%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : TOP037+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 02:34:26 PM UTC 2026
% Result : Theorem 0.51s 0.48s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 25
% Syntax : Number of formulae : 185 ( 30 unt; 5 def)
% Number of atoms : 706 ( 84 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 884 ( 363 ~; 381 |; 100 &)
% ( 9 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 6 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-4 aty)
% Number of variables : 214 ( 0 sgn 208 !; 6 ?)
% 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,k1_zfmisc_1(u1_struct_0(X0)))
=> k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2) = k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),k3_tex_4(X0,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_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,k1_zfmisc_1(u1_struct_0(X0)))
=> k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2) = k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),k3_tex_4(X0,X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f21,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f51,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(f59,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(k4_tsp_2(X0,X1))
& v1_funct_2(k4_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
& v5_pre_topc(k4_tsp_2(X0,X1),X0,X1)
& m2_relset_1(k4_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tsp_2) ).
fof(f62,axiom,
! [X0] :
( l1_pre_topc(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f67,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f68,axiom,
! [X0] :
( l1_pre_topc(X0)
=> ! [X1] :
( m2_tsp_1(X1,X0)
=> l1_pre_topc(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_tsp_1) ).
fof(f77,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f80,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(f93,axiom,
! [X0,X1,X2,X3] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1)
& m1_relset_1(X2,X0,X1) )
=> k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(f94,axiom,
! [X0,X1,X2,X3] :
( ( l1_struct_0(X0)
& l1_struct_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> k4_pre_topc(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_pre_topc) ).
fof(f95,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) )
=> k4_tsp_2(X0,X1) = k1_tsp_2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_tsp_2) ).
fof(f96,axiom,
! [X0,X1,X2,X3] :
( ( l1_struct_0(X0)
& l1_struct_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> k5_pre_topc(X0,X1,X2,X3) = k10_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_pre_topc) ).
fof(f97,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f98,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(f100,axiom,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ( r1_tarski(X0,k2_relat_1(X1))
=> k9_relat_1(X1,k10_relat_1(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f101,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X0,X1)
=> r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).
fof(f103,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] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> k5_pre_topc(X0,X1,k4_tsp_2(X0,X1),k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2)) = k3_tex_4(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tsp_2) ).
fof(f105,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f106,axiom,
! [X0,X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1)
& m2_relset_1(X2,X0,X1) )
=> ( ( X1 = k1_xboole_0
=> X0 = k1_xboole_0 )
=> k2_funct_2(X0,X1,X2,X0) = k2_relat_1(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).
fof(f113,plain,
! [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))
& m2_relset_1(k1_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1)) ) ),
inference(pure_predicate_removal,[],[f51]) ).
fof(f114,plain,
! [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(k4_tsp_2(X0,X1))
& v1_funct_2(k4_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(k4_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1)) ) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f142,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2) != k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),k3_tex_4(X0,X2))
& m1_subset_1(X2,k1_zfmisc_1(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(f143,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2) != k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),k3_tex_4(X0,X2))
& m1_subset_1(X2,k1_zfmisc_1(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,[],[f142]) ).
fof(f163,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f21]) ).
fof(f206,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))
& 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,[],[f113]) ).
fof(f207,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))
& 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,[],[f206]) ).
fof(f214,plain,
! [X0,X1] :
( ( v1_funct_1(k4_tsp_2(X0,X1))
& v1_funct_2(k4_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(k4_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,[],[f114]) ).
fof(f215,plain,
! [X0,X1] :
( ( v1_funct_1(k4_tsp_2(X0,X1))
& v1_funct_2(k4_tsp_2(X0,X1),u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(k4_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,[],[f214]) ).
fof(f218,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f62]) ).
fof(f220,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( l1_pre_topc(X1)
| ~ m2_tsp_1(X1,X0) )
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f224,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f225,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f224]) ).
fof(f244,plain,
! [X0,X1,X2,X3] :
( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f93]) ).
fof(f245,plain,
! [X0,X1,X2,X3] :
( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(flattening,[],[f244]) ).
fof(f246,plain,
! [X0,X1,X2,X3] :
( k4_pre_topc(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) ),
inference(ennf_transformation,[],[f94]) ).
fof(f247,plain,
! [X0,X1,X2,X3] :
( k4_pre_topc(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) ),
inference(flattening,[],[f246]) ).
fof(f248,plain,
! [X0,X1] :
( k4_tsp_2(X0,X1) = 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(ennf_transformation,[],[f95]) ).
fof(f249,plain,
! [X0,X1] :
( k4_tsp_2(X0,X1) = 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(flattening,[],[f248]) ).
fof(f250,plain,
! [X0,X1,X2,X3] :
( k5_pre_topc(X0,X1,X2,X3) = k10_relat_1(X2,X3)
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) ),
inference(ennf_transformation,[],[f96]) ).
fof(f251,plain,
! [X0,X1,X2,X3] :
( k5_pre_topc(X0,X1,X2,X3) = k10_relat_1(X2,X3)
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) ),
inference(flattening,[],[f250]) ).
fof(f252,plain,
! [X0] :
( ! [X1] :
( m2_tsp_1(X1,X0)
<=> m1_pre_topc(X1,X0) )
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f253,plain,
! [X0,X1] :
( k9_relat_1(X1,k10_relat_1(X1,X0)) = X0
| ~ r1_tarski(X0,k2_relat_1(X1))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(ennf_transformation,[],[f100]) ).
fof(f254,plain,
! [X0,X1] :
( k9_relat_1(X1,k10_relat_1(X1,X0)) = X0
| ~ r1_tarski(X0,k2_relat_1(X1))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(flattening,[],[f253]) ).
fof(f255,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f101]) ).
fof(f256,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(flattening,[],[f255]) ).
fof(f258,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k5_pre_topc(X0,X1,k4_tsp_2(X0,X1),k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2)) = k3_tex_4(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(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,[],[f103]) ).
fof(f259,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k5_pre_topc(X0,X1,k4_tsp_2(X0,X1),k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2)) = k3_tex_4(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(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,[],[f258]) ).
fof(f262,plain,
! [X0,X1,X2] :
( k2_funct_2(X0,X1,X2,X0) = k2_relat_1(X2)
| ( k1_xboole_0 != X0
& X1 = k1_xboole_0 )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f106]) ).
fof(f263,plain,
! [X0,X1,X2] :
( k2_funct_2(X0,X1,X2,X0) = k2_relat_1(X2)
| ( k1_xboole_0 != X0
& X1 = k1_xboole_0 )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(flattening,[],[f262]) ).
fof(f274,plain,
( k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),sK4) != k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),k3_tex_4(sK2,sK4))
& m1_subset_1(sK4,k1_zfmisc_1(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]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f143]) ).
fof(f297,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f97]) ).
fof(f298,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,[],[f252]) ).
fof(f299,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,[],[f105]) ).
fof(f300,plain,
l1_pre_topc(sK2),
inference(cnf_transformation,[],[f274]) ).
fof(f301,plain,
v2_pre_topc(sK2),
inference(cnf_transformation,[],[f274]) ).
fof(f302,plain,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f274]) ).
fof(f303,plain,
m2_tsp_1(sK3,sK2),
inference(cnf_transformation,[],[f274]) ).
fof(f304,plain,
v2_tsp_2(sK3,sK2),
inference(cnf_transformation,[],[f274]) ).
fof(f305,plain,
~ v3_struct_0(sK3),
inference(cnf_transformation,[],[f274]) ).
fof(f306,plain,
m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2))),
inference(cnf_transformation,[],[f274]) ).
fof(f307,plain,
k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),sK4) != k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),k3_tex_4(sK2,sK4)),
inference(cnf_transformation,[],[f274]) ).
fof(f340,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f163]) ).
fof(f409,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,[],[f207]) ).
fof(f410,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,[],[f207]) ).
fof(f417,plain,
! [X0,X1] :
( v1_funct_1(k4_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,[],[f215]) ).
fof(f419,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f421,plain,
! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f422,plain,
! [X0,X1] :
( ~ m2_tsp_1(X1,X0)
| l1_pre_topc(X1)
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f430,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f225]) ).
fof(f438,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f80]) ).
fof(f487,plain,
! [X2,X3,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f245]) ).
fof(f488,plain,
! [X2,X3,X0,X1] :
( ~ m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| k4_pre_topc(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f247]) ).
fof(f489,plain,
! [X0,X1] :
( ~ m1_pre_topc(X1,X0)
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_struct_0(X1)
| ~ v2_tsp_2(X1,X0)
| k4_tsp_2(X0,X1) = k1_tsp_2(X0,X1) ),
inference(cnf_transformation,[],[f249]) ).
fof(f490,plain,
! [X2,X3,X0,X1] :
( ~ m1_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
| k5_pre_topc(X0,X1,X2,X3) = k10_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f251]) ).
fof(f491,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f297]) ).
fof(f493,plain,
! [X0,X1] :
( ~ m2_tsp_1(X1,X0)
| m1_pre_topc(X1,X0)
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f496,plain,
! [X0,X1] :
( ~ r1_tarski(X0,k2_relat_1(X1))
| k9_relat_1(X1,k10_relat_1(X1,X0)) = X0
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(cnf_transformation,[],[f254]) ).
fof(f497,plain,
! [X2,X0,X1] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f499,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| k3_tex_4(X0,X2) = k5_pre_topc(X0,X1,k4_tsp_2(X0,X1),k4_pre_topc(X0,X1,k4_tsp_2(X0,X1),X2))
| 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,[],[f259]) ).
fof(f501,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f299]) ).
fof(f503,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k1_xboole_0 = X1
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| k2_funct_2(X0,X1,X2,X0) = k2_relat_1(X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f533,plain,
l1_struct_0(sK2),
inference(resolution,[],[f419,f300]) ).
fof(f580,plain,
( l1_pre_topc(sK3)
| ~ l1_pre_topc(sK2) ),
inference(resolution,[],[f422,f303]) ).
fof(f583,plain,
l1_pre_topc(sK3),
inference(forward_subsumption_resolution,[],[f580,f300]) ).
fof(f585,plain,
l1_struct_0(sK3),
inference(resolution,[],[f583,f419]) ).
fof(f598,plain,
r1_tarski(sK4,u1_struct_0(sK2)),
inference(resolution,[],[f501,f306]) ).
fof(f833,plain,
( m1_pre_topc(sK3,sK2)
| ~ l1_pre_topc(sK2) ),
inference(resolution,[],[f493,f303]) ).
fof(f836,plain,
m1_pre_topc(sK3,sK2),
inference(forward_subsumption_resolution,[],[f833,f300]) ).
fof(f911,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(resolution,[],[f421,f340]) ).
fof(f1420,plain,
( v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| k4_tsp_2(sK2,sK3) = k1_tsp_2(sK2,sK3) ),
inference(resolution,[],[f489,f836]) ).
fof(f1424,plain,
( ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| k4_tsp_2(sK2,sK3) = k1_tsp_2(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f1420,f302]) ).
fof(f1425,plain,
( ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| k4_tsp_2(sK2,sK3) = k1_tsp_2(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f1424,f301]) ).
fof(f1426,plain,
( v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| k4_tsp_2(sK2,sK3) = k1_tsp_2(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f1425,f300]) ).
fof(f1427,plain,
( ~ v2_tsp_2(sK3,sK2)
| k4_tsp_2(sK2,sK3) = k1_tsp_2(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f1426,f305]) ).
fof(f1428,plain,
k4_tsp_2(sK2,sK3) = k1_tsp_2(sK2,sK3),
inference(forward_subsumption_resolution,[],[f1427,f304]) ).
fof(f1435,plain,
( m2_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| 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) ),
inference(superposition,[],[f409,f1428]) ).
fof(f1436,plain,
( m2_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1435,f302]) ).
fof(f1438,plain,
( m2_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1436,f301]) ).
fof(f1439,plain,
( m2_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1438,f300]) ).
fof(f1440,plain,
( m2_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1439,f305]) ).
fof(f1441,plain,
( m2_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1440,f304]) ).
fof(f1442,plain,
m2_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3)),
inference(forward_subsumption_resolution,[],[f1441,f836]) ).
fof(f1443,plain,
( k1_xboole_0 = u1_struct_0(sK3)
| ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k2_funct_2(u1_struct_0(sK2),u1_struct_0(sK3),k4_tsp_2(sK2,sK3),u1_struct_0(sK2)) = k2_relat_1(k4_tsp_2(sK2,sK3)) ),
inference(resolution,[],[f1442,f503]) ).
fof(f1444,plain,
v1_relat_1(k4_tsp_2(sK2,sK3)),
inference(resolution,[],[f1442,f911]) ).
fof(f1445,plain,
m1_relset_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3)),
inference(resolution,[],[f1442,f491]) ).
fof(f1447,definition,
( spl24_25
<=> k2_funct_2(u1_struct_0(sK2),u1_struct_0(sK3),k4_tsp_2(sK2,sK3),u1_struct_0(sK2)) = k2_relat_1(k4_tsp_2(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl24_25])],[avatar_definition]) ).
fof(f1449,plain,
( k2_funct_2(u1_struct_0(sK2),u1_struct_0(sK3),k4_tsp_2(sK2,sK3),u1_struct_0(sK2)) = k2_relat_1(k4_tsp_2(sK2,sK3))
| ~ spl24_25 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f1451,definition,
( spl24_26
<=> v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl24_26])],[avatar_definition]) ).
fof(f1452,plain,
( v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ spl24_26 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f1455,definition,
( spl24_27
<=> v1_funct_1(k4_tsp_2(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl24_27])],[avatar_definition]) ).
fof(f1456,plain,
( v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ spl24_27 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f1457,plain,
( ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| spl24_27 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f1459,definition,
( spl24_28
<=> k1_xboole_0 = u1_struct_0(sK3) ),
introduced(definition,[new_symbols(definition,[spl24_28])],[avatar_definition]) ).
fof(f1461,plain,
( k1_xboole_0 = u1_struct_0(sK3)
| ~ spl24_28 ),
inference(avatar_component_clause,[],[f1459]) ).
fof(f1462,plain,
( spl24_25
| ~ spl24_26
| ~ spl24_27
| spl24_28 ),
inference(avatar_split_clause,[],[f1443,f1459,f1455,f1451,f1447]) ).
fof(f1463,plain,
( v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| 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) ),
inference(superposition,[],[f410,f1428]) ).
fof(f1464,plain,
( v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1463,f302]) ).
fof(f1465,plain,
( v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1464,f301]) ).
fof(f1466,plain,
( v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1465,f300]) ).
fof(f1467,plain,
( v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1466,f305]) ).
fof(f1468,plain,
( v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| ~ m1_pre_topc(sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f1467,f304]) ).
fof(f1469,plain,
v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3)),
inference(forward_subsumption_resolution,[],[f1468,f836]) ).
fof(f1470,plain,
spl24_26,
inference(avatar_split_clause,[],[f1469,f1451]) ).
fof(f1475,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)
| spl24_27 ),
inference(resolution,[],[f1457,f417]) ).
fof(f1476,plain,
( ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl24_27 ),
inference(forward_subsumption_resolution,[],[f1475,f302]) ).
fof(f1477,plain,
( ~ l1_pre_topc(sK2)
| v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl24_27 ),
inference(forward_subsumption_resolution,[],[f1476,f301]) ).
fof(f1478,plain,
( v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl24_27 ),
inference(forward_subsumption_resolution,[],[f1477,f300]) ).
fof(f1479,plain,
( ~ v2_tsp_2(sK3,sK2)
| ~ m1_pre_topc(sK3,sK2)
| spl24_27 ),
inference(forward_subsumption_resolution,[],[f1478,f305]) ).
fof(f1480,plain,
( ~ m1_pre_topc(sK3,sK2)
| spl24_27 ),
inference(forward_subsumption_resolution,[],[f1479,f304]) ).
fof(f1481,plain,
( $false
| spl24_27 ),
inference(forward_subsumption_resolution,[],[f1480,f836]) ).
fof(f1482,plain,
spl24_27,
inference(avatar_contradiction_clause,[],[f1481]) ).
fof(f1517,plain,
! [X0] :
( ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k2_funct_2(u1_struct_0(sK2),u1_struct_0(sK3),k4_tsp_2(sK2,sK3),X0) = k9_relat_1(k4_tsp_2(sK2,sK3),X0) ),
inference(resolution,[],[f1445,f487]) ).
fof(f1519,plain,
( ! [X0] :
( ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k2_funct_2(u1_struct_0(sK2),u1_struct_0(sK3),k4_tsp_2(sK2,sK3),X0) = k9_relat_1(k4_tsp_2(sK2,sK3),X0) )
| ~ spl24_27 ),
inference(forward_subsumption_resolution,[],[f1517,f1456]) ).
fof(f1521,definition,
( spl24_29
<=> ! [X0] : k2_funct_2(u1_struct_0(sK2),u1_struct_0(sK3),k4_tsp_2(sK2,sK3),X0) = k9_relat_1(k4_tsp_2(sK2,sK3),X0) ),
introduced(definition,[new_symbols(definition,[spl24_29])],[avatar_definition]) ).
fof(f1522,plain,
( ! [X0] : k2_funct_2(u1_struct_0(sK2),u1_struct_0(sK3),k4_tsp_2(sK2,sK3),X0) = k9_relat_1(k4_tsp_2(sK2,sK3),X0)
| ~ spl24_29 ),
inference(avatar_component_clause,[],[f1521]) ).
fof(f1523,plain,
( spl24_29
| ~ spl24_26
| ~ spl24_27 ),
inference(avatar_split_clause,[],[f1519,f1455,f1451,f1521]) ).
fof(f1558,plain,
! [X0] :
( ~ l1_struct_0(sK2)
| ~ l1_struct_0(sK3)
| ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) ),
inference(resolution,[],[f488,f1445]) ).
fof(f1561,plain,
! [X0] :
( ~ l1_struct_0(sK3)
| ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[],[f1558,f533]) ).
fof(f1562,plain,
! [X0] :
( ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[],[f1561,f585]) ).
fof(f1563,plain,
( ! [X0] :
( ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) )
| ~ spl24_27 ),
inference(forward_subsumption_resolution,[],[f1562,f1456]) ).
fof(f1564,plain,
( ! [X0] : k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0)
| ~ spl24_26
| ~ spl24_27 ),
inference(forward_subsumption_resolution,[],[f1563,f1452]) ).
fof(f1565,plain,
( k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),sK4) != k9_relat_1(k4_tsp_2(sK2,sK3),k3_tex_4(sK2,sK4))
| ~ spl24_26
| ~ spl24_27 ),
inference(superposition,[],[f307,f1564]) ).
fof(f1568,plain,
( k9_relat_1(k4_tsp_2(sK2,sK3),k3_tex_4(sK2,sK4)) != k9_relat_1(k4_tsp_2(sK2,sK3),sK4)
| ~ spl24_26
| ~ spl24_27 ),
inference(forward_demodulation,[],[f1565,f1564]) ).
fof(f1573,plain,
! [X0] :
( ~ l1_struct_0(sK2)
| ~ l1_struct_0(sK3)
| ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) = k10_relat_1(k4_tsp_2(sK2,sK3),X0) ),
inference(resolution,[],[f490,f1445]) ).
fof(f1576,plain,
! [X0] :
( ~ l1_struct_0(sK3)
| ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) = k10_relat_1(k4_tsp_2(sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[],[f1573,f533]) ).
fof(f1577,plain,
! [X0] :
( ~ v1_funct_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) = k10_relat_1(k4_tsp_2(sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[],[f1576,f585]) ).
fof(f1578,plain,
( ! [X0] :
( ~ v1_funct_2(k4_tsp_2(sK2,sK3),u1_struct_0(sK2),u1_struct_0(sK3))
| k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) = k10_relat_1(k4_tsp_2(sK2,sK3),X0) )
| ~ spl24_27 ),
inference(forward_subsumption_resolution,[],[f1577,f1456]) ).
fof(f1579,plain,
( ! [X0] : k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),X0) = k10_relat_1(k4_tsp_2(sK2,sK3),X0)
| ~ spl24_26
| ~ spl24_27 ),
inference(forward_subsumption_resolution,[],[f1578,f1452]) ).
fof(f1685,plain,
! [X0] :
( k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),k4_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),sK4))
| v3_struct_0(X0)
| ~ v2_tsp_2(X0,sK2)
| ~ m2_tsp_1(X0,sK2)
| v3_struct_0(sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2) ),
inference(resolution,[],[f499,f306]) ).
fof(f1708,plain,
! [X0] :
( k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),k4_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),sK4))
| v3_struct_0(X0)
| ~ v2_tsp_2(X0,sK2)
| ~ m2_tsp_1(X0,sK2)
| ~ v2_pre_topc(sK2)
| ~ l1_pre_topc(sK2) ),
inference(forward_subsumption_resolution,[],[f1685,f302]) ).
fof(f1712,plain,
! [X0] :
( k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),k4_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),sK4))
| v3_struct_0(X0)
| ~ v2_tsp_2(X0,sK2)
| ~ m2_tsp_1(X0,sK2)
| ~ l1_pre_topc(sK2) ),
inference(forward_subsumption_resolution,[],[f1708,f301]) ).
fof(f1714,plain,
! [X0] :
( ~ m2_tsp_1(X0,sK2)
| v3_struct_0(X0)
| ~ v2_tsp_2(X0,sK2)
| k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),k4_pre_topc(sK2,X0,k4_tsp_2(sK2,X0),sK4)) ),
inference(forward_subsumption_resolution,[],[f1712,f300]) ).
fof(f1716,plain,
( v3_struct_0(sK3)
| ~ v2_tsp_2(sK3,sK2)
| k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),sK4)) ),
inference(resolution,[],[f1714,f303]) ).
fof(f1721,plain,
( ~ v2_tsp_2(sK3,sK2)
| k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),sK4)) ),
inference(forward_subsumption_resolution,[],[f1716,f305]) ).
fof(f1748,plain,
k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),k4_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),sK4)),
inference(forward_subsumption_resolution,[],[f1721,f304]) ).
fof(f1749,plain,
( k3_tex_4(sK2,sK4) = k5_pre_topc(sK2,sK3,k4_tsp_2(sK2,sK3),k9_relat_1(k4_tsp_2(sK2,sK3),sK4))
| ~ spl24_26
| ~ spl24_27 ),
inference(forward_demodulation,[],[f1748,f1564]) ).
fof(f1938,plain,
( k3_tex_4(sK2,sK4) = k10_relat_1(k4_tsp_2(sK2,sK3),k9_relat_1(k4_tsp_2(sK2,sK3),sK4))
| ~ spl24_26
| ~ spl24_27 ),
inference(forward_demodulation,[],[f1749,f1579]) ).
fof(f2542,plain,
( ~ v1_xboole_0(k1_xboole_0)
| v3_struct_0(sK3)
| ~ l1_struct_0(sK3)
| ~ spl24_28 ),
inference(superposition,[],[f430,f1461]) ).
fof(f2585,plain,
( v3_struct_0(sK3)
| ~ l1_struct_0(sK3)
| ~ spl24_28 ),
inference(forward_subsumption_resolution,[],[f2542,f438]) ).
fof(f2633,plain,
( ~ l1_struct_0(sK3)
| ~ spl24_28 ),
inference(forward_subsumption_resolution,[],[f2585,f305]) ).
fof(f2648,plain,
( $false
| ~ spl24_28 ),
inference(forward_subsumption_resolution,[],[f2633,f585]) ).
fof(f2649,plain,
~ spl24_28,
inference(avatar_contradiction_clause,[],[f2648]) ).
fof(f2654,plain,
( k2_relat_1(k4_tsp_2(sK2,sK3)) = k9_relat_1(k4_tsp_2(sK2,sK3),u1_struct_0(sK2))
| ~ spl24_25
| ~ spl24_29 ),
inference(forward_demodulation,[],[f1449,f1522]) ).
fof(f3159,plain,
( ! [X0] :
( r1_tarski(k9_relat_1(k4_tsp_2(sK2,sK3),X0),k2_relat_1(k4_tsp_2(sK2,sK3)))
| ~ r1_tarski(X0,u1_struct_0(sK2))
| ~ v1_relat_1(k4_tsp_2(sK2,sK3)) )
| ~ spl24_25
| ~ spl24_29 ),
inference(superposition,[],[f497,f2654]) ).
fof(f3162,plain,
( ! [X0] :
( r1_tarski(k9_relat_1(k4_tsp_2(sK2,sK3),X0),k2_relat_1(k4_tsp_2(sK2,sK3)))
| ~ r1_tarski(X0,u1_struct_0(sK2)) )
| ~ spl24_25
| ~ spl24_29 ),
inference(forward_subsumption_resolution,[],[f3159,f1444]) ).
fof(f3200,plain,
( ! [X0] :
( ~ r1_tarski(X0,u1_struct_0(sK2))
| k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k9_relat_1(k4_tsp_2(sK2,sK3),k10_relat_1(k4_tsp_2(sK2,sK3),k9_relat_1(k4_tsp_2(sK2,sK3),X0)))
| ~ v1_relat_1(k4_tsp_2(sK2,sK3))
| ~ v1_funct_1(k4_tsp_2(sK2,sK3)) )
| ~ spl24_25
| ~ spl24_29 ),
inference(resolution,[],[f3162,f496]) ).
fof(f3234,plain,
( ! [X0] :
( ~ r1_tarski(X0,u1_struct_0(sK2))
| k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k9_relat_1(k4_tsp_2(sK2,sK3),k10_relat_1(k4_tsp_2(sK2,sK3),k9_relat_1(k4_tsp_2(sK2,sK3),X0)))
| ~ v1_funct_1(k4_tsp_2(sK2,sK3)) )
| ~ spl24_25
| ~ spl24_29 ),
inference(forward_subsumption_resolution,[],[f3200,f1444]) ).
fof(f3235,plain,
( ! [X0] :
( ~ r1_tarski(X0,u1_struct_0(sK2))
| k9_relat_1(k4_tsp_2(sK2,sK3),X0) = k9_relat_1(k4_tsp_2(sK2,sK3),k10_relat_1(k4_tsp_2(sK2,sK3),k9_relat_1(k4_tsp_2(sK2,sK3),X0))) )
| ~ spl24_25
| ~ spl24_27
| ~ spl24_29 ),
inference(forward_subsumption_resolution,[],[f3234,f1456]) ).
fof(f3484,plain,
( k9_relat_1(k4_tsp_2(sK2,sK3),sK4) = k9_relat_1(k4_tsp_2(sK2,sK3),k10_relat_1(k4_tsp_2(sK2,sK3),k9_relat_1(k4_tsp_2(sK2,sK3),sK4)))
| ~ spl24_25
| ~ spl24_27
| ~ spl24_29 ),
inference(resolution,[],[f3235,f598]) ).
fof(f3504,plain,
( k9_relat_1(k4_tsp_2(sK2,sK3),k3_tex_4(sK2,sK4)) = k9_relat_1(k4_tsp_2(sK2,sK3),sK4)
| ~ spl24_25
| ~ spl24_26
| ~ spl24_27
| ~ spl24_29 ),
inference(forward_demodulation,[],[f3484,f1938]) ).
fof(f3514,plain,
( $false
| ~ spl24_25
| ~ spl24_26
| ~ spl24_27
| ~ spl24_29 ),
inference(forward_subsumption_resolution,[],[f3504,f1568]) ).
fof(f3515,plain,
( ~ spl24_25
| ~ spl24_26
| ~ spl24_27
| ~ spl24_29 ),
inference(avatar_contradiction_clause,[],[f3514]) ).
cnf(s19,plain,
( spl24_25
| ~ spl24_26
| ~ spl24_27
| spl24_28 ),
inference(sat_conversion,[],[f1462]) ).
cnf(s20,plain,
spl24_26,
inference(sat_conversion,[],[f1470]) ).
cnf(s21,plain,
spl24_27,
inference(sat_conversion,[],[f1482]) ).
cnf(s22,plain,
( ~ spl24_26
| ~ spl24_27
| spl24_29 ),
inference(sat_conversion,[],[f1523]) ).
cnf(s80,plain,
~ spl24_28,
inference(sat_conversion,[],[f2649]) ).
cnf(s133,plain,
( ~ spl24_25
| ~ spl24_26
| ~ spl24_27
| ~ spl24_29 ),
inference(sat_conversion,[],[f3515]) ).
cnf(s134,plain,
spl24_29,
inference(rat,[],[s22,s21,s20]) ).
cnf(s135,plain,
~ spl24_25,
inference(rat,[],[s133,s20,s21,s134]) ).
cnf(s136,plain,
$false,
inference(rat,[],[s19,s80,s21,s20,s135]) ).
fof(f3518,plain,
$false,
inference(avatar_sat_refutation,[],[s136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP037+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 % Computer : n015.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 19:02:48 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.32 Running first-order model finding
% 0.26/0.32 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.48 % (2909545)Will run a generic schedule for satisfiability detection.
% 0.51/0.48 % (2909554)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=218192802:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.51/0.48 % (2909551)% WARNING: option uhcvi not known.
% 0.51/0.48 % (2909553)dis+10_1_sil=32000:sp=arity:random_seed=284866318:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.51/0.48 % (2909550)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3109168637_2999 on theBenchmark for (2999ds/0Mi)
% 0.51/0.48 % (2909552)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2992510859:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.51/0.48 % (2909551)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3826768188:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.51/0.48 % (2909555)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2451745477:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.51/0.48 % (2909556)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2174977325:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.51/0.48 % TRYING [1]
% 0.51/0.48 % TRYING [2]
% 0.51/0.48 % TRYING [3]
% 0.51/0.48 % (2909554)Instruction limit reached!
% 0.51/0.48 % (2909554)------------------------------
% 0.51/0.48 % (2909554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.48 % (2909554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.48 % (2909554)CaDiCaL version: 2.1.3
% 0.51/0.48 % (2909554)Termination reason: Instruction limit
% 0.51/0.48 % (2909554)Termination phase: Saturation
% 0.51/0.48 % (2909554)Time elapsed: 0.062 s
% 0.51/0.48 % (2909554)Peak memory usage: 13 MB
% 0.51/0.48 % (2909554)Instructions burned: 117 (million)
% 0.51/0.48 % TRYING [4]
% 0.51/0.48 % (2909564)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3194702153:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.51/0.48 % TRYING [1]
% 0.51/0.48 % TRYING [2]
% 0.51/0.48 % TRYING [3]
% 0.51/0.48 % TRYING [4]
% 0.51/0.48 % (2909553) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2909545-2909553"...
% 0.51/0.48 % (2909553)...printing done.
% 0.51/0.48 % (2909553)Refutation found. Thanks to Tanya!
% 0.51/0.48 % SZS status Theorem for theBenchmark
% 0.51/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.51/0.48 % (2909553)------------------------------
% 0.51/0.48 % (2909553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.48 % (2909553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.48 % (2909553)CaDiCaL version: 2.1.3
% 0.51/0.48 % (2909553)Termination reason: Refutation
% 0.51/0.48 % (2909553)Time elapsed: 0.109 s
% 0.51/0.48 % (2909553)Peak memory usage: 14 MB
% 0.51/0.48 % (2909553)Instructions burned: 109 (million)
% 0.51/0.48 % (2909545)Success in time 0.152 s
% 0.51/0.48 % Vampire exiting
%------------------------------------------------------------------------------