%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP035+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:33:58 PM UTC 2026
% Result : Theorem 2.74s 1.18s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 124 ( 37 unt; 15 def)
% Number of atoms : 568 ( 29 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 738 ( 294 ~; 337 |; 65 &)
% ( 20 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 15 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 85 ( 0 sgn 77 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_tsp_2(X1,X0)
& m2_tsp_1(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( X2 = X3
=> k5_pre_topc(X0,X1,k1_tsp_2(X0,X1),k6_pre_topc(X1,k1_struct_0(X1,X3))) = k6_pre_topc(X0,k1_struct_0(X0,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_tsp_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_tsp_2(X1,X0)
& m2_tsp_1(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( X2 = X3
=> k5_pre_topc(X0,X1,k1_tsp_2(X0,X1),k6_pre_topc(X1,k1_struct_0(X1,X3))) = k6_pre_topc(X0,k1_struct_0(X0,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f50,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_tsp_2(X1,X0)
& m2_tsp_1(X1,X0) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v5_pre_topc(X2,X0,X1)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> ( X2 = k1_tsp_2(X0,X1)
<=> v3_borsuk_1(X2,X0,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_tsp_2) ).
fof(f54,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0)
& ~ v3_struct_0(X1)
& v2_tsp_2(X1,X0)
& m1_pre_topc(X1,X0) )
=> ( v1_funct_1(k1_tsp_2(X0,X1))
& v1_funct_2(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
& v5_pre_topc(k1_tsp_2(X0,X1),X0,X1)
& m2_relset_1(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tsp_2) ).
fof(f86,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_tsp_2(X1,X0)
& m2_tsp_1(X1,X0) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v5_pre_topc(X2,X0,X1)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> ( v3_borsuk_1(X2,X0,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( X3 = X4
=> k5_pre_topc(X0,X1,X2,k6_pre_topc(X1,k1_struct_0(X1,X4))) = k6_pre_topc(X0,k1_struct_0(X0,X3)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l33_tsp_2) ).
fof(f102,axiom,
! [X0] :
( l1_pre_topc(X0)
=> ! [X1] :
( m2_tsp_1(X1,X0)
<=> m1_pre_topc(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_tsp_1) ).
fof(f127,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( k5_pre_topc(X0,X1,k1_tsp_2(X0,X1),k6_pre_topc(X1,k1_struct_0(X1,X3))) != k6_pre_topc(X0,k1_struct_0(X0,X2))
& X2 = X3
& m1_subset_1(X3,u1_struct_0(X1)) )
& m1_subset_1(X2,u1_struct_0(X0)) )
& ~ v3_struct_0(X1)
& v2_tsp_2(X1,X0)
& m2_tsp_1(X1,X0) )
& ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f128,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( k5_pre_topc(X0,X1,k1_tsp_2(X0,X1),k6_pre_topc(X1,k1_struct_0(X1,X3))) != k6_pre_topc(X0,k1_struct_0(X0,X2))
& X2 = X3
& m1_subset_1(X3,u1_struct_0(X1)) )
& m1_subset_1(X2,u1_struct_0(X0)) )
& ~ v3_struct_0(X1)
& v2_tsp_2(X1,X0)
& m2_tsp_1(X1,X0) )
& ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) ),
inference(flattening,[],[f127]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k1_tsp_2(X0,X1)
<=> v3_borsuk_1(X2,X0,X1) )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k1_tsp_2(X0,X1)
<=> v3_borsuk_1(X2,X0,X1) )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(flattening,[],[f195]) ).
fof(f199,plain,
! [X0,X1] :
( ( v1_funct_1(k1_tsp_2(X0,X1))
& v1_funct_2(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
& v5_pre_topc(k1_tsp_2(X0,X1),X0,X1)
& m2_relset_1(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1)) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m1_pre_topc(X1,X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f200,plain,
! [X0,X1] :
( ( v1_funct_1(k1_tsp_2(X0,X1))
& v1_funct_2(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
& v5_pre_topc(k1_tsp_2(X0,X1),X0,X1)
& m2_relset_1(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1)) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m1_pre_topc(X1,X0) ),
inference(flattening,[],[f199]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( k5_pre_topc(X0,X1,X2,k6_pre_topc(X1,k1_struct_0(X1,X4))) = k6_pre_topc(X0,k1_struct_0(X0,X3))
| X3 != X4
| ~ m1_subset_1(X4,u1_struct_0(X1)) )
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ v3_borsuk_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( k5_pre_topc(X0,X1,X2,k6_pre_topc(X1,k1_struct_0(X1,X4))) = k6_pre_topc(X0,k1_struct_0(X0,X3))
| X3 != X4
| ~ m1_subset_1(X4,u1_struct_0(X1)) )
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ v3_borsuk_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(flattening,[],[f222]) ).
fof(f244,plain,
! [X0] :
( ! [X1] :
( m2_tsp_1(X1,X0)
<=> m1_pre_topc(X1,X0) )
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f102]) ).
fof(f259,plain,
( k5_pre_topc(sK2,sK3,k1_tsp_2(sK2,sK3),k6_pre_topc(sK3,k1_struct_0(sK3,sK5))) != k6_pre_topc(sK2,k1_struct_0(sK2,sK4))
& sK4 = sK5
& m1_subset_1(sK5,u1_struct_0(sK3))
& m1_subset_1(sK4,u1_struct_0(sK2))
& ~ v3_struct_0(sK3)
& v2_tsp_2(sK3,sK2)
& m2_tsp_1(sK3,sK2)
& ~ v3_struct_0(sK2)
& v2_pre_topc(sK2)
& l1_pre_topc(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f128]) ).
fof(f262,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k1_tsp_2(X0,X1)
| ~ v3_borsuk_1(X2,X0,X1) )
& ( v3_borsuk_1(X2,X0,X1)
| k1_tsp_2(X0,X1) != X2 ) )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(nnf_transformation,[],[f196]) ).
fof(f284,plain,
! [X0] :
( ! [X1] :
( ( m2_tsp_1(X1,X0)
| ~ m1_pre_topc(X1,X0) )
& ( m1_pre_topc(X1,X0)
| ~ m2_tsp_1(X1,X0) ) )
| ~ l1_pre_topc(X0) ),
inference(nnf_transformation,[],[f244]) ).
fof(f285,plain,
l1_pre_topc(sK2),
inference(cnf_transformation,[],[f259]) ).
fof(f286,plain,
v2_pre_topc(sK2),
inference(cnf_transformation,[],[f259]) ).
fof(f287,plain,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f259]) ).
fof(f288,plain,
m2_tsp_1(sK3,sK2),
inference(cnf_transformation,[],[f259]) ).
fof(f289,plain,
v2_tsp_2(sK3,sK2),
inference(cnf_transformation,[],[f259]) ).
fof(f290,plain,
~ v3_struct_0(sK3),
inference(cnf_transformation,[],[f259]) ).
fof(f291,plain,
m1_subset_1(sK4,u1_struct_0(sK2)),
inference(cnf_transformation,[],[f259]) ).
fof(f292,plain,
m1_subset_1(sK5,u1_struct_0(sK3)),
inference(cnf_transformation,[],[f259]) ).
fof(f293,plain,
sK4 = sK5,
inference(cnf_transformation,[],[f259]) ).
fof(f294,plain,
k5_pre_topc(sK2,sK3,k1_tsp_2(sK2,sK3),k6_pre_topc(sK3,k1_struct_0(sK3,sK5))) != k6_pre_topc(sK2,k1_struct_0(sK2,sK4)),
inference(cnf_transformation,[],[f259]) ).
fof(f410,plain,
! [X2,X0,X1] :
( v3_borsuk_1(X2,X0,X1)
| k1_tsp_2(X0,X1) != X2
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0)
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f413,plain,
! [X0,X1] :
( m2_relset_1(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m1_pre_topc(X1,X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f414,plain,
! [X0,X1] :
( v5_pre_topc(k1_tsp_2(X0,X1),X0,X1)
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m1_pre_topc(X1,X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f415,plain,
! [X0,X1] :
( v1_funct_2(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m1_pre_topc(X1,X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f416,plain,
! [X0,X1] :
( v1_funct_1(k1_tsp_2(X0,X1))
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m1_pre_topc(X1,X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f456,plain,
! [X2,X3,X0,X1,X4] :
( k5_pre_topc(X0,X1,X2,k6_pre_topc(X1,k1_struct_0(X1,X4))) = k6_pre_topc(X0,k1_struct_0(X0,X3))
| X3 != X4
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ v3_borsuk_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0)
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f509,plain,
! [X0,X1] :
( ~ m2_tsp_1(X1,X0)
| m1_pre_topc(X1,X0)
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f520,plain,
k5_pre_topc(sK2,sK3,k1_tsp_2(sK2,sK3),k6_pre_topc(sK3,k1_struct_0(sK3,sK5))) != k6_pre_topc(sK2,k1_struct_0(sK2,sK5)),
inference(definition_unfolding,[],[f294,f293]) ).
fof(f521,plain,
m1_subset_1(sK5,u1_struct_0(sK2)),
inference(definition_unfolding,[],[f291,f293]) ).
fof(f522,plain,
! [X0,X1] :
( v3_borsuk_1(k1_tsp_2(X0,X1),X0,X1)
| ~ v1_funct_1(k1_tsp_2(X0,X1))
| ~ v1_funct_2(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(k1_tsp_2(X0,X1),X0,X1)
| ~ m2_relset_1(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0)
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(equality_resolution,[],[f410]) ).
fof(f523,plain,
! [X2,X0,X1,X4] :
( k5_pre_topc(X0,X1,X2,k6_pre_topc(X1,k1_struct_0(X1,X4))) = k6_pre_topc(X0,k1_struct_0(X0,X4))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X0))
| ~ v3_borsuk_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0)
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(equality_resolution,[],[f456]) ).
fof(f524,definition,
! [X0,X1] :
( sQ25_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ25_eqProxy])],[equality_proxy_definition]) ).
fof(f525,plain,
~ sQ25_eqProxy(k5_pre_topc(sK2,sK3,k1_tsp_2(sK2,sK3),k6_pre_topc(sK3,k1_struct_0(sK3,sK5))),k6_pre_topc(sK2,k1_struct_0(sK2,sK5))),
inference(equality_proxy_replacement,[],[f520,f524]) ).
fof(f527,plain,
! [X2,X0,X1,X4] :
( sQ25_eqProxy(k5_pre_topc(X0,X1,X2,k6_pre_topc(X1,k1_struct_0(X1,X4))),k6_pre_topc(X0,k1_struct_0(X0,X4)))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X0))
| ~ v3_borsuk_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ v5_pre_topc(X2,X0,X1)
| ~ m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| ~ m2_tsp_1(X1,X0)
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(equality_proxy_replacement,[],[f523,f524]) ).
fof(f596,definition,
( spl26_1
<=> l1_pre_topc(sK2) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f597,plain,
( ~ l1_pre_topc(sK2)
| spl26_1 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f602,plain,
( $false
| spl26_1 ),
inference(resolution,[],[f597,f285]) ).
fof(f603,plain,
spl26_1,
inference(avatar_contradiction_clause,[],[f602]) ).
fof(f716,plain,
( m1_pre_topc(sK3,sK2)
| ~ l1_pre_topc(sK2) ),
inference(resolution,[],[f509,f288]) ).
fof(f720,definition,
( spl26_11
<=> m1_pre_topc(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl26_11])],[avatar_definition]) ).
fof(f722,plain,
( ~ spl26_1
| spl26_11 ),
inference(avatar_split_clause,[],[f716,f720,f596]) ).
fof(f741,definition,
( spl26_12
<=> v2_pre_topc(sK2) ),
introduced(definition,[new_symbols(definition,[spl26_12])],[avatar_definition]) ).
fof(f742,plain,
( ~ v2_pre_topc(sK2)
| spl26_12 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f747,plain,
( $false
| spl26_12 ),
inference(resolution,[],[f742,f286]) ).
fof(f748,plain,
spl26_12,
inference(avatar_contradiction_clause,[],[f747]) ).
fof(f838,definition,
( spl26_16
<=> v3_struct_0(sK2) ),
introduced(definition,[new_symbols(definition,[spl26_16])],[avatar_definition]) ).
fof(f839,plain,
( v3_struct_0(sK2)
| ~ spl26_16 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f845,definition,
( spl26_18
<=> v3_struct_0(sK3) ),
introduced(definition,[new_symbols(definition,[spl26_18])],[avatar_definition]) ).
fof(f846,plain,
( v3_struct_0(sK3)
| ~ spl26_18 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f848,plain,
( $false
| ~ spl26_16 ),
inference(resolution,[],[f839,f287]) ).
fof(f849,plain,
~ spl26_16,
inference(avatar_contradiction_clause,[],[f848]) ).
fof(f923,plain,
( ~ m1_subset_1(sK5,u1_struct_0(sK3))
| ~ m1_subset_1(sK5,u1_struct_0(sK2))
| ~ v3_borsuk_1(k1_tsp_2(sK2,sK3),sK2,sK3)
| ~ v1_funct_1(k1_tsp_2(sK2,sK3))
| ~ v1_funct_2(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ v5_pre_topc(k1_tsp_2(sK2,sK3),sK2,sK3)
| ~ m2_relset_1(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m2_tsp_1(sK3,sK2)
| v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2) ),
inference(resolution,[],[f527,f525]) ).
fof(f925,definition,
( spl26_20
<=> m2_tsp_1(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl26_20])],[avatar_definition]) ).
fof(f926,plain,
( ~ m2_tsp_1(sK3,sK2)
| spl26_20 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f928,definition,
( spl26_21
<=> v2_tsp_2(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl26_21])],[avatar_definition]) ).
fof(f929,plain,
( ~ v2_tsp_2(sK3,sK2)
| spl26_21 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f931,definition,
( spl26_22
<=> m2_relset_1(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl26_22])],[avatar_definition]) ).
fof(f932,plain,
( ~ m2_relset_1(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| spl26_22 ),
inference(avatar_component_clause,[],[f931]) ).
fof(f934,definition,
( spl26_23
<=> v5_pre_topc(k1_tsp_2(sK2,sK3),sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl26_23])],[avatar_definition]) ).
fof(f935,plain,
( ~ v5_pre_topc(k1_tsp_2(sK2,sK3),sK2,sK3)
| spl26_23 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f937,definition,
( spl26_24
<=> v1_funct_2(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl26_24])],[avatar_definition]) ).
fof(f938,plain,
( ~ v1_funct_2(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| spl26_24 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f940,definition,
( spl26_25
<=> v1_funct_1(k1_tsp_2(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl26_25])],[avatar_definition]) ).
fof(f941,plain,
( ~ v1_funct_1(k1_tsp_2(sK2,sK3))
| spl26_25 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f943,definition,
( spl26_26
<=> v3_borsuk_1(k1_tsp_2(sK2,sK3),sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl26_26])],[avatar_definition]) ).
fof(f944,plain,
( ~ v3_borsuk_1(k1_tsp_2(sK2,sK3),sK2,sK3)
| spl26_26 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f946,definition,
( spl26_27
<=> m1_subset_1(sK5,u1_struct_0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl26_27])],[avatar_definition]) ).
fof(f947,plain,
( ~ m1_subset_1(sK5,u1_struct_0(sK2))
| spl26_27 ),
inference(avatar_component_clause,[],[f946]) ).
fof(f949,definition,
( spl26_28
<=> m1_subset_1(sK5,u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl26_28])],[avatar_definition]) ).
fof(f950,plain,
( ~ m1_subset_1(sK5,u1_struct_0(sK3))
| spl26_28 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f951,plain,
( ~ spl26_1
| ~ spl26_12
| spl26_16
| ~ spl26_20
| ~ spl26_21
| spl26_18
| ~ spl26_22
| ~ spl26_23
| ~ spl26_24
| ~ spl26_25
| ~ spl26_26
| ~ spl26_27
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f923,f949,f946,f943,f940,f937,f934,f931,f845,f928,f925,f838,f741,f596]) ).
fof(f952,plain,
( $false
| spl26_20 ),
inference(resolution,[],[f926,f288]) ).
fof(f954,plain,
spl26_20,
inference(avatar_contradiction_clause,[],[f952]) ).
fof(f956,plain,
( $false
| spl26_21 ),
inference(resolution,[],[f929,f289]) ).
fof(f957,plain,
spl26_21,
inference(avatar_contradiction_clause,[],[f956]) ).
fof(f958,plain,
( v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl26_22 ),
inference(resolution,[],[f932,f413]) ).
fof(f959,plain,
( ~ spl26_11
| ~ spl26_21
| spl26_18
| ~ spl26_1
| ~ spl26_12
| spl26_16
| spl26_22 ),
inference(avatar_split_clause,[],[f958,f931,f838,f741,f596,f845,f928,f720]) ).
fof(f960,plain,
( $false
| ~ spl26_18 ),
inference(resolution,[],[f846,f290]) ).
fof(f961,plain,
~ spl26_18,
inference(avatar_contradiction_clause,[],[f960]) ).
fof(f962,plain,
( v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl26_23 ),
inference(resolution,[],[f935,f414]) ).
fof(f963,plain,
( ~ spl26_11
| ~ spl26_21
| spl26_18
| ~ spl26_1
| ~ spl26_12
| spl26_16
| spl26_23 ),
inference(avatar_split_clause,[],[f962,f934,f838,f741,f596,f845,f928,f720]) ).
fof(f964,plain,
( v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl26_24 ),
inference(resolution,[],[f938,f415]) ).
fof(f965,plain,
( ~ spl26_11
| ~ spl26_21
| spl26_18
| ~ spl26_1
| ~ spl26_12
| spl26_16
| spl26_24 ),
inference(avatar_split_clause,[],[f964,f937,f838,f741,f596,f845,f928,f720]) ).
fof(f966,plain,
( v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl26_25 ),
inference(resolution,[],[f941,f416]) ).
fof(f967,plain,
( ~ spl26_11
| ~ spl26_21
| spl26_18
| ~ spl26_1
| ~ spl26_12
| spl26_16
| spl26_25 ),
inference(avatar_split_clause,[],[f966,f940,f838,f741,f596,f845,f928,f720]) ).
fof(f968,plain,
( ~ v1_funct_1(k1_tsp_2(sK2,sK3))
| ~ v1_funct_2(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ v5_pre_topc(k1_tsp_2(sK2,sK3),sK2,sK3)
| ~ m2_relset_1(k1_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m2_tsp_1(sK3,sK2)
| v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| spl26_26 ),
inference(resolution,[],[f944,f522]) ).
fof(f969,plain,
( ~ spl26_1
| ~ spl26_12
| spl26_16
| ~ spl26_20
| ~ spl26_21
| spl26_18
| ~ spl26_22
| ~ spl26_23
| ~ spl26_24
| ~ spl26_25
| spl26_26 ),
inference(avatar_split_clause,[],[f968,f943,f940,f937,f934,f931,f845,f928,f925,f838,f741,f596]) ).
fof(f970,plain,
( $false
| spl26_27 ),
inference(resolution,[],[f947,f521]) ).
fof(f971,plain,
spl26_27,
inference(avatar_contradiction_clause,[],[f970]) ).
fof(f972,plain,
( $false
| spl26_28 ),
inference(resolution,[],[f950,f292]) ).
fof(f973,plain,
spl26_28,
inference(avatar_contradiction_clause,[],[f972]) ).
cnf(s2,plain,
spl26_1,
inference(sat_conversion,[],[f603]) ).
cnf(s9,plain,
( ~ spl26_1
| spl26_11 ),
inference(sat_conversion,[],[f722]) ).
cnf(s11,plain,
spl26_12,
inference(sat_conversion,[],[f748]) ).
cnf(s15,plain,
~ spl26_16,
inference(sat_conversion,[],[f849]) ).
cnf(s17,plain,
( ~ spl26_1
| ~ spl26_12
| spl26_16
| spl26_18
| ~ spl26_20
| ~ spl26_21
| ~ spl26_22
| ~ spl26_23
| ~ spl26_24
| ~ spl26_25
| ~ spl26_26
| ~ spl26_27
| ~ spl26_28 ),
inference(sat_conversion,[],[f951]) ).
cnf(s18,plain,
spl26_20,
inference(sat_conversion,[],[f954]) ).
cnf(s20,plain,
spl26_21,
inference(sat_conversion,[],[f957]) ).
cnf(s21,plain,
( ~ spl26_1
| ~ spl26_11
| ~ spl26_12
| spl26_16
| spl26_18
| ~ spl26_21
| spl26_22 ),
inference(sat_conversion,[],[f959]) ).
cnf(s22,plain,
~ spl26_18,
inference(sat_conversion,[],[f961]) ).
cnf(s23,plain,
( ~ spl26_1
| ~ spl26_11
| ~ spl26_12
| spl26_16
| spl26_18
| ~ spl26_21
| spl26_23 ),
inference(sat_conversion,[],[f963]) ).
cnf(s24,plain,
( ~ spl26_1
| ~ spl26_11
| ~ spl26_12
| spl26_16
| spl26_18
| ~ spl26_21
| spl26_24 ),
inference(sat_conversion,[],[f965]) ).
cnf(s25,plain,
( ~ spl26_1
| ~ spl26_11
| ~ spl26_12
| spl26_16
| spl26_18
| ~ spl26_21
| spl26_25 ),
inference(sat_conversion,[],[f967]) ).
cnf(s26,plain,
( ~ spl26_1
| ~ spl26_12
| spl26_16
| spl26_18
| ~ spl26_20
| ~ spl26_21
| ~ spl26_22
| ~ spl26_23
| ~ spl26_24
| ~ spl26_25
| spl26_26 ),
inference(sat_conversion,[],[f969]) ).
cnf(s27,plain,
spl26_27,
inference(sat_conversion,[],[f971]) ).
cnf(s28,plain,
spl26_28,
inference(sat_conversion,[],[f973]) ).
cnf(s29,plain,
( ~ spl26_1
| ~ spl26_11
| ~ spl26_12
| spl26_16
| ~ spl26_21
| spl26_22 ),
inference(rat,[],[s21,s22]) ).
cnf(s30,plain,
( ~ spl26_1
| ~ spl26_12
| spl26_16
| ~ spl26_22
| ~ spl26_23
| ~ spl26_24
| ~ spl26_25
| ~ spl26_26 ),
inference(rat,[],[s17,s28,s27,s20,s18,s22]) ).
cnf(s33,plain,
spl26_11,
inference(rat,[],[s9,s2]) ).
cnf(s34,plain,
spl26_25,
inference(rat,[],[s25,s2,s20,s22,s15,s11,s33]) ).
cnf(s35,plain,
spl26_24,
inference(rat,[],[s24,s2,s20,s22,s15,s11,s33]) ).
cnf(s36,plain,
spl26_23,
inference(rat,[],[s23,s2,s20,s22,s15,s11,s33]) ).
cnf(s37,plain,
spl26_22,
inference(rat,[],[s29,s2,s20,s15,s11,s33]) ).
cnf(s40,plain,
spl26_26,
inference(rat,[],[s26,s36,s34,s35,s2,s11,s20,s18,s22,s15,s37]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s30,s36,s34,s35,s2,s11,s15,s40,s37]) ).
fof(f974,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP035+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 % Computer : n026.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Mon Sep 28 19:00:27 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.29 Running first-order theorem proving
% 0.19/0.29 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.74/1.18 % (4157360)Detected formulas, will run a generic FOF schedule.
% 2.74/1.18 % (4157368)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=148198356:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.18 % (4157368)Refutation not found, incomplete strategy
% 2.74/1.18 % (4157368)------------------------------
% 2.74/1.18 % (4157368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.18 % (4157368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.18 % (4157368)CaDiCaL version: 2.1.3
% 2.74/1.18 % (4157368)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.18 % (4157368)Time elapsed: 0.001 s
% 2.74/1.18 % (4157368)Peak memory usage: 88 MB
% 2.74/1.18 % (4157368)Instructions burned: 1 (million)
% 2.74/1.18 % (4157366)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=2650397647:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.18 % (4157367)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=335558716:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.18 % (4157365)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=3332260543:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.18 % (4157370)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3836910244:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.18 % (4157369)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1235835145:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.18 % (4157371)dis-21_1_sil=8000:lcm=predicate:random_seed=3226882755: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)
% 2.74/1.18 % (4157369)Refutation not found, incomplete strategy
% 2.74/1.18 % (4157369)------------------------------
% 2.74/1.18 % (4157369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.18 % (4157369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.18 % (4157369)CaDiCaL version: 2.1.3
% 2.74/1.18 % (4157369)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.18 % (4157369)Time elapsed: 0.004 s
% 2.74/1.18 % (4157369)Peak memory usage: 88 MB
% 2.74/1.18 % (4157369)Instructions burned: 5 (million)
% 2.74/1.18 % (4157371)First to succeed.
% 2.74/1.18 % (4157371)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4157360"
% 2.74/1.18 % (4157370)Also succeeded, but the first one will report.
% 2.74/1.18 % (4157368)------------------------------
% 2.74/1.18 % (4157368)------------------------------
% 2.74/1.18 % (4157369)------------------------------
% 2.74/1.18 % (4157369)------------------------------
% 2.74/1.18 % (4157379)lrs+10_1_sil=8000:sp=occurrence:random_seed=1240151616:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.74/1.18 % (4157371)Refutation found. Thanks to Tanya!
% 2.74/1.18 % SZS status Theorem for theBenchmark
% 2.74/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.37 % (4157371)------------------------------
% 3.69/1.37 % (4157371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.37 % (4157371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.37 % (4157371)CaDiCaL version: 2.1.3
% 3.69/1.37 % (4157371)Termination reason: Refutation
% 3.69/1.37 % (4157371)Time elapsed: 0.016 s
% 3.69/1.37 % (4157371)Peak memory usage: 90 MB
% 3.69/1.37 % (4157371)Instructions burned: 24 (million)
% 3.69/1.37 % (4157371)------------------------------
% 3.69/1.37 % (4157371)------------------------------
% 3.69/1.37 % (4157360)Success in time 0.44 s
% 3.69/1.37 % Vampire exiting
%------------------------------------------------------------------------------