%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP629+4 : 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 : n003.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 10:15:06 AM UTC 2026
% Result : Theorem 7.62s 3.87s
% Output : Refutation 9.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 142 ( 19 unt; 6 def)
% Number of atoms : 612 ( 130 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 822 ( 352 ~; 362 |; 78 &)
% ( 9 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 128 ( 0 sgn 124 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18891,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( X2 = k3_group_1(X0,X1)
<=> ( k1_group_1(X0,X1,X2) = k2_group_1(X0)
& k1_group_1(X0,X2,X1) = k2_group_1(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_group_1) ).
fof(f18897,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> k3_group_1(X0,k2_group_1(X0)) = k2_group_1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_group_1) ).
fof(f18899,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( k3_group_1(X0,X1) = k2_group_1(X0)
=> X1 = k2_group_1(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_group_1) ).
fof(f18900,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k3_group_1(X0,k3_group_1(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_group_1) ).
fof(f18993,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f18994,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_subset_1(X1,u1_struct_0(X0)) )
=> m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_group_1) ).
fof(f22542,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( k1_group_1(X0,k1_group_1(X0,X1,X2),k3_group_1(X0,X2)) = X1
& k1_group_1(X0,k1_group_1(X0,X1,k3_group_1(X0,X2)),X2) = X1
& k1_group_1(X0,k1_group_1(X0,k3_group_1(X0,X2),X2),X1) = X1
& k1_group_1(X0,k1_group_1(X0,X2,k3_group_1(X0,X2)),X1) = X1
& k1_group_1(X0,X1,k1_group_1(X0,X2,k3_group_1(X0,X2))) = X1
& k1_group_1(X0,X1,k1_group_1(X0,k3_group_1(X0,X2),X2)) = X1
& k1_group_1(X0,k3_group_1(X0,X2),k1_group_1(X0,X2,X1)) = X1
& k1_group_1(X0,X2,k1_group_1(X0,k3_group_1(X0,X2),X1)) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_group_3) ).
fof(f33422,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> k6_autgroup(X0,k1_group_1(X0,X1,X2)) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_autgroup) ).
fof(f33425,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k3_group_1(X0,X1)),k6_autgroup(X0,X1)) = k6_autgroup(X0,k2_group_1(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_autgroup) ).
fof(f33426,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k3_group_1(X0,X1)),k6_autgroup(X0,X1)) = k6_autgroup(X0,k2_group_1(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f33425]) ).
fof(f33436,plain,
? [X0] :
( ? [X1] :
( k6_autgroup(X0,k2_group_1(X0)) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k3_group_1(X0,X1)),k6_autgroup(X0,X1))
& m1_subset_1(X1,u1_struct_0(X0)) )
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f33426]) ).
fof(f33437,plain,
? [X0] :
( ? [X1] :
( k6_autgroup(X0,k2_group_1(X0)) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k3_group_1(X0,X1)),k6_autgroup(X0,X1))
& m1_subset_1(X1,u1_struct_0(X0)) )
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f33436]) ).
fof(f33458,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f18993]) ).
fof(f33459,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33458]) ).
fof(f33464,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k1_group_1(X0,k1_group_1(X0,X1,X2),k3_group_1(X0,X2)) = X1
& k1_group_1(X0,k1_group_1(X0,X1,k3_group_1(X0,X2)),X2) = X1
& k1_group_1(X0,k1_group_1(X0,k3_group_1(X0,X2),X2),X1) = X1
& k1_group_1(X0,k1_group_1(X0,X2,k3_group_1(X0,X2)),X1) = X1
& k1_group_1(X0,X1,k1_group_1(X0,X2,k3_group_1(X0,X2))) = X1
& k1_group_1(X0,X1,k1_group_1(X0,k3_group_1(X0,X2),X2)) = X1
& k1_group_1(X0,k3_group_1(X0,X2),k1_group_1(X0,X2,X1)) = X1
& k1_group_1(X0,X2,k1_group_1(X0,k3_group_1(X0,X2),X1)) = X1 )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f22542]) ).
fof(f33465,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k1_group_1(X0,k1_group_1(X0,X1,X2),k3_group_1(X0,X2)) = X1
& k1_group_1(X0,k1_group_1(X0,X1,k3_group_1(X0,X2)),X2) = X1
& k1_group_1(X0,k1_group_1(X0,k3_group_1(X0,X2),X2),X1) = X1
& k1_group_1(X0,k1_group_1(X0,X2,k3_group_1(X0,X2)),X1) = X1
& k1_group_1(X0,X1,k1_group_1(X0,X2,k3_group_1(X0,X2))) = X1
& k1_group_1(X0,X1,k1_group_1(X0,k3_group_1(X0,X2),X2)) = X1
& k1_group_1(X0,k3_group_1(X0,X2),k1_group_1(X0,X2,X1)) = X1
& k1_group_1(X0,X2,k1_group_1(X0,k3_group_1(X0,X2),X1)) = X1 )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33464]) ).
fof(f33472,plain,
! [X0,X1] :
( m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f18994]) ).
fof(f33473,plain,
! [X0,X1] :
( m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(flattening,[],[f33472]) ).
fof(f33490,plain,
! [X0] :
( ! [X1] :
( k3_group_1(X0,k3_group_1(X0,X1)) = X1
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f18900]) ).
fof(f33491,plain,
! [X0] :
( ! [X1] :
( k3_group_1(X0,k3_group_1(X0,X1)) = X1
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33490]) ).
fof(f33492,plain,
! [X0] :
( ! [X1] :
( X1 = k2_group_1(X0)
| k2_group_1(X0) != k3_group_1(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f18899]) ).
fof(f33493,plain,
! [X0] :
( ! [X1] :
( X1 = k2_group_1(X0)
| k2_group_1(X0) != k3_group_1(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33492]) ).
fof(f33496,plain,
! [X0] :
( k3_group_1(X0,k2_group_1(X0)) = k2_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f18897]) ).
fof(f33497,plain,
! [X0] :
( k3_group_1(X0,k2_group_1(X0)) = k2_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33496]) ).
fof(f33500,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k3_group_1(X0,X1)
<=> ( k1_group_1(X0,X1,X2) = k2_group_1(X0)
& k1_group_1(X0,X2,X1) = k2_group_1(X0) ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f18891]) ).
fof(f33501,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k3_group_1(X0,X1)
<=> ( k1_group_1(X0,X1,X2) = k2_group_1(X0)
& k1_group_1(X0,X2,X1) = k2_group_1(X0) ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33500]) ).
fof(f33506,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k6_autgroup(X0,k1_group_1(X0,X1,X2)) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,X2))
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f33422]) ).
fof(f33507,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k6_autgroup(X0,k1_group_1(X0,X1,X2)) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,X2))
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33506]) ).
fof(f33517,plain,
( k6_autgroup(sK3,k2_group_1(sK3)) != k7_funct_2(u1_struct_0(sK3),u1_struct_0(sK3),u1_struct_0(sK3),k6_autgroup(sK3,k3_group_1(sK3,sK4)),k6_autgroup(sK3,sK4))
& m1_subset_1(sK4,u1_struct_0(sK3))
& ~ v3_struct_0(sK3)
& v1_group_1(sK3)
& v3_group_1(sK3)
& v4_group_1(sK3)
& l1_group_1(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f33437]) ).
fof(f33541,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k3_group_1(X0,X1)
| k1_group_1(X0,X1,X2) != k2_group_1(X0)
| k1_group_1(X0,X2,X1) != k2_group_1(X0) )
& ( ( k1_group_1(X0,X1,X2) = k2_group_1(X0)
& k1_group_1(X0,X2,X1) = k2_group_1(X0) )
| k3_group_1(X0,X1) != X2 ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(nnf_transformation,[],[f33501]) ).
fof(f33542,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k3_group_1(X0,X1)
| k1_group_1(X0,X1,X2) != k2_group_1(X0)
| k1_group_1(X0,X2,X1) != k2_group_1(X0) )
& ( ( k1_group_1(X0,X1,X2) = k2_group_1(X0)
& k1_group_1(X0,X2,X1) = k2_group_1(X0) )
| k3_group_1(X0,X1) != X2 ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f33541]) ).
fof(f33546,plain,
l1_group_1(sK3),
inference(cnf_transformation,[],[f33517]) ).
fof(f33547,plain,
v4_group_1(sK3),
inference(cnf_transformation,[],[f33517]) ).
fof(f33548,plain,
v3_group_1(sK3),
inference(cnf_transformation,[],[f33517]) ).
fof(f33549,plain,
v1_group_1(sK3),
inference(cnf_transformation,[],[f33517]) ).
fof(f33550,plain,
~ v3_struct_0(sK3),
inference(cnf_transformation,[],[f33517]) ).
fof(f33551,plain,
m1_subset_1(sK4,u1_struct_0(sK3)),
inference(cnf_transformation,[],[f33517]) ).
fof(f33552,plain,
k6_autgroup(sK3,k2_group_1(sK3)) != k7_funct_2(u1_struct_0(sK3),u1_struct_0(sK3),u1_struct_0(sK3),k6_autgroup(sK3,k3_group_1(sK3,sK4)),k6_autgroup(sK3,sK4)),
inference(cnf_transformation,[],[f33517]) ).
fof(f33587,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33459]) ).
fof(f33593,plain,
! [X2,X0,X1] :
( ~ v4_group_1(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| k1_group_1(X0,k3_group_1(X0,X2),k1_group_1(X0,X2,X1)) = X1
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33465]) ).
fof(f33594,plain,
! [X2,X0,X1] :
( ~ v4_group_1(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| k1_group_1(X0,X1,k1_group_1(X0,k3_group_1(X0,X2),X2)) = X1
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33465]) ).
fof(f33613,plain,
! [X0,X1] :
( m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f33473]) ).
fof(f33631,plain,
! [X0,X1] :
( ~ v4_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| k3_group_1(X0,k3_group_1(X0,X1)) = X1
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33491]) ).
fof(f33632,plain,
! [X0,X1] :
( ~ v4_group_1(X0)
| k2_group_1(X0) != k3_group_1(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| k2_group_1(X0) = X1
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33493]) ).
fof(f33634,plain,
! [X0] :
( k2_group_1(X0) = k3_group_1(X0,k2_group_1(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33497]) ).
fof(f33637,plain,
! [X2,X0,X1] :
( k1_group_1(X0,X1,X2) = k2_group_1(X0)
| k3_group_1(X0,X1) != X2
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33542]) ).
fof(f33641,plain,
! [X2,X0,X1] :
( ~ v4_group_1(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| k6_autgroup(X0,k1_group_1(X0,X1,X2)) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,X2))
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f33507]) ).
fof(f33653,plain,
! [X0,X1] :
( ~ v4_group_1(X0)
| ~ m1_subset_1(k3_group_1(X0,X1),u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| k2_group_1(X0) = k1_group_1(X0,X1,k3_group_1(X0,X1))
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f33637]) ).
fof(f33669,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| k3_group_1(sK3,k3_group_1(sK3,X0)) = X0
| ~ l1_group_1(sK3) ),
inference(resolution,[],[f33631,f33547]) ).
fof(f33670,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ v3_group_1(sK3)
| k3_group_1(sK3,k3_group_1(sK3,X0)) = X0
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33669,f33550]) ).
fof(f33671,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| k3_group_1(sK3,k3_group_1(sK3,X0)) = X0
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33670,f33548]) ).
fof(f33672,plain,
! [X0] :
( k3_group_1(sK3,k3_group_1(sK3,X0)) = X0
| ~ m1_subset_1(X0,u1_struct_0(sK3)) ),
inference(forward_subsumption_resolution,[],[f33671,f33546]) ).
fof(f33675,plain,
! [X0] :
( k2_group_1(sK3) != k3_group_1(sK3,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| k2_group_1(sK3) = X0
| ~ l1_group_1(sK3) ),
inference(resolution,[],[f33632,f33547]) ).
fof(f33676,plain,
! [X0] :
( k2_group_1(sK3) != k3_group_1(sK3,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ v3_group_1(sK3)
| k2_group_1(sK3) = X0
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33675,f33550]) ).
fof(f33677,plain,
! [X0] :
( k2_group_1(sK3) != k3_group_1(sK3,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| k2_group_1(sK3) = X0
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33676,f33548]) ).
fof(f33678,plain,
! [X0] :
( k2_group_1(sK3) != k3_group_1(sK3,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| k2_group_1(sK3) = X0 ),
inference(forward_subsumption_resolution,[],[f33677,f33546]) ).
fof(f33679,plain,
! [X0] :
( k2_group_1(sK3) != X0
| ~ m1_subset_1(k3_group_1(sK3,X0),u1_struct_0(sK3))
| k2_group_1(sK3) = k3_group_1(sK3,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK3)) ),
inference(superposition,[],[f33678,f33672]) ).
fof(f33682,plain,
( ~ m1_subset_1(k3_group_1(sK3,k2_group_1(sK3)),u1_struct_0(sK3))
| k2_group_1(sK3) = k3_group_1(sK3,k2_group_1(sK3))
| ~ m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3)) ),
inference(equality_resolution,[],[f33679]) ).
fof(f33684,definition,
( spl17_1
<=> m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f33685,plain,
( m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3))
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f33684]) ).
fof(f33686,plain,
( ~ m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3))
| spl17_1 ),
inference(avatar_component_clause,[],[f33684]) ).
fof(f33688,definition,
( spl17_2
<=> k2_group_1(sK3) = k3_group_1(sK3,k2_group_1(sK3)) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f33690,plain,
( k2_group_1(sK3) = k3_group_1(sK3,k2_group_1(sK3))
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f33688]) ).
fof(f33692,definition,
( spl17_3
<=> m1_subset_1(k3_group_1(sK3,k2_group_1(sK3)),u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f33694,plain,
( ~ m1_subset_1(k3_group_1(sK3,k2_group_1(sK3)),u1_struct_0(sK3))
| spl17_3 ),
inference(avatar_component_clause,[],[f33692]) ).
fof(f33695,plain,
( ~ spl17_1
| spl17_2
| ~ spl17_3 ),
inference(avatar_split_clause,[],[f33682,f33692,f33688,f33684]) ).
fof(f33700,plain,
( v3_struct_0(sK3)
| ~ l1_group_1(sK3)
| spl17_1 ),
inference(resolution,[],[f33686,f33587]) ).
fof(f33701,plain,
( ~ l1_group_1(sK3)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f33700,f33550]) ).
fof(f33702,plain,
( $false
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f33701,f33546]) ).
fof(f33703,plain,
spl17_1,
inference(avatar_contradiction_clause,[],[f33702]) ).
fof(f33709,plain,
( ~ m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3)
| spl17_3 ),
inference(superposition,[],[f33694,f33634]) ).
fof(f33710,plain,
( v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f33709,f33587]) ).
fof(f33712,plain,
( ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f33710,f33550]) ).
fof(f33714,plain,
( ~ v4_group_1(sK3)
| ~ l1_group_1(sK3)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f33712,f33548]) ).
fof(f33716,plain,
( ~ l1_group_1(sK3)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f33714,f33547]) ).
fof(f33718,plain,
( $false
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f33716,f33546]) ).
fof(f33719,plain,
spl17_3,
inference(avatar_contradiction_clause,[],[f33718]) ).
fof(f33782,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| k1_group_1(sK3,k3_group_1(sK3,X0),k1_group_1(sK3,X0,X1)) = X1
| ~ l1_group_1(sK3) ),
inference(resolution,[],[f33593,f33547]) ).
fof(f33783,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| ~ v3_group_1(sK3)
| k1_group_1(sK3,k3_group_1(sK3,X0),k1_group_1(sK3,X0,X1)) = X1
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33782,f33550]) ).
fof(f33784,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| k1_group_1(sK3,k3_group_1(sK3,X0),k1_group_1(sK3,X0,X1)) = X1
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33783,f33548]) ).
fof(f33785,plain,
! [X0,X1] :
( k1_group_1(sK3,k3_group_1(sK3,X0),k1_group_1(sK3,X0,X1)) = X1
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| ~ m1_subset_1(X0,u1_struct_0(sK3)) ),
inference(forward_subsumption_resolution,[],[f33784,f33546]) ).
fof(f33794,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| k1_group_1(sK3,X1,k1_group_1(sK3,k3_group_1(sK3,X0),X0)) = X1
| ~ l1_group_1(sK3) ),
inference(resolution,[],[f33594,f33547]) ).
fof(f33795,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| ~ v3_group_1(sK3)
| k1_group_1(sK3,X1,k1_group_1(sK3,k3_group_1(sK3,X0),X0)) = X1
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33794,f33550]) ).
fof(f33796,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| k1_group_1(sK3,X1,k1_group_1(sK3,k3_group_1(sK3,X0),X0)) = X1
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33795,f33548]) ).
fof(f33797,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| k1_group_1(sK3,X1,k1_group_1(sK3,k3_group_1(sK3,X0),X0)) = X1 ),
inference(forward_subsumption_resolution,[],[f33796,f33546]) ).
fof(f33819,plain,
( ! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| k1_group_1(sK3,X0,k1_group_1(sK3,k3_group_1(sK3,k2_group_1(sK3)),k2_group_1(sK3))) = X0 )
| ~ spl17_1 ),
inference(resolution,[],[f33797,f33685]) ).
fof(f33830,plain,
( ! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| k1_group_1(sK3,X0,k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))) = X0 )
| ~ spl17_1
| ~ spl17_2 ),
inference(forward_demodulation,[],[f33819,f33690]) ).
fof(f33947,plain,
! [X0] :
( ~ m1_subset_1(k3_group_1(sK3,X0),u1_struct_0(sK3))
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| k2_group_1(sK3) = k1_group_1(sK3,X0,k3_group_1(sK3,X0))
| ~ l1_group_1(sK3) ),
inference(resolution,[],[f33653,f33547]) ).
fof(f33948,plain,
! [X0] :
( ~ m1_subset_1(k3_group_1(sK3,X0),u1_struct_0(sK3))
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ v3_group_1(sK3)
| k2_group_1(sK3) = k1_group_1(sK3,X0,k3_group_1(sK3,X0))
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33947,f33550]) ).
fof(f33949,plain,
! [X0] :
( ~ m1_subset_1(k3_group_1(sK3,X0),u1_struct_0(sK3))
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| k2_group_1(sK3) = k1_group_1(sK3,X0,k3_group_1(sK3,X0))
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f33948,f33548]) ).
fof(f33950,plain,
! [X0] :
( ~ m1_subset_1(k3_group_1(sK3,X0),u1_struct_0(sK3))
| ~ m1_subset_1(X0,u1_struct_0(sK3))
| k2_group_1(sK3) = k1_group_1(sK3,X0,k3_group_1(sK3,X0)) ),
inference(forward_subsumption_resolution,[],[f33949,f33546]) ).
fof(f33962,plain,
( sK4 = k1_group_1(sK3,sK4,k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)))
| ~ spl17_1
| ~ spl17_2 ),
inference(resolution,[],[f33830,f33551]) ).
fof(f33975,plain,
( k1_group_1(sK3,k3_group_1(sK3,sK4),sK4) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| ~ m1_subset_1(k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)),u1_struct_0(sK3))
| ~ m1_subset_1(sK4,u1_struct_0(sK3))
| ~ spl17_1
| ~ spl17_2 ),
inference(superposition,[],[f33785,f33962]) ).
fof(f33981,plain,
( k1_group_1(sK3,k3_group_1(sK3,sK4),sK4) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| ~ m1_subset_1(k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)),u1_struct_0(sK3))
| ~ spl17_1
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f33975,f33551]) ).
fof(f33985,definition,
( spl17_18
<=> m1_subset_1(k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)),u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
fof(f33987,plain,
( ~ m1_subset_1(k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)),u1_struct_0(sK3))
| spl17_18 ),
inference(avatar_component_clause,[],[f33985]) ).
fof(f33989,definition,
( spl17_19
<=> k1_group_1(sK3,k3_group_1(sK3,sK4),sK4) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)) ),
introduced(definition,[new_symbols(definition,[spl17_19])],[avatar_definition]) ).
fof(f33991,plain,
( k1_group_1(sK3,k3_group_1(sK3,sK4),sK4) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f33989]) ).
fof(f33992,plain,
( ~ spl17_18
| spl17_19
| ~ spl17_1
| ~ spl17_2 ),
inference(avatar_split_clause,[],[f33981,f33688,f33684,f33989,f33985]) ).
fof(f34005,definition,
( spl17_21
<=> k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)) ),
introduced(definition,[new_symbols(definition,[spl17_21])],[avatar_definition]) ).
fof(f34007,plain,
( k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f34005]) ).
fof(f34287,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v1_group_1(sK3)
| ~ v3_group_1(sK3)
| k6_autgroup(sK3,k1_group_1(sK3,X1,X0)) = k7_funct_2(u1_struct_0(sK3),u1_struct_0(sK3),u1_struct_0(sK3),k6_autgroup(sK3,X1),k6_autgroup(sK3,X0))
| ~ l1_group_1(sK3) ),
inference(resolution,[],[f33641,f33547]) ).
fof(f34288,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| ~ v1_group_1(sK3)
| ~ v3_group_1(sK3)
| k6_autgroup(sK3,k1_group_1(sK3,X1,X0)) = k7_funct_2(u1_struct_0(sK3),u1_struct_0(sK3),u1_struct_0(sK3),k6_autgroup(sK3,X1),k6_autgroup(sK3,X0))
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f34287,f33550]) ).
fof(f34289,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| ~ v3_group_1(sK3)
| k6_autgroup(sK3,k1_group_1(sK3,X1,X0)) = k7_funct_2(u1_struct_0(sK3),u1_struct_0(sK3),u1_struct_0(sK3),k6_autgroup(sK3,X1),k6_autgroup(sK3,X0))
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f34288,f33549]) ).
fof(f34290,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK3))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| k6_autgroup(sK3,k1_group_1(sK3,X1,X0)) = k7_funct_2(u1_struct_0(sK3),u1_struct_0(sK3),u1_struct_0(sK3),k6_autgroup(sK3,X1),k6_autgroup(sK3,X0))
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f34289,f33548]) ).
fof(f34291,plain,
! [X0,X1] :
( k6_autgroup(sK3,k1_group_1(sK3,X1,X0)) = k7_funct_2(u1_struct_0(sK3),u1_struct_0(sK3),u1_struct_0(sK3),k6_autgroup(sK3,X1),k6_autgroup(sK3,X0))
| ~ m1_subset_1(X1,u1_struct_0(sK3))
| ~ m1_subset_1(X0,u1_struct_0(sK3)) ),
inference(forward_subsumption_resolution,[],[f34290,f33546]) ).
fof(f34433,plain,
( ~ m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3))
| ~ m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3))
| k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3) ),
inference(superposition,[],[f33950,f33634]) ).
fof(f34434,plain,
( ~ m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3))
| k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3) ),
inference(duplicate_literal_removal,[],[f34433]) ).
fof(f34439,plain,
( k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f34434,f33587]) ).
fof(f34443,plain,
( k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f34439,f33550]) ).
fof(f34447,plain,
( k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f34443,f33548]) ).
fof(f34449,plain,
( k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3))
| ~ l1_group_1(sK3) ),
inference(forward_subsumption_resolution,[],[f34447,f33547]) ).
fof(f34451,plain,
k2_group_1(sK3) = k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)),
inference(forward_subsumption_resolution,[],[f34449,f33546]) ).
fof(f34914,plain,
( k6_autgroup(sK3,k2_group_1(sK3)) != k6_autgroup(sK3,k1_group_1(sK3,k3_group_1(sK3,sK4),sK4))
| ~ m1_subset_1(k3_group_1(sK3,sK4),u1_struct_0(sK3))
| ~ m1_subset_1(sK4,u1_struct_0(sK3)) ),
inference(superposition,[],[f33552,f34291]) ).
fof(f34915,plain,
( k6_autgroup(sK3,k2_group_1(sK3)) != k6_autgroup(sK3,k1_group_1(sK3,k3_group_1(sK3,sK4),sK4))
| ~ m1_subset_1(k3_group_1(sK3,sK4),u1_struct_0(sK3)) ),
inference(forward_subsumption_resolution,[],[f34914,f33551]) ).
fof(f34941,plain,
spl17_21,
inference(avatar_split_clause,[],[f34451,f34005]) ).
fof(f34968,plain,
( k6_autgroup(sK3,k2_group_1(sK3)) != k6_autgroup(sK3,k1_group_1(sK3,k2_group_1(sK3),k2_group_1(sK3)))
| ~ m1_subset_1(k3_group_1(sK3,sK4),u1_struct_0(sK3))
| ~ spl17_19 ),
inference(forward_demodulation,[],[f34915,f33991]) ).
fof(f34992,plain,
( k6_autgroup(sK3,k2_group_1(sK3)) != k6_autgroup(sK3,k2_group_1(sK3))
| ~ m1_subset_1(k3_group_1(sK3,sK4),u1_struct_0(sK3))
| ~ spl17_19
| ~ spl17_21 ),
inference(forward_demodulation,[],[f34968,f34007]) ).
fof(f34993,plain,
( ~ m1_subset_1(k3_group_1(sK3,sK4),u1_struct_0(sK3))
| ~ spl17_19
| ~ spl17_21 ),
inference(trivial_inequality_removal,[],[f34992]) ).
fof(f35027,plain,
( v3_struct_0(sK3)
| ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3)
| ~ m1_subset_1(sK4,u1_struct_0(sK3))
| ~ spl17_19
| ~ spl17_21 ),
inference(resolution,[],[f34993,f33613]) ).
fof(f35028,plain,
( ~ v3_group_1(sK3)
| ~ v4_group_1(sK3)
| ~ l1_group_1(sK3)
| ~ m1_subset_1(sK4,u1_struct_0(sK3))
| ~ spl17_19
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f35027,f33550]) ).
fof(f35029,plain,
( ~ v4_group_1(sK3)
| ~ l1_group_1(sK3)
| ~ m1_subset_1(sK4,u1_struct_0(sK3))
| ~ spl17_19
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f35028,f33548]) ).
fof(f35030,plain,
( ~ l1_group_1(sK3)
| ~ m1_subset_1(sK4,u1_struct_0(sK3))
| ~ spl17_19
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f35029,f33547]) ).
fof(f35031,plain,
( ~ m1_subset_1(sK4,u1_struct_0(sK3))
| ~ spl17_19
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f35030,f33546]) ).
fof(f35032,plain,
( $false
| ~ spl17_19
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f35031,f33551]) ).
fof(f35033,plain,
( ~ spl17_19
| ~ spl17_21 ),
inference(avatar_contradiction_clause,[],[f35032]) ).
fof(f35034,plain,
( ~ m1_subset_1(k2_group_1(sK3),u1_struct_0(sK3))
| spl17_18
| ~ spl17_21 ),
inference(forward_demodulation,[],[f33987,f34007]) ).
fof(f35057,plain,
( $false
| ~ spl17_1
| spl17_18
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f35034,f33685]) ).
fof(f35058,plain,
( ~ spl17_1
| spl17_18
| ~ spl17_21 ),
inference(avatar_contradiction_clause,[],[f35057]) ).
cnf(s1,plain,
( ~ spl17_1
| spl17_2
| ~ spl17_3 ),
inference(sat_conversion,[],[f33695]) ).
cnf(s2,plain,
spl17_1,
inference(sat_conversion,[],[f33703]) ).
cnf(s3,plain,
spl17_3,
inference(sat_conversion,[],[f33719]) ).
cnf(s8,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_18
| spl17_19 ),
inference(sat_conversion,[],[f33992]) ).
cnf(s23,plain,
spl17_21,
inference(sat_conversion,[],[f34941]) ).
cnf(s24,plain,
( ~ spl17_19
| ~ spl17_21 ),
inference(sat_conversion,[],[f35033]) ).
cnf(s25,plain,
( ~ spl17_1
| spl17_18
| ~ spl17_21 ),
inference(sat_conversion,[],[f35058]) ).
cnf(s27,plain,
~ spl17_19,
inference(rat,[],[s24,s23]) ).
cnf(s29,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_18 ),
inference(rat,[],[s8,s27]) ).
cnf(s31,plain,
spl17_18,
inference(rat,[],[s25,s23,s2]) ).
cnf(s32,plain,
~ spl17_2,
inference(rat,[],[s29,s31,s2]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s3,s32,s2]) ).
fof(f35074,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP629+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:17:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 7.62/3.87 % (292810)Detected formulas, will run a generic FOF schedule.
% 7.62/3.87 % (292817)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=4206585693:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2979 on theBenchmark for (2979ds/134677Mi)
% 7.62/3.87 % (292816)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=2593281208:i=141193_2979 on theBenchmark for (2979ds/141193Mi)
% 7.62/3.87 % (292819)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1012540425:i=109:sd=1:ins=1:gsp=on:ss=axioms_2979 on theBenchmark for (2979ds/109Mi)
% 7.62/3.87 % (292818)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=4193855157:i=141695:sd=1:nm=32:gsp=on:ss=included_2979 on theBenchmark for (2979ds/141695Mi)
% 7.62/3.87 % (292820)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3779808066:i=119:av=off:ss=axioms_2979 on theBenchmark for (2979ds/119Mi)
% 7.62/3.87 % (292822)dis-21_1_sil=8000:lcm=predicate:random_seed=250749697:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2979 on theBenchmark for (2979ds/129Mi)
% 7.62/3.87 % (292821)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2278803297:s2a=on:i=139:gtg=position_2979 on theBenchmark for (2979ds/139Mi)
% 7.62/3.87 % (292821)Instruction limit reached!
% 7.62/3.87 % (292821)------------------------------
% 7.62/3.87 % (292821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292821)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292821)Termination reason: Instruction limit
% 7.62/3.87 % (292821)Termination phase: Property scanning
% 7.62/3.87 % (292821)Time elapsed: 0.064 s
% 7.62/3.87 % (292821)Peak memory usage: 133 MB
% 7.62/3.87 % (292821)Instructions burned: 139 (million)
% 7.62/3.87 % (292819)Instruction limit reached!
% 7.62/3.87 % (292819)------------------------------
% 7.62/3.87 % (292819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292819)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292819)Termination reason: Instruction limit
% 7.62/3.87 % (292819)Termination phase: SInE selection
% 7.62/3.87 % (292819)Time elapsed: 0.082 s
% 7.62/3.87 % (292819)Peak memory usage: 133 MB
% 7.62/3.87 % (292819)Instructions burned: 109 (million)
% 7.62/3.87 % (292820)Instruction limit reached!
% 7.62/3.87 % (292820)------------------------------
% 7.62/3.87 % (292820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292820)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292820)Termination reason: Instruction limit
% 7.62/3.87 % (292820)Termination phase: SInE selection
% 7.62/3.87 % (292820)Time elapsed: 0.089 s
% 7.62/3.87 % (292820)Peak memory usage: 133 MB
% 7.62/3.87 % (292820)Instructions burned: 119 (million)
% 7.62/3.87 % (292822)Instruction limit reached!
% 7.62/3.87 % (292822)------------------------------
% 7.62/3.87 % (292822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292822)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292822)Termination reason: Instruction limit
% 7.62/3.87 % (292822)Termination phase: SInE selection
% 7.62/3.87 % (292822)Time elapsed: 0.094 s
% 7.62/3.87 % (292822)Peak memory usage: 133 MB
% 7.62/3.87 % (292822)Instructions burned: 129 (million)
% 7.62/3.87 % (292830)lrs+10_1_sil=8000:sp=occurrence:random_seed=2588291580:i=285:sd=3:ss=axioms:sgt=8_2976 on theBenchmark for (2976ds/285Mi)
% 7.62/3.87 % (292831)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4042185377:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2976 on theBenchmark for (2976ds/157Mi)
% 7.62/3.87 % (292832)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2239634531:i=325:sd=1:ss=axioms:sgt=32_2976 on theBenchmark for (2976ds/325Mi)
% 7.62/3.87 % (292833)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=606370493:s2a=on:i=248:s2at=1.23:gtg=position_2976 on theBenchmark for (2976ds/248Mi)
% 7.62/3.87 % (292831)Instruction limit reached!
% 7.62/3.87 % (292831)------------------------------
% 7.62/3.87 % (292831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292831)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292831)Termination reason: Instruction limit
% 7.62/3.87 % (292831)Termination phase: Property scanning
% 7.62/3.87 % (292831)Time elapsed: 0.071 s
% 7.62/3.87 % (292831)Peak memory usage: 133 MB
% 7.62/3.87 % (292831)Instructions burned: 159 (million)
% 7.62/3.87 % (292833)Instruction limit reached!
% 7.62/3.87 % (292833)------------------------------
% 7.62/3.87 % (292833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292833)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292833)Termination reason: Instruction limit
% 7.62/3.87 % (292833)Termination phase: Property scanning
% 7.62/3.87 % (292833)Time elapsed: 0.111 s
% 7.62/3.87 % (292833)Peak memory usage: 133 MB
% 7.62/3.87 % (292833)Instructions burned: 249 (million)
% 7.62/3.87 % (292838)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=967176690:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2974 on theBenchmark for (2974ds/294Mi)
% 7.62/3.87 % (292830)Instruction limit reached!
% 7.62/3.87 % (292830)------------------------------
% 7.62/3.87 % (292830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292830)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292830)Termination reason: Instruction limit
% 7.62/3.87 % (292830)Termination phase: Property scanning
% 7.62/3.87 % (292830)Time elapsed: 0.238 s
% 7.62/3.87 % (292830)Peak memory usage: 138 MB
% 7.62/3.87 % (292830)Instructions burned: 287 (million)
% 7.62/3.87 % (292832)First to succeed.
% 7.62/3.87 % (292832)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-292810"
% 7.62/3.87 % (292839)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=680823443:i=2350_2974 on theBenchmark for (2974ds/2350Mi)
% 7.62/3.87 % (292841)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3313328740:cts=off:i=113:fsr=off:ss=included:sgt=4_2973 on theBenchmark for (2973ds/113Mi)
% 7.62/3.87 % (292838)Instruction limit reached!
% 7.62/3.87 % (292838)------------------------------
% 7.62/3.87 % (292838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292838)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292838)Termination reason: Instruction limit
% 7.62/3.87 % (292838)Termination phase: SInE selection
% 7.62/3.87 % (292838)Time elapsed: 0.190 s
% 7.62/3.87 % (292838)Peak memory usage: 134 MB
% 7.62/3.87 % (292838)Instructions burned: 295 (million)
% 7.62/3.87 % (292841)Instruction limit reached!
% 7.62/3.87 % (292841)------------------------------
% 7.62/3.87 % (292841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/3.87 % (292841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/3.87 % (292841)CaDiCaL version: 2.1.3
% 7.62/3.87 % (292841)Termination reason: Instruction limit
% 7.62/3.87 % (292841)Termination phase: SInE selection
% 7.62/3.87 % (292841)Time elapsed: 0.086 s
% 7.62/3.87 % (292841)Peak memory usage: 133 MB
% 7.62/3.87 % (292841)Instructions burned: 114 (million)
% 7.62/3.87 % (292844)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2668715094:i=127:av=off:fsr=off:sup=off_2971 on theBenchmark for (2971ds/127Mi)
% 7.62/3.87 % (292832)Refutation found. Thanks to Tanya!
% 7.62/3.87 % SZS status Theorem for theBenchmark
% 7.62/3.87 % SZS output start Proof for theBenchmark
% See solution above
% 9.32/4.11 % (292832)------------------------------
% 9.32/4.11 % (292832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/4.11 % (292832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/4.11 % (292832)CaDiCaL version: 2.1.3
% 9.32/4.11 % (292832)Termination reason: Refutation
% 9.32/4.11 % (292832)Time elapsed: 0.242 s
% 9.32/4.11 % (292832)Peak memory usage: 140 MB
% 9.32/4.11 % (292832)Instructions burned: 309 (million)
% 9.32/4.11 % (292832)------------------------------
% 9.32/4.11 % (292832)------------------------------
% 9.32/4.11 % (292810)Success in time 3.013 s
% 9.32/4.11 % Vampire exiting
%------------------------------------------------------------------------------