden(X3,X0) )
| ~ r2_pboole(X0,X1,X2) ) )
| ~ m1_pboole(X2,X0) )
| ~ m1_pboole(X1,X0) ),
inference(nnf_transformation,[],[f134]) ).
fof(f195,plain,
! [X0,X1] :
( ! [X2] :
( ( ( r2_pboole(X0,X1,X2)
| ? [X3] :
( ~ r1_tarski(k1_funct_1(X1,X3),k1_funct_1(X2,X3))
& r2_hidden(X3,X0) ) )
& ( ! [X4] :
( r1_tarski(k1_funct_1(X1,X4),k1_funct_1(X2,X4))
| ~ r2_hidden(X4,X0) )
| ~ r2_pboole(X0,X1,X2) ) )
| ~ m1_pboole(X2,X0) )
| ~ m1_pboole(X1,X0) ),
inference(rectify,[],[f194]) ).
fof(f196,plain,
! [X0,X1] :
( ! [X2] :
( ( ( r2_pboole(X0,X1,X2)
| ( ~ r1_tarski(k1_funct_1(X1,sK9(X0,X1,X2)),k1_funct_1(X2,sK9(X0,X1,X2)))
& r2_hidden(sK9(X0,X1,X2),X0) ) )
& ( ! [X4] :
( r1_tarski(k1_funct_1(X1,X4),k1_funct_1(X2,X4))
| ~ r2_hidden(X4,X0) )
| ~ r2_pboole(X0,X1,X2) ) )
| ~ m1_pboole(X2,X0) )
| ~ m1_pboole(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f195]) ).
fof(f202,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
| ! [X5] :
( ~ m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
| k1_funct_1(X5,X4) != X0
| ~ r2_hidden(X5,X3) ) )
& ( ? [X5] :
( m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
& X0 = k1_funct_1(X5,X4)
& r2_hidden(X5,X3) )
| ~ r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4)) ) )
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(nnf_transformation,[],[f155]) ).
fof(f203,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
| ! [X5] :
( ~ m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
| k1_funct_1(X5,X4) != X0
| ~ r2_hidden(X5,X3) ) )
& ( ? [X6] :
( m1_closure2(X6,X1,X2,k6_closure2(X1,X2))
& k1_funct_1(X6,X4) = X0
& r2_hidden(X6,X3) )
| ~ r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4)) ) )
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(rectify,[],[f202]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
| ! [X5] :
( ~ m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
| k1_funct_1(X5,X4) != X0
| ~ r2_hidden(X5,X3) ) )
& ( ( m1_closure2(sK15(X0,X1,X2,X3,X4),X1,X2,k6_closure2(X1,X2))
& k1_funct_1(sK15(X0,X1,X2,X3,X4),X4) = X0
& r2_hidden(sK15(X0,X1,X2,X3,X4),X3) )
| ~ r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4)) ) )
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X6,sK15(X0,X1,X2,X3,X4))],[f203]) ).
fof(f229,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( m1_closure2(X3,X0,X1,X2)
| ~ m1_subset_1(X3,X2) )
& ( m1_subset_1(X3,X2)
| ~ m1_closure2(X3,X0,X1,X2) ) )
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) ),
inference(nnf_transformation,[],[f169]) ).
fof(f233,plain,
! [X0,X1] :
( ( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
& ( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f234,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f184]) ).
fof(f235,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f184]) ).
fof(f236,plain,
m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f184]) ).
fof(f237,plain,
r1_tarski(sK2,sK3),
inference(cnf_transformation,[],[f184]) ).
fof(f238,plain,
~ r2_pboole(sK0,k2_closure3(sK0,sK1,sK2),k2_closure3(sK0,sK1,sK3)),
inference(cnf_transformation,[],[f184]) ).
fof(f253,plain,
! [X3,X0,X1] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
fof(f254,plain,
! [X0,X1] :
( r2_hidden(sK4(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
fof(f255,plain,
! [X0,X1] :
( ~ r2_hidden(sK4(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
fof(f256,plain,
! [X2,X3,X0,X1,X5] :
( k1_funct_1(X3,X5) = k3_tarski(a_4_0_closure3(X0,X1,X2,X5))
| ~ r2_hidden(X5,X0)
| k2_closure3(X0,X1,X2) != X3
| ~ m4_pboole(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f259,plain,
! [X0,X1,X5] :
( r2_hidden(sK8(X0,X5),X0)
| ~ r2_hidden(X5,X1)
| k3_tarski(X0) != X1 ),
inference(cnf_transformation,[],[f193]) ).
fof(f260,plain,
! [X0,X1,X5] :
( r2_hidden(X5,sK8(X0,X5))
| ~ r2_hidden(X5,X1)
| k3_tarski(X0) != X1 ),
inference(cnf_transformation,[],[f193]) ).
fof(f261,plain,
! [X0,X1,X6,X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X0)
| k3_tarski(X0) != X1 ),
inference(cnf_transformation,[],[f193]) ).
fof(f266,plain,
! [X2,X0,X1] :
( r2_hidden(sK9(X0,X1,X2),X0)
| r2_pboole(X0,X1,X2)
| ~ m1_pboole(X2,X0)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f267,plain,
! [X2,X0,X1] :
( ~ r1_tarski(k1_funct_1(X1,sK9(X0,X1,X2)),k1_funct_1(X2,sK9(X0,X1,X2)))
| r2_pboole(X0,X1,X2)
| ~ m1_pboole(X2,X0)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f268,plain,
! [X2,X0,X1] :
( m4_pboole(k2_closure3(X0,X1,X2),X0,X1)
| ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1))) ),
inference(cnf_transformation,[],[f136]) ).
fof(f278,plain,
! [X2,X0,X1] :
( ~ m4_pboole(X2,X0,X1)
| m1_pboole(X2,X0)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f286,plain,
! [X0,X1] :
( ~ v1_xboole_0(k1_closure2(X0,X1))
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f292,plain,
! [X2,X3,X0,X1,X4] :
( r2_hidden(sK15(X0,X1,X2,X3,X4),X3)
| ~ r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(cnf_transformation,[],[f204]) ).
fof(f293,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
| k1_funct_1(sK15(X0,X1,X2,X3,X4),X4) = X0
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(cnf_transformation,[],[f204]) ).
fof(f295,plain,
! [X2,X3,X0,X1,X4,X5] :
( r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
| ~ m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
| k1_funct_1(X5,X4) != X0
| ~ r2_hidden(X5,X3)
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(cnf_transformation,[],[f204]) ).
fof(f364,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_closure2(X0,X1) = k6_closure2(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
fof(f366,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ m1_subset_1(X3,X2)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X2)
| m1_closure2(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f229]) ).
fof(f369,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f82]) ).
fof(f376,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f233]) ).
fof(f377,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(cnf_transformation,[],[f179]) ).
fof(f382,plain,
! [X2,X0,X1,X5] :
( k3_tarski(a_4_0_closure3(X0,X1,X2,X5)) = k1_funct_1(k2_closure3(X0,X1,X2),X5)
| ~ r2_hidden(X5,X0)
| ~ m4_pboole(k2_closure3(X0,X1,X2),X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ m1_pboole(X1,X0) ),
inference(equality_resolution,[],[f256]) ).
fof(f383,plain,
! [X0,X6,X5] :
( ~ r2_hidden(X6,X0)
| ~ r2_hidden(X5,X6)
| r2_hidden(X5,k3_tarski(X0)) ),
inference(equality_resolution,[],[f261]) ).
fof(f384,plain,
! [X0,X5] :
( r2_hidden(X5,sK8(X0,X5))
| ~ r2_hidden(X5,k3_tarski(X0)) ),
inference(equality_resolution,[],[f260]) ).
fof(f385,plain,
! [X0,X5] :
( r2_hidden(sK8(X0,X5),X0)
| ~ r2_hidden(X5,k3_tarski(X0)) ),
inference(equality_resolution,[],[f259]) ).
fof(f386,plain,
! [X2,X3,X1,X4,X5] :
( ~ m1_closure2(X5,X1,X2,k6_closure2(X1,X2))
| r2_hidden(k1_funct_1(X5,X4),a_4_0_closure3(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(equality_resolution,[],[f295]) ).
fof(f388,definition,
sF39 = k2_closure3(sK0,sK1,sK2),
introduced(definition,[new_symbols(definition,[sF39])],[function_definition]) ).
fof(f389,plain,
k2_closure3(sK0,sK1,sK2) = sF39,
inference(reorient_equations,[],[f388]) ).
fof(f390,definition,
sF40 = k2_closure3(sK0,sK1,sK3),
introduced(definition,[new_symbols(definition,[sF40])],[function_definition]) ).
fof(f391,plain,
k2_closure3(sK0,sK1,sK3) = sF40,
inference(reorient_equations,[],[f390]) ).
fof(f392,plain,
~ r2_pboole(sK0,sF39,sF40),
inference(definition_folding,[],[f238,f391,f389]) ).
fof(f393,definition,
sF41 = k1_closure2(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF41])],[function_definition]) ).
fof(f394,plain,
k1_closure2(sK0,sK1) = sF41,
inference(reorient_equations,[],[f393]) ).
fof(f395,definition,
sF42 = k1_zfmisc_1(sF41),
introduced(definition,[new_symbols(definition,[sF42])],[function_definition]) ).
fof(f396,plain,
k1_zfmisc_1(sF41) = sF42,
inference(reorient_equations,[],[f395]) ).
fof(f397,plain,
m1_subset_1(sK3,sF42),
inference(definition_folding,[],[f236,f396,f394]) ).
fof(f398,plain,
m1_subset_1(sK2,sF42),
inference(definition_folding,[],[f235,f396,f394]) ).
fof(f399,plain,
! [X2,X0,X1,X5] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ r2_hidden(X5,X0)
| k3_tarski(a_4_0_closure3(X0,X1,X2,X5)) = k1_funct_1(k2_closure3(X0,X1,X2),X5)
| ~ m1_pboole(X1,X0) ),
inference(forward_subsumption_resolution,[],[f382,f268]) ).
fof(f401,plain,
k1_closure2(sK0,sK1) = k6_closure2(sK0,sK1),
inference(resolution,[],[f364,f234]) ).
fof(f402,plain,
sF41 = k6_closure2(sK0,sK1),
inference(forward_demodulation,[],[f401,f394]) ).
fof(f413,plain,
( m4_pboole(sF40,sK0,sK1)
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(superposition,[],[f268,f391]) ).
fof(f414,plain,
( m4_pboole(sF39,sK0,sK1)
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(superposition,[],[f268,f389]) ).
fof(f415,plain,
( m4_pboole(sF39,sK0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(forward_subsumption_resolution,[],[f414,f234]) ).
fof(f416,plain,
( m4_pboole(sF40,sK0,sK1)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(forward_subsumption_resolution,[],[f413,f234]) ).
fof(f417,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(sF41))
| m4_pboole(sF39,sK0,sK1) ),
inference(forward_demodulation,[],[f415,f394]) ).
fof(f418,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(sF41))
| m4_pboole(sF40,sK0,sK1) ),
inference(forward_demodulation,[],[f416,f394]) ).
fof(f419,plain,
( ~ m1_subset_1(sK2,sF42)
| m4_pboole(sF39,sK0,sK1) ),
inference(forward_demodulation,[],[f417,f396]) ).
fof(f420,plain,
( ~ m1_subset_1(sK3,sF42)
| m4_pboole(sF40,sK0,sK1) ),
inference(forward_demodulation,[],[f418,f396]) ).
fof(f421,plain,
m4_pboole(sF39,sK0,sK1),
inference(forward_subsumption_resolution,[],[f419,f398]) ).
fof(f422,plain,
m4_pboole(sF40,sK0,sK1),
inference(forward_subsumption_resolution,[],[f420,f397]) ).
fof(f433,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sF41))
| ~ m1_subset_1(X1,X0)
| ~ m1_pboole(sK1,sK0)
| v1_xboole_0(X0)
| m1_closure2(X1,sK0,sK1,X0) ),
inference(superposition,[],[f366,f394]) ).
fof(f434,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sF41))
| ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| m1_closure2(X1,sK0,sK1,X0) ),
inference(forward_subsumption_resolution,[],[f433,f234]) ).
fof(f435,plain,
! [X0,X1] :
( m1_closure2(X1,sK0,sK1,X0)
| ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| ~ m1_subset_1(X0,sF42) ),
inference(forward_demodulation,[],[f434,f396]) ).
fof(f452,plain,
! [X2,X3,X0,X1,X4,X5] :
( r2_hidden(sK15(X0,X1,X2,X3,X4),X5)
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2)))
| ~ r2_hidden(X0,a_4_0_closure3(X1,X2,X3,X4))
| ~ r1_tarski(X3,X5) ),
inference(resolution,[],[f292,f253]) ).
fof(f454,plain,
! [X2,X0,X1] :
( r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2)
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k6_closure2(sK0,sK1))
| v1_xboole_0(k6_closure2(sK0,sK1))
| ~ m1_subset_1(k6_closure2(sK0,sK1),sF42) ),
inference(resolution,[],[f386,f435]) ).
fof(f457,plain,
! [X2,X0,X1] :
( r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k6_closure2(sK0,sK1))
| v1_xboole_0(k6_closure2(sK0,sK1))
| ~ m1_subset_1(k6_closure2(sK0,sK1),sF42) ),
inference(forward_subsumption_resolution,[],[f454,f234]) ).
fof(f459,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(sF41))
| r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2)
| ~ m1_subset_1(X0,k6_closure2(sK0,sK1))
| v1_xboole_0(k6_closure2(sK0,sK1))
| ~ m1_subset_1(k6_closure2(sK0,sK1),sF42) ),
inference(forward_demodulation,[],[f457,f394]) ).
fof(f461,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,sF42)
| r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2)
| ~ m1_subset_1(X0,k6_closure2(sK0,sK1))
| v1_xboole_0(k6_closure2(sK0,sK1))
| ~ m1_subset_1(k6_closure2(sK0,sK1),sF42) ),
inference(forward_demodulation,[],[f459,f396]) ).
fof(f462,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X0,sF41)
| ~ m1_subset_1(X2,sF42)
| r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2)
| v1_xboole_0(k6_closure2(sK0,sK1))
| ~ m1_subset_1(k6_closure2(sK0,sK1),sF42) ),
inference(forward_demodulation,[],[f461,f402]) ).
fof(f463,plain,
! [X2,X0,X1] :
( v1_xboole_0(sF41)
| ~ m1_subset_1(X0,sF41)
| ~ m1_subset_1(X2,sF42)
| r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2)
| ~ m1_subset_1(k6_closure2(sK0,sK1),sF42) ),
inference(forward_demodulation,[],[f462,f402]) ).
fof(f464,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(sF41,sF42)
| v1_xboole_0(sF41)
| ~ m1_subset_1(X0,sF41)
| ~ m1_subset_1(X2,sF42)
| r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2) ),
inference(forward_demodulation,[],[f463,f402]) ).
fof(f466,definition,
( spl43_4
<=> ! [X2,X0,X1] :
( ~ m1_subset_1(X0,sF41)
| ~ r2_hidden(X0,X2)
| r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ m1_subset_1(X2,sF42) ) ),
introduced(definition,[new_symbols(definition,[spl43_4])],[avatar_definition]) ).
fof(f467,plain,
( ! [X2,X0,X1] :
( r2_hidden(k1_funct_1(X0,X1),a_4_0_closure3(sK0,sK1,X2,X1))
| ~ r2_hidden(X0,X2)
| ~ m1_subset_1(X0,sF41)
| ~ m1_subset_1(X2,sF42) )
| ~ spl43_4 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f469,definition,
( spl43_5
<=> v1_xboole_0(sF41) ),
introduced(definition,[new_symbols(definition,[spl43_5])],[avatar_definition]) ).
fof(f471,plain,
( v1_xboole_0(sF41)
| ~ spl43_5 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f473,definition,
( spl43_6
<=> m1_subset_1(sF41,sF42) ),
introduced(definition,[new_symbols(definition,[spl43_6])],[avatar_definition]) ).
fof(f475,plain,
( ~ m1_subset_1(sF41,sF42)
| spl43_6 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f476,plain,
( spl43_4
| spl43_5
| ~ spl43_6 ),
inference(avatar_split_clause,[],[f464,f473,f469,f466]) ).
fof(f483,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sF41))
| ~ r2_hidden(X1,sK0)
| k3_tarski(a_4_0_closure3(sK0,sK1,X0,X1)) = k1_funct_1(k2_closure3(sK0,sK1,X0),X1)
| ~ m1_pboole(sK1,sK0) ),
inference(superposition,[],[f399,f394]) ).
fof(f484,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sF41))
| ~ r2_hidden(X1,sK0)
| k3_tarski(a_4_0_closure3(sK0,sK1,X0,X1)) = k1_funct_1(k2_closure3(sK0,sK1,X0),X1) ),
inference(forward_subsumption_resolution,[],[f483,f234]) ).
fof(f485,plain,
! [X0,X1] :
( ~ r2_hidden(X1,sK0)
| ~ m1_subset_1(X0,sF42)
| k3_tarski(a_4_0_closure3(sK0,sK1,X0,X1)) = k1_funct_1(k2_closure3(sK0,sK1,X0),X1) ),
inference(forward_demodulation,[],[f484,f396]) ).
fof(f488,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X0,sF42)
| k3_tarski(a_4_0_closure3(sK0,sK1,X0,sK9(sK0,X1,X2))) = k1_funct_1(k2_closure3(sK0,sK1,X0),sK9(sK0,X1,X2))
| r2_pboole(sK0,X1,X2)
| ~ m1_pboole(X2,sK0)
| ~ m1_pboole(X1,sK0) ),
inference(resolution,[],[f485,f266]) ).
fof(f507,plain,
! [X0] :
( ~ r1_tarski(X0,sF41)
| m1_subset_1(X0,sF42) ),
inference(superposition,[],[f376,f396]) ).
fof(f521,plain,
( m1_pboole(sF39,sK0)
| ~ m1_pboole(sK1,sK0) ),
inference(resolution,[],[f278,f421]) ).
fof(f522,plain,
( m1_pboole(sF40,sK0)
| ~ m1_pboole(sK1,sK0) ),
inference(resolution,[],[f278,f422]) ).
fof(f524,plain,
m1_pboole(sF40,sK0),
inference(forward_subsumption_resolution,[],[f522,f234]) ).
fof(f525,plain,
m1_pboole(sF39,sK0),
inference(forward_subsumption_resolution,[],[f521,f234]) ).
fof(f532,plain,
m1_subset_1(sF41,sF42),
inference(resolution,[],[f507,f369]) ).
fof(f533,plain,
( $false
| spl43_6 ),
inference(forward_subsumption_resolution,[],[f532,f475]) ).
fof(f534,plain,
spl43_6,
inference(avatar_contradiction_clause,[],[f533]) ).
fof(f577,plain,
! [X2,X0,X1] :
( ~ r1_tarski(sK8(X1,X0),X2)
| r2_hidden(X0,X2)
| ~ r2_hidden(X0,k3_tarski(X1)) ),
inference(resolution,[],[f384,f253]) ).
fof(f578,plain,
( ~ v1_xboole_0(sF41)
| ~ m1_pboole(sK1,sK0) ),
inference(superposition,[],[f286,f394]) ).
fof(f579,plain,
( ~ m1_pboole(sK1,sK0)
| ~ spl43_5 ),
inference(forward_subsumption_resolution,[],[f578,f471]) ).
fof(f580,plain,
( $false
| ~ spl43_5 ),
inference(forward_subsumption_resolution,[],[f579,f234]) ).
fof(f581,plain,
~ spl43_5,
inference(avatar_contradiction_clause,[],[f580]) ).
fof(f673,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ m1_subset_1(X0,sF42)
| m1_subset_1(X1,sF41) ),
inference(superposition,[],[f377,f396]) ).
fof(f1018,plain,
( ! [X2,X3,X0,X1] :
( ~ r2_hidden(X0,k1_funct_1(X1,X2))
| r2_hidden(X0,k3_tarski(a_4_0_closure3(sK0,sK1,X3,X2)))
| ~ r2_hidden(X1,X3)
| ~ m1_subset_1(X1,sF41)
| ~ m1_subset_1(X3,sF42) )
| ~ spl43_4 ),
inference(resolution,[],[f383,f467]) ).
fof(f1037,plain,
( ! [X2,X3,X0,X1] :
( ~ r2_hidden(X0,k1_funct_1(X1,X2))
| r2_hidden(X0,k3_tarski(a_4_0_closure3(sK0,sK1,X3,X2)))
| ~ r2_hidden(X1,X3)
| ~ m1_subset_1(X3,sF42) )
| ~ spl43_4 ),
inference(forward_subsumption_resolution,[],[f1018,f673]) ).
fof(f1038,plain,
( ! [X2,X3,X0,X1] :
( r2_hidden(sK4(k1_funct_1(X0,X1),X2),k3_tarski(a_4_0_closure3(sK0,sK1,X3,X1)))
| ~ r2_hidden(X0,X3)
| ~ m1_subset_1(X3,sF42)
| r1_tarski(k1_funct_1(X0,X1),X2) )
| ~ spl43_4 ),
inference(resolution,[],[f1037,f254]) ).
fof(f1267,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2_hidden(X0,k3_tarski(a_4_0_closure3(X1,X2,X3,X4)))
| sK8(a_4_0_closure3(X1,X2,X3,X4),X0) = k1_funct_1(sK15(sK8(a_4_0_closure3(X1,X2,X3,X4),X0),X1,X2,X3,X4),X4)
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(resolution,[],[f385,f293]) ).
fof(f2658,plain,
! [X0,X1] :
( k3_tarski(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,X0,X1))) = k1_funct_1(k2_closure3(sK0,sK1,sK2),sK9(sK0,X0,X1))
| r2_pboole(sK0,X0,X1)
| ~ m1_pboole(X1,sK0)
| ~ m1_pboole(X0,sK0) ),
inference(resolution,[],[f488,f398]) ).
fof(f2659,plain,
! [X0,X1] :
( k3_tarski(a_4_0_closure3(sK0,sK1,sK3,sK9(sK0,X0,X1))) = k1_funct_1(k2_closure3(sK0,sK1,sK3),sK9(sK0,X0,X1))
| r2_pboole(sK0,X0,X1)
| ~ m1_pboole(X1,sK0)
| ~ m1_pboole(X0,sK0) ),
inference(resolution,[],[f488,f397]) ).
fof(f2665,plain,
! [X0,X1] :
( r2_pboole(sK0,X0,X1)
| k3_tarski(a_4_0_closure3(sK0,sK1,sK3,sK9(sK0,X0,X1))) = k1_funct_1(sF40,sK9(sK0,X0,X1))
| ~ m1_pboole(X1,sK0)
| ~ m1_pboole(X0,sK0) ),
inference(forward_demodulation,[],[f2659,f391]) ).
fof(f2666,plain,
! [X0,X1] :
( r2_pboole(sK0,X0,X1)
| k3_tarski(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,X0,X1))) = k1_funct_1(sF39,sK9(sK0,X0,X1))
| ~ m1_pboole(X1,sK0)
| ~ m1_pboole(X0,sK0) ),
inference(forward_demodulation,[],[f2658,f389]) ).
fof(f2667,plain,
( k3_tarski(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40))) = k1_funct_1(sF39,sK9(sK0,sF39,sF40))
| ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0) ),
inference(resolution,[],[f2666,f392]) ).
fof(f2670,plain,
( k3_tarski(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40))) = k1_funct_1(sF39,sK9(sK0,sF39,sF40))
| ~ m1_pboole(sF39,sK0) ),
inference(forward_subsumption_resolution,[],[f2667,f524]) ).
fof(f2671,plain,
k3_tarski(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40))) = k1_funct_1(sF39,sK9(sK0,sF39,sF40)),
inference(forward_subsumption_resolution,[],[f2670,f525]) ).
fof(f2672,plain,
! [X0] :
( ~ r2_hidden(X0,k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40))
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(superposition,[],[f1267,f2671]) ).
fof(f2673,plain,
! [X0] :
( ~ r2_hidden(X0,k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40))
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(forward_subsumption_resolution,[],[f2672,f234]) ).
fof(f2674,plain,
! [X0] :
( ~ m1_subset_1(sK2,k1_zfmisc_1(sF41))
| ~ r2_hidden(X0,k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40)) ),
inference(forward_demodulation,[],[f2673,f394]) ).
fof(f2675,plain,
! [X0] :
( ~ m1_subset_1(sK2,sF42)
| ~ r2_hidden(X0,k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40)) ),
inference(forward_demodulation,[],[f2674,f396]) ).
fof(f2676,plain,
! [X0] :
( ~ r2_hidden(X0,k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),X0),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40)) ),
inference(forward_subsumption_resolution,[],[f2675,f398]) ).
fof(f2677,plain,
( k3_tarski(a_4_0_closure3(sK0,sK1,sK3,sK9(sK0,sF39,sF40))) = k1_funct_1(sF40,sK9(sK0,sF39,sF40))
| ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0) ),
inference(resolution,[],[f2665,f392]) ).
fof(f2680,plain,
( k3_tarski(a_4_0_closure3(sK0,sK1,sK3,sK9(sK0,sF39,sF40))) = k1_funct_1(sF40,sK9(sK0,sF39,sF40))
| ~ m1_pboole(sF39,sK0) ),
inference(forward_subsumption_resolution,[],[f2677,f524]) ).
fof(f2681,plain,
k3_tarski(a_4_0_closure3(sK0,sK1,sK3,sK9(sK0,sF39,sF40))) = k1_funct_1(sF40,sK9(sK0,sF39,sF40)),
inference(forward_subsumption_resolution,[],[f2680,f525]) ).
fof(f2687,plain,
! [X0] :
( r1_tarski(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),X0)
| sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),X0)) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),X0)),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40)) ),
inference(resolution,[],[f2676,f254]) ).
fof(f2867,plain,
( sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40))
| r2_pboole(sK0,sF39,sF40)
| ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0) ),
inference(resolution,[],[f2687,f267]) ).
fof(f2927,plain,
( sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40))
| ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0) ),
inference(forward_subsumption_resolution,[],[f2867,f392]) ).
fof(f2929,plain,
( sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40))
| ~ m1_pboole(sF39,sK0) ),
inference(forward_subsumption_resolution,[],[f2927,f524]) ).
fof(f2930,plain,
sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))) = k1_funct_1(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK9(sK0,sF39,sF40)),
inference(forward_subsumption_resolution,[],[f2929,f525]) ).
fof(f16806,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,sF42)
| r1_tarski(k1_funct_1(X0,X2),k3_tarski(a_4_0_closure3(sK0,sK1,X1,X2)))
| r1_tarski(k1_funct_1(X0,X2),k3_tarski(a_4_0_closure3(sK0,sK1,X1,X2))) )
| ~ spl43_4 ),
inference(resolution,[],[f1038,f255]) ).
fof(f16899,plain,
( ! [X2,X0,X1] :
( r1_tarski(k1_funct_1(X0,X2),k3_tarski(a_4_0_closure3(sK0,sK1,X1,X2)))
| ~ m1_subset_1(X1,sF42)
| ~ r2_hidden(X0,X1) )
| ~ spl43_4 ),
inference(duplicate_literal_removal,[],[f16806]) ).
fof(f17056,plain,
( ! [X0] :
( r1_tarski(k1_funct_1(X0,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ m1_subset_1(sK3,sF42)
| ~ r2_hidden(X0,sK3) )
| ~ spl43_4 ),
inference(superposition,[],[f16899,f2681]) ).
fof(f17067,plain,
( ! [X0] :
( r1_tarski(k1_funct_1(X0,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ r2_hidden(X0,sK3) )
| ~ spl43_4 ),
inference(forward_subsumption_resolution,[],[f17056,f397]) ).
fof(f17129,plain,
( r1_tarski(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ r2_hidden(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK3)
| ~ spl43_4 ),
inference(superposition,[],[f17067,f2930]) ).
fof(f17383,definition,
( spl43_1129
<=> r2_hidden(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK3) ),
introduced(definition,[new_symbols(definition,[spl43_1129])],[avatar_definition]) ).
fof(f17385,plain,
( ~ r2_hidden(sK15(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK3)
| spl43_1129 ),
inference(avatar_component_clause,[],[f17383]) ).
fof(f17387,definition,
( spl43_1130
<=> r1_tarski(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),k1_funct_1(sF40,sK9(sK0,sF39,sF40))) ),
introduced(definition,[new_symbols(definition,[spl43_1130])],[avatar_definition]) ).
fof(f17389,plain,
( r1_tarski(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ spl43_1130 ),
inference(avatar_component_clause,[],[f17387]) ).
fof(f17390,plain,
( ~ spl43_1129
| spl43_1130
| ~ spl43_4 ),
inference(avatar_split_clause,[],[f17129,f466,f17387,f17383]) ).
fof(f18046,plain,
( ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ r2_hidden(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)))
| ~ r1_tarski(sK2,sK3)
| spl43_1129 ),
inference(resolution,[],[f17385,f452]) ).
fof(f18047,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ r2_hidden(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)))
| ~ r1_tarski(sK2,sK3)
| spl43_1129 ),
inference(forward_subsumption_resolution,[],[f18046,f234]) ).
fof(f18048,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ r2_hidden(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)))
| spl43_1129 ),
inference(forward_subsumption_resolution,[],[f18047,f237]) ).
fof(f18049,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(sF41))
| ~ r2_hidden(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)))
| spl43_1129 ),
inference(forward_demodulation,[],[f18048,f394]) ).
fof(f18050,plain,
( ~ m1_subset_1(sK2,sF42)
| ~ r2_hidden(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)))
| spl43_1129 ),
inference(forward_demodulation,[],[f18049,f396]) ).
fof(f18051,plain,
( ~ r2_hidden(sK8(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)),sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))),a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40)))
| spl43_1129 ),
inference(forward_subsumption_resolution,[],[f18050,f398]) ).
fof(f18052,plain,
( ~ r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k3_tarski(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40))))
| spl43_1129 ),
inference(resolution,[],[f18051,f385]) ).
fof(f18055,plain,
( ~ r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| spl43_1129 ),
inference(forward_demodulation,[],[f18052,f2671]) ).
fof(f18057,plain,
( r1_tarski(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| spl43_1129 ),
inference(resolution,[],[f18055,f254]) ).
fof(f18060,plain,
( r2_pboole(sK0,sF39,sF40)
| ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0)
| spl43_1129 ),
inference(resolution,[],[f18057,f267]) ).
fof(f18067,plain,
( ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0)
| spl43_1129 ),
inference(forward_subsumption_resolution,[],[f18060,f392]) ).
fof(f18068,plain,
( ~ m1_pboole(sF39,sK0)
| spl43_1129 ),
inference(forward_subsumption_resolution,[],[f18067,f524]) ).
fof(f18069,plain,
( $false
| spl43_1129 ),
inference(forward_subsumption_resolution,[],[f18068,f525]) ).
fof(f18070,plain,
spl43_1129,
inference(avatar_contradiction_clause,[],[f18069]) ).
fof(f18071,plain,
( r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k3_tarski(a_4_0_closure3(sK0,sK1,sK2,sK9(sK0,sF39,sF40))))
| ~ spl43_1130 ),
inference(resolution,[],[f17389,f577]) ).
fof(f18078,plain,
( ~ r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ spl43_1130 ),
inference(forward_demodulation,[],[f18071,f2671]) ).
fof(f18080,definition,
( spl43_1251
<=> r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF40,sK9(sK0,sF39,sF40))) ),
introduced(definition,[new_symbols(definition,[spl43_1251])],[avatar_definition]) ).
fof(f18082,plain,
( r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ spl43_1251 ),
inference(avatar_component_clause,[],[f18080]) ).
fof(f18084,definition,
( spl43_1252
<=> r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF39,sK9(sK0,sF39,sF40))) ),
introduced(definition,[new_symbols(definition,[spl43_1252])],[avatar_definition]) ).
fof(f18086,plain,
( ~ r2_hidden(sK4(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40))),k1_funct_1(sF39,sK9(sK0,sF39,sF40)))
| spl43_1252 ),
inference(avatar_component_clause,[],[f18084]) ).
fof(f18087,plain,
( spl43_1251
| ~ spl43_1252
| ~ spl43_1130 ),
inference(avatar_split_clause,[],[f18078,f17387,f18084,f18080]) ).
fof(f18088,plain,
( r1_tarski(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| spl43_1252 ),
inference(resolution,[],[f18086,f254]) ).
fof(f18091,plain,
( r2_pboole(sK0,sF39,sF40)
| ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0)
| spl43_1252 ),
inference(resolution,[],[f18088,f267]) ).
fof(f18098,plain,
( ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0)
| spl43_1252 ),
inference(forward_subsumption_resolution,[],[f18091,f392]) ).
fof(f18099,plain,
( ~ m1_pboole(sF39,sK0)
| spl43_1252 ),
inference(forward_subsumption_resolution,[],[f18098,f524]) ).
fof(f18100,plain,
( $false
| spl43_1252 ),
inference(forward_subsumption_resolution,[],[f18099,f525]) ).
fof(f18101,plain,
spl43_1252,
inference(avatar_contradiction_clause,[],[f18100]) ).
fof(f18123,plain,
( r1_tarski(k1_funct_1(sF39,sK9(sK0,sF39,sF40)),k1_funct_1(sF40,sK9(sK0,sF39,sF40)))
| ~ spl43_1251 ),
inference(resolution,[],[f18082,f255]) ).
fof(f18137,plain,
( r2_pboole(sK0,sF39,sF40)
| ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0)
| ~ spl43_1251 ),
inference(resolution,[],[f18123,f267]) ).
fof(f18144,plain,
( ~ m1_pboole(sF40,sK0)
| ~ m1_pboole(sF39,sK0)
| ~ spl43_1251 ),
inference(forward_subsumption_resolution,[],[f18137,f392]) ).
fof(f18145,plain,
( ~ m1_pboole(sF39,sK0)
| ~ spl43_1251 ),
inference(forward_subsumption_resolution,[],[f18144,f524]) ).
fof(f18146,plain,
( $false
| ~ spl43_1251 ),
inference(forward_subsumption_resolution,[],[f18145,f525]) ).
fof(f18147,plain,
~ spl43_1251,
inference(avatar_contradiction_clause,[],[f18146]) ).
cnf(s3,plain,
( spl43_4
| spl43_5
| ~ spl43_6 ),
inference(sat_conversion,[],[f476]) ).
cnf(s5,plain,
spl43_6,
inference(sat_conversion,[],[f534]) ).
cnf(s6,plain,
~ spl43_5,
inference(sat_conversion,[],[f581]) ).
cnf(s803,plain,
( ~ spl43_4
| ~ spl43_1129
| spl43_1130 ),
inference(sat_conversion,[],[f17390]) ).
cnf(s865,plain,
spl43_1129,
inference(sat_conversion,[],[f18070]) ).
cnf(s866,plain,
( ~ spl43_1130
| spl43_1251
| ~ spl43_1252 ),
inference(sat_conversion,[],[f18087]) ).
cnf(s867,plain,
spl43_1252,
inference(sat_conversion,[],[f18101]) ).
cnf(s868,plain,
~ spl43_1251,
inference(sat_conversion,[],[f18147]) ).
cnf(s869,plain,
~ spl43_1130,
inference(rat,[],[s866,s867,s868]) ).
cnf(s870,plain,
~ spl43_4,
inference(rat,[],[s803,s869,s865]) ).
cnf(s907,plain,
$false,
inference(rat,[],[s3,s5,s6,s870]) ).
fof(f18148,plain,
$false,
inference(avatar_sat_refutation,[],[s907]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG231+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n018.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 19:57:11 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.65/3.23 % (3708319)Detected formulas, will run a generic FOF schedule.
% 17.65/3.23 % (3708355)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1675056254:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 17.65/3.23 % (3708355)Refutation not found, incomplete strategy
% 17.65/3.23 % (3708355)------------------------------
% 17.65/3.23 % (3708355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.65/3.23 % (3708355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.65/3.23 % (3708355)CaDiCaL version: 2.1.3
% 17.65/3.23 % (3708355)Termination reason: Refutation not found, incomplete strategy
% 17.65/3.23 % (3708355)Time elapsed: 0.002 s
% 17.65/3.23 % (3708355)Peak memory usage: 88 MB
% 17.65/3.23 % (3708355)Instructions burned: 2 (million)
% 17.65/3.23 % (3708354)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=3450387457:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 17.65/3.23 % (3708353)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=4094640258:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 17.65/3.23 % (3708357)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3267162340:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 17.65/3.23 % (3708358)dis-21_1_sil=8000:lcm=predicate:random_seed=338299599: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)
% 17.65/3.23 % (3708352)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=2167369222:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 17.65/3.23 % (3708356)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1855206328:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 17.65/3.23 % (3708356)Instruction limit reached!
% 17.65/3.23 % (3708356)------------------------------
% 17.65/3.23 % (3708356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.65/3.23 % (3708356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.65/3.23 % (3708356)CaDiCaL version: 2.1.3
% 17.65/3.23 % (3708356)Termination reason: Instruction limit
% 17.65/3.23 % (3708356)Termination phase: Saturation
% 17.65/3.23 % (3708356)Time elapsed: 0.117 s
% 17.65/3.23 % (3708356)Peak memory usage: 88 MB
% 17.65/3.23 % (3708356)Instructions burned: 119 (million)
% 17.65/3.23 % (3708358)Instruction limit reached!
% 17.65/3.23 % (3708358)------------------------------
% 17.65/3.23 % (3708358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.65/3.23 % (3708358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.65/3.23 % (3708358)CaDiCaL version: 2.1.3
% 17.65/3.23 % (3708358)Termination reason: Instruction limit
% 17.65/3.23 % (3708358)Termination phase: Saturation
% 17.65/3.23 % (3708358)Time elapsed: 0.127 s
% 17.65/3.23 % (3708358)Peak memory usage: 89 MB
% 17.65/3.23 % (3708358)Instructions burned: 129 (million)
% 17.65/3.23 % (3708357)Instruction limit reached!
% 17.65/3.23 % (3708357)------------------------------
% 17.65/3.23 % (3708357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.65/3.23 % (3708357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.65/3.23 % (3708357)CaDiCaL version: 2.1.3
% 17.65/3.23 % (3708357)Termination reason: Instruction limit
% 17.65/3.23 % (3708357)Termination phase: Saturation
% 17.65/3.23 % (3708357)Time elapsed: 0.149 s
% 17.65/3.23 % (3708357)Peak memory usage: 90 MB
% 17.65/3.23 % (3708357)Instructions burned: 139 (million)
% 17.65/3.23 % (3708355)------------------------------
% 17.65/3.23 % (3708355)------------------------------
% 17.65/3.23 % (3708374)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3054274002:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 17.65/3.23 % (3708373)lrs+10_1_sil=8000:sp=occurrence:random_seed=2473080503:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 17.65/3.23 % (3708374)Instruction limit reached!
% 17.65/3.23 % (3708374)------------------------------
% 17.65/3.23 % (3708374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.65/3.23 % (3708374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.65/3.23 % (3708374)CaDiCaL version: 2.1.3
% 31.70/5.16 % (3708374)Termination reason: Instruction limit
% 31.70/5.16 % (3708374)Termination phase: Saturation
% 31.70/5.16 % (3708374)Time elapsed: 0.065 s
% 31.70/5.16 % (3708374)Peak memory usage: 89 MB
% 31.70/5.16 % (3708374)Instructions burned: 159 (million)
% 31.70/5.16 % (3708375)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3157229571:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 31.70/5.16 % (3708376)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=1066767077:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 31.70/5.16 % (3708379)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4048360318:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 31.70/5.16 % (3708379)Refutation not found, incomplete strategy
% 31.70/5.16 % (3708379)------------------------------
% 31.70/5.16 % (3708379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.70/5.16 % (3708379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.70/5.16 % (3708379)CaDiCaL version: 2.1.3
% 31.70/5.16 % (3708379)Termination reason: Refutation not found, incomplete strategy
% 31.70/5.16 % (3708379)Time elapsed: 0.004 s
% 31.70/5.16 % (3708379)Peak memory usage: 89 MB
% 31.70/5.16 % (3708379)Instructions burned: 6 (million)
% 31.70/5.16 % (3708373)Instruction limit reached!
% 31.70/5.16 % (3708373)------------------------------
% 31.70/5.16 % (3708373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.70/5.16 % (3708373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.70/5.16 % (3708373)CaDiCaL version: 2.1.3
% 31.70/5.16 % (3708373)Termination reason: Instruction limit
% 31.70/5.16 % (3708373)Termination phase: Saturation
% 31.70/5.16 % (3708373)Time elapsed: 0.281 s
% 31.70/5.16 % (3708373)Peak memory usage: 91 MB
% 31.70/5.16 % (3708373)Instructions burned: 285 (million)
% 31.70/5.16 % (3708376)Instruction limit reached!
% 31.70/5.16 % (3708376)------------------------------
% 31.70/5.16 % (3708376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.70/5.16 % (3708376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.70/5.16 % (3708376)CaDiCaL version: 2.1.3
% 31.70/5.16 % (3708376)Termination reason: Instruction limit
% 31.70/5.16 % (3708376)Termination phase: Saturation
% 31.70/5.16 % (3708376)Time elapsed: 0.244 s
% 31.70/5.16 % (3708376)Peak memory usage: 92 MB
% 31.70/5.16 % (3708376)Instructions burned: 249 (million)
% 31.70/5.16 % (3708375)Instruction limit reached!
% 31.70/5.16 % (3708375)------------------------------
% 31.70/5.16 % (3708375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.70/5.16 % (3708375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.70/5.16 % (3708375)CaDiCaL version: 2.1.3
% 31.70/5.16 % (3708375)Termination reason: Instruction limit
% 31.70/5.16 % (3708375)Termination phase: Saturation
% 31.70/5.16 % (3708375)Time elapsed: 0.340 s
% 31.70/5.16 % (3708375)Peak memory usage: 91 MB
% 31.70/5.16 % (3708375)Instructions burned: 325 (million)
% 31.70/5.16 % (3708379)------------------------------
% 31.70/5.16 % (3708379)------------------------------
% 31.70/5.16 % (3708384)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4088975065:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 31.70/5.16 % (3708386)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3517697321:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 31.70/5.16 % (3708388)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1987670836:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 31.70/5.16 % (3708387)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2119584246:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 31.70/5.16 % (3708388)Instruction limit reached!
% 31.70/5.16 % (3708388)------------------------------
% 31.70/5.16 % (3708388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.70/5.16 % (3708388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.70/5.16 % (3708388)CaDiCaL version: 2.1.3
% 31.70/5.16 % (3708388)Termination reason: Instruction limit
% 31.70/5.16 % (3708388)Termination phase: Saturation
% 31.70/5.16 % (3708388)Time elapsed: 0.063 s
% 31.70/5.16 % (3708388)Peak memory usage: 89 MB
% 31.70/5.16 % (3708388)Instructions burned: 116 (million)
% 31.70/5.16 % (3708387)Instruction limit reached!
% 16.88/5.32 % (3708387)------------------------------
% 16.88/5.32 % (3708387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708387)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708387)Termination reason: Instruction limit
% 16.88/5.32 % (3708387)Termination phase: Saturation
% 16.88/5.32 % (3708387)Time elapsed: 0.076 s
% 16.88/5.32 % (3708387)Peak memory usage: 89 MB
% 16.88/5.32 % (3708387)Instructions burned: 129 (million)
% 16.88/5.32 % (3708386)Instruction limit reached!
% 16.88/5.32 % (3708386)------------------------------
% 16.88/5.32 % (3708386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708386)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708386)Termination reason: Instruction limit
% 16.88/5.32 % (3708386)Termination phase: Saturation
% 16.88/5.32 % (3708386)Time elapsed: 0.121 s
% 16.88/5.32 % (3708386)Peak memory usage: 91 MB
% 16.88/5.32 % (3708386)Instructions burned: 113 (million)
% 16.88/5.32 % (3708398)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3315082699:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 16.88/5.32 % (3708397)lrs+10_1_sil=8000:sp=occurrence:random_seed=1396746825:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 16.88/5.32 % (3708398)Refutation not found, incomplete strategy
% 16.88/5.32 % (3708398)------------------------------
% 16.88/5.32 % (3708398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708398)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708398)Termination reason: Refutation not found, incomplete strategy
% 16.88/5.32 % (3708398)Time elapsed: 0.011 s
% 16.88/5.32 % (3708398)Peak memory usage: 89 MB
% 16.88/5.32 % (3708398)Instructions burned: 10 (million)
% 16.88/5.32 % (3708399)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2993026034:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 16.88/5.32 % (3708398)------------------------------
% 16.88/5.32 % (3708398)------------------------------
% 16.88/5.32 % (3708407)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2812539194:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2982 on theBenchmark for (2982ds/134Mi)
% 16.88/5.32 % (3708407)Instruction limit reached!
% 16.88/5.32 % (3708407)------------------------------
% 16.88/5.32 % (3708407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708407)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708407)Termination reason: Instruction limit
% 16.88/5.32 % (3708407)Termination phase: Saturation
% 16.88/5.32 % (3708407)Time elapsed: 0.124 s
% 16.88/5.32 % (3708407)Peak memory usage: 91 MB
% 16.88/5.32 % (3708407)Instructions burned: 134 (million)
% 16.88/5.32 % (3708397)Instruction limit reached!
% 16.88/5.32 % (3708397)------------------------------
% 16.88/5.32 % (3708397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708397)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708397)Termination reason: Instruction limit
% 16.88/5.32 % (3708397)Termination phase: Saturation
% 16.88/5.32 % (3708397)Time elapsed: 0.886 s
% 16.88/5.32 % (3708397)Peak memory usage: 98 MB
% 16.88/5.32 % (3708397)Instructions burned: 907 (million)
% 16.88/5.32 % (3708409)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4143209478:st=8:i=592:sd=3:ep=RST:ss=axioms_2978 on theBenchmark for (2978ds/592Mi)
% 16.88/5.32 % (3708409)Refutation not found, incomplete strategy
% 16.88/5.32 % (3708409)------------------------------
% 16.88/5.32 % (3708409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708409)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708409)Termination reason: Refutation not found, incomplete strategy
% 16.88/5.32 % (3708409)Time elapsed: 0.013 s
% 16.88/5.32 % (3708409)Peak memory usage: 88 MB
% 16.88/5.32 % (3708409)Instructions burned: 10 (million)
% 16.88/5.32 % (3708410)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4033070266:st=3:i=13193:sd=3:ss=axioms_2977 on theBenchmark for (2977ds/13193Mi)
% 16.88/5.32 % (3708409)------------------------------
% 16.88/5.32 % (3708409)------------------------------
% 16.88/5.32 % (3708415)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=360982092:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2972 on theBenchmark for (2972ds/125Mi)
% 16.88/5.32 % (3708415)Instruction limit reached!
% 16.88/5.32 % (3708415)------------------------------
% 16.88/5.32 % (3708415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708415)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708415)Termination reason: Instruction limit
% 16.88/5.32 % (3708415)Termination phase: Saturation
% 16.88/5.32 % (3708415)Time elapsed: 0.105 s
% 16.88/5.32 % (3708415)Peak memory usage: 91 MB
% 16.88/5.32 % (3708415)Instructions burned: 125 (million)
% 16.88/5.32 % (3708417)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=1400917617:i=134:gtgl=5:slsql=off:gtg=exists_sym_2970 on theBenchmark for (2970ds/134Mi)
% 16.88/5.32 % (3708417)Instruction limit reached!
% 16.88/5.32 % (3708417)------------------------------
% 16.88/5.32 % (3708417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708417)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708417)Termination reason: Instruction limit
% 16.88/5.32 % (3708417)Termination phase: Saturation
% 16.88/5.32 % (3708417)Time elapsed: 0.156 s
% 16.88/5.32 % (3708417)Peak memory usage: 90 MB
% 16.88/5.32 % (3708417)Instructions burned: 134 (million)
% 16.88/5.32 % (3708384)Instruction limit reached!
% 16.88/5.32 % (3708384)------------------------------
% 16.88/5.32 % (3708384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708384)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708384)Termination reason: Instruction limit
% 16.88/5.32 % (3708384)Termination phase: Saturation
% 16.88/5.32 % (3708384)Time elapsed: 2.457 s
% 16.88/5.32 % (3708384)Peak memory usage: 141 MB
% 16.88/5.32 % (3708384)Instructions burned: 2350 (million)
% 16.88/5.32 % (3708419)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2758776653:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2966 on theBenchmark for (2966ds/141Mi)
% 16.88/5.32 % (3708420)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=3703388380:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2965 on theBenchmark for (2965ds/431Mi)
% 16.88/5.32 % (3708419)Instruction limit reached!
% 16.88/5.32 % (3708419)------------------------------
% 16.88/5.32 % (3708419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708419)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708419)Termination reason: Instruction limit
% 16.88/5.32 % (3708419)Termination phase: Saturation
% 16.88/5.32 % (3708419)Time elapsed: 0.091 s
% 16.88/5.32 % (3708419)Peak memory usage: 89 MB
% 16.88/5.32 % (3708419)Instructions burned: 142 (million)
% 16.88/5.32 % (3708423)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=3221128813:i=6060:aac=none:ins=25_2963 on theBenchmark for (2963ds/6060Mi)
% 16.88/5.32 % (3708420)Instruction limit reached!
% 16.88/5.32 % (3708420)------------------------------
% 16.88/5.32 % (3708420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708420)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708420)Termination reason: Instruction limit
% 16.88/5.32 % (3708420)Termination phase: Saturation
% 16.88/5.32 % (3708420)Time elapsed: 0.406 s
% 16.88/5.32 % (3708420)Peak memory usage: 94 MB
% 16.88/5.32 % (3708420)Instructions burned: 431 (million)
% 16.88/5.32 % (3708352)First to succeed.
% 16.88/5.32 % (3708352)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3708319"
% 16.88/5.32 % (3708427)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=2859951717:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2959 on theBenchmark for (2959ds/150Mi)
% 16.88/5.32 % (3708427)Instruction limit reached!
% 16.88/5.32 % (3708427)------------------------------
% 16.88/5.32 % (3708427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.88/5.32 % (3708427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.88/5.32 % (3708427)CaDiCaL version: 2.1.3
% 16.88/5.32 % (3708427)Termination reason: Instruction limit
% 16.88/5.32 % (3708427)Termination phase: Saturation
% 16.88/5.32 % (3708427)Time elapsed: 0.155 s
% 16.88/5.32 % (3708427)Peak memory usage: 91 MB
% 16.88/5.32 % (3708427)Instructions burned: 151 (million)
% 16.88/5.32 % (3708352)Refutation found. Thanks to Tanya!
% 16.88/5.32 % SZS status Theorem for theBenchmark
% 16.88/5.32 % SZS output start Proof for theBenchmark
% See solution above
% 33.00/5.57 % (3708352)------------------------------
% 33.00/5.57 % (3708352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.00/5.57 % (3708352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.00/5.57 % (3708352)CaDiCaL version: 2.1.3
% 33.00/5.57 % (3708352)Termination reason: Refutation
% 33.00/5.57 % (3708352)Time elapsed: 3.912 s
% 33.00/5.57 % (3708352)Peak memory usage: 161 MB
% 33.00/5.57 % (3708352)Instructions burned: 4565 (million)
% 33.00/5.57 % (3708352)------------------------------
% 33.00/5.57 % (3708352)------------------------------
% 33.00/5.57 % (3708319)Success in time 4.57 s
% 33.00/5.57 % Vampire exiting
%------------------------------------------------------------------------------