TSTP Solution File: GRP639+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRP639+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:23:12 EDT 2024
% Result : Theorem 3.89s 1.13s
% Output : CNFRefutation 4.23s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_latsubgr) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f6,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(f9,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ! [X2] :
( ( m1_group_2(X2,X0)
& v1_group_1(X2) )
=> ( k5_group_4(X0,X1) = X2
<=> ( ! [X3] :
( ( m1_group_2(X3,X0)
& v1_group_1(X3) )
=> ( r1_tarski(X1,u1_struct_0(X3))
=> m1_group_2(X2,X3) ) )
& r1_tarski(X1,u1_struct_0(X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_4) ).
fof(f15,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( m1_group_2(k5_group_4(X0,X1),X0)
& v1_group_1(k5_group_4(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_group_4) ).
fof(f22,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(f44,axiom,
! [X0,X1,X2,X3] :
( ( m1_relset_1(X2,X0,X1)
& v1_funct_2(X2,X0,X1)
& v1_funct_1(X2) )
=> k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(f45,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(f47,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(f57,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2) )
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f58,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2) )
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) ),
inference(flattening,[],[f57]) ).
fof(f64,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k5_group_4(X0,X1) = X2
<=> ( ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3) )
& r1_tarski(X1,u1_struct_0(X2)) ) )
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k5_group_4(X0,X1) = X2
<=> ( ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3) )
& r1_tarski(X1,u1_struct_0(X2)) ) )
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f69]) ).
fof(f75,plain,
! [X0,X1] :
( ( m1_group_2(k5_group_4(X0,X1),X0)
& v1_group_1(k5_group_4(X0,X1)) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
! [X0,X1] :
( ( m1_group_2(k5_group_4(X0,X1),X0)
& v1_group_1(k5_group_4(X0,X1)) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f75]) ).
fof(f80,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,[],[f22]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2) ),
inference(flattening,[],[f93]) ).
fof(f95,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,[],[f47]) ).
fof(f96,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,[],[f95]) ).
fof(f106,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& v1_funct_1(X2) )
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(sK0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(sK0))) )
& m2_relset_1(X2,u1_struct_0(sK0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(sK0),u1_struct_0(X1))
& v1_funct_1(X2) )
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(sK0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(sK0))) )
& m2_relset_1(X2,u1_struct_0(sK0),u1_struct_0(X1))
& v1_funct_2(X2,u1_struct_0(sK0),u1_struct_0(X1))
& v1_funct_1(X2) )
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),X2,X3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),X2,u1_struct_0(k5_group_4(sK0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(sK0))) )
& m2_relset_1(X2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_2(X2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_1(X2) )
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),X2,X3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),X2,u1_struct_0(k5_group_4(sK0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(sK0))) )
& m2_relset_1(X2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_2(X2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_1(X2) )
=> ( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(sK0))) )
& m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_1(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(sK0))) )
=> ( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3))))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3))))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
& m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& v1_funct_1(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1)
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f58,f109,f108,f107,f106]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( k5_group_4(X0,X1) = X2
| ? [X3] :
( ~ m1_group_2(X2,X3)
& r1_tarski(X1,u1_struct_0(X3))
& m1_group_2(X3,X0)
& v1_group_1(X3) )
| ~ r1_tarski(X1,u1_struct_0(X2)) )
& ( ( ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3) )
& r1_tarski(X1,u1_struct_0(X2)) )
| k5_group_4(X0,X1) != X2 ) )
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(nnf_transformation,[],[f70]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( k5_group_4(X0,X1) = X2
| ? [X3] :
( ~ m1_group_2(X2,X3)
& r1_tarski(X1,u1_struct_0(X3))
& m1_group_2(X3,X0)
& v1_group_1(X3) )
| ~ r1_tarski(X1,u1_struct_0(X2)) )
& ( ( ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3) )
& r1_tarski(X1,u1_struct_0(X2)) )
| k5_group_4(X0,X1) != X2 ) )
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( k5_group_4(X0,X1) = X2
| ? [X3] :
( ~ m1_group_2(X2,X3)
& r1_tarski(X1,u1_struct_0(X3))
& m1_group_2(X3,X0)
& v1_group_1(X3) )
| ~ r1_tarski(X1,u1_struct_0(X2)) )
& ( ( ! [X4] :
( m1_group_2(X2,X4)
| ~ r1_tarski(X1,u1_struct_0(X4))
| ~ m1_group_2(X4,X0)
| ~ v1_group_1(X4) )
& r1_tarski(X1,u1_struct_0(X2)) )
| k5_group_4(X0,X1) != X2 ) )
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(rectify,[],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ m1_group_2(X2,X3)
& r1_tarski(X1,u1_struct_0(X3))
& m1_group_2(X3,X0)
& v1_group_1(X3) )
=> ( ~ m1_group_2(X2,sK4(X0,X1,X2))
& r1_tarski(X1,u1_struct_0(sK4(X0,X1,X2)))
& m1_group_2(sK4(X0,X1,X2),X0)
& v1_group_1(sK4(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( k5_group_4(X0,X1) = X2
| ( ~ m1_group_2(X2,sK4(X0,X1,X2))
& r1_tarski(X1,u1_struct_0(sK4(X0,X1,X2)))
& m1_group_2(sK4(X0,X1,X2),X0)
& v1_group_1(sK4(X0,X1,X2)) )
| ~ r1_tarski(X1,u1_struct_0(X2)) )
& ( ( ! [X4] :
( m1_group_2(X2,X4)
| ~ r1_tarski(X1,u1_struct_0(X4))
| ~ m1_group_2(X4,X0)
| ~ v1_group_1(X4) )
& r1_tarski(X1,u1_struct_0(X2)) )
| k5_group_4(X0,X1) != X2 ) )
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f113,f114]) ).
fof(f144,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,[],[f45]) ).
fof(f146,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f110]) ).
fof(f147,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f110]) ).
fof(f148,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f110]) ).
fof(f149,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f110]) ).
fof(f154,plain,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f110]) ).
fof(f155,plain,
v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f110]) ).
fof(f156,plain,
m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f110]) ).
fof(f157,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f110]) ).
fof(f158,plain,
~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(cnf_transformation,[],[f110]) ).
fof(f163,plain,
! [X2,X0,X1] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f171,plain,
! [X2,X0,X1] :
( r1_tarski(X1,u1_struct_0(X2))
| k5_group_4(X0,X1) != X2
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f180,plain,
! [X0,X1] :
( v1_group_1(k5_group_4(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f181,plain,
! [X0,X1] :
( m1_group_2(k5_group_4(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f186,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,[],[f80]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f220,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f221,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f223,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,[],[f96]) ).
fof(f234,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ v1_group_1(k5_group_4(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(equality_resolution,[],[f171]) ).
cnf(c_49,negated_conjecture,
~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(cnf_transformation,[],[f158]) ).
cnf(c_50,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f157]) ).
cnf(c_51,negated_conjecture,
m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f156]) ).
cnf(c_52,negated_conjecture,
v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f155]) ).
cnf(c_53,negated_conjecture,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f154]) ).
cnf(c_58,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f149]) ).
cnf(c_59,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f148]) ).
cnf(c_60,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
cnf(c_61,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f146]) ).
cnf(c_65,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| v1_relat_1(X0) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_74,plain,
( ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_group_1(k5_group_4(X0,X1))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f234]) ).
cnf(c_78,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| m1_group_2(k5_group_4(X1,X0),X1)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_79,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v1_group_1(k5_group_4(X1,X0))
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f180]) ).
cnf(c_84,plain,
( ~ m2_relset_1(X0,X1,X2)
| m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_117,plain,
( ~ v1_funct_2(X0,X1,X2)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_1(X0)
| k2_funct_2(X1,X2,X0,X3) = k9_relat_1(X0,X3) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_118,plain,
( ~ m1_relset_1(X0,X1,X2)
| m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f221]) ).
cnf(c_119,plain,
( ~ m2_relset_1(X0,X1,X2)
| m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f220]) ).
cnf(c_121,plain,
( ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2)
| r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_185,plain,
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_119]) ).
cnf(c_186,plain,
( ~ m2_relset_1(X0,X1,X2)
| m1_relset_1(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_185]) ).
cnf(c_209,plain,
( ~ m1_relset_1(X0,X1,X2)
| m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_118,c_84]) ).
cnf(c_696,plain,
( ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_74,c_79]) ).
cnf(c_712,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| r1_tarski(X0,u1_struct_0(k5_group_4(X1,X0)))
| v3_struct_0(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_696,c_78]) ).
cnf(c_1228,plain,
( u1_struct_0(sK0) != X0
| u1_struct_0(sK1) != X1
| X2 != sK2
| m1_relset_1(X2,X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_51,c_186]) ).
cnf(c_1229,plain,
m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(unflattening,[status(thm)],[c_1228]) ).
cnf(c_1390,plain,
( u1_struct_0(sK0) != X0
| u1_struct_0(sK1) != X1
| X2 != sK2
| ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(resolution_lifted,[status(thm)],[c_52,c_117]) ).
cnf(c_1391,plain,
( ~ m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
| ~ v1_funct_1(sK2)
| k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0) ),
inference(unflattening,[status(thm)],[c_1390]) ).
cnf(c_1393,plain,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0),
inference(global_subsumption_just,[status(thm)],[c_1391,c_53,c_1229,c_1391]) ).
cnf(c_2378,plain,
( X0 != sK0
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| v3_struct_0(X0) ),
inference(resolution_lifted,[status(thm)],[c_59,c_712]) ).
cnf(c_2379,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0)))
| v3_struct_0(sK0) ),
inference(unflattening,[status(thm)],[c_2378]) ).
cnf(c_2381,plain,
( r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_2379,c_60,c_58,c_61,c_2379]) ).
cnf(c_2382,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0))) ),
inference(renaming,[status(thm)],[c_2381]) ).
cnf(c_2605,plain,
u1_struct_0(sK0) = sP2_iProver_def,
definition ).
cnf(c_2606,plain,
k1_zfmisc_1(sP2_iProver_def) = sP3_iProver_def,
definition ).
cnf(c_2607,plain,
u1_struct_0(sK1) = sP4_iProver_def,
definition ).
cnf(c_2608,plain,
k2_funct_2(sP2_iProver_def,sP4_iProver_def,sK2,sK3) = sP5_iProver_def,
definition ).
cnf(c_2609,plain,
k5_group_4(sK0,sK3) = sP6_iProver_def,
definition ).
cnf(c_2610,plain,
u1_struct_0(sP6_iProver_def) = sP7_iProver_def,
definition ).
cnf(c_2611,plain,
k2_funct_2(sP2_iProver_def,sP4_iProver_def,sK2,sP7_iProver_def) = sP8_iProver_def,
definition ).
cnf(c_2618,negated_conjecture,
m1_subset_1(sK3,sP3_iProver_def),
inference(demodulation,[status(thm)],[c_50,c_2605,c_2606]) ).
cnf(c_2619,negated_conjecture,
~ r1_tarski(sP5_iProver_def,sP8_iProver_def),
inference(demodulation,[status(thm)],[c_49,c_2609,c_2610,c_2611,c_2607,c_2608]) ).
cnf(c_4477,plain,
m1_relset_1(sK2,sP2_iProver_def,sP4_iProver_def),
inference(light_normalisation,[status(thm)],[c_1229,c_2605,c_2607]) ).
cnf(c_4507,plain,
k2_funct_2(sP2_iProver_def,sP4_iProver_def,sK2,X0) = k9_relat_1(sK2,X0),
inference(light_normalisation,[status(thm)],[c_1393,c_2605,c_2607]) ).
cnf(c_4521,plain,
( ~ m1_subset_1(X0,sP3_iProver_def)
| r1_tarski(X0,u1_struct_0(k5_group_4(sK0,X0))) ),
inference(light_normalisation,[status(thm)],[c_2382,c_2605,c_2606]) ).
cnf(c_4736,plain,
( ~ m1_subset_1(sK3,sP3_iProver_def)
| r1_tarski(sK3,u1_struct_0(sP6_iProver_def)) ),
inference(superposition,[status(thm)],[c_2609,c_4521]) ).
cnf(c_4741,plain,
( ~ m1_subset_1(sK3,sP3_iProver_def)
| r1_tarski(sK3,sP7_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_4736,c_2610]) ).
cnf(c_4742,plain,
r1_tarski(sK3,sP7_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_4741,c_2618]) ).
cnf(c_5031,plain,
k9_relat_1(sK2,sK3) = sP5_iProver_def,
inference(demodulation,[status(thm)],[c_2608,c_4507]) ).
cnf(c_5171,plain,
k9_relat_1(sK2,sP7_iProver_def) = sP8_iProver_def,
inference(demodulation,[status(thm)],[c_2611,c_4507]) ).
cnf(c_5332,plain,
( ~ m1_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(superposition,[status(thm)],[c_209,c_65]) ).
cnf(c_5711,plain,
( ~ r1_tarski(sK3,X0)
| ~ v1_relat_1(sK2)
| r1_tarski(sP5_iProver_def,k9_relat_1(sK2,X0)) ),
inference(superposition,[status(thm)],[c_5031,c_121]) ).
cnf(c_6200,plain,
v1_relat_1(sK2),
inference(superposition,[status(thm)],[c_4477,c_5332]) ).
cnf(c_7947,plain,
( ~ r1_tarski(sK3,X0)
| r1_tarski(sP5_iProver_def,k9_relat_1(sK2,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_5711,c_5711,c_6200]) ).
cnf(c_7955,plain,
( ~ r1_tarski(sK3,sP7_iProver_def)
| r1_tarski(sP5_iProver_def,sP8_iProver_def) ),
inference(superposition,[status(thm)],[c_5171,c_7947]) ).
cnf(c_7958,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7955,c_2619,c_4742]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : GRP639+1 : TPTP v8.1.2. Released v3.4.0.
% 0.05/0.11 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 00:04:36 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.89/1.13 % SZS status Started for theBenchmark.p
% 3.89/1.13 % SZS status Theorem for theBenchmark.p
% 3.89/1.13
% 3.89/1.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.89/1.13
% 3.89/1.13 ------ iProver source info
% 3.89/1.13
% 3.89/1.13 git: date: 2024-05-02 19:28:25 +0000
% 3.89/1.13 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.89/1.13 git: non_committed_changes: false
% 3.89/1.13
% 3.89/1.13 ------ Parsing...
% 3.89/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.89/1.13
% 3.89/1.13 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e
% 3.89/1.13
% 3.89/1.13 ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.89/1.13
% 3.89/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.89/1.13 ------ Proving...
% 3.89/1.13 ------ Problem Properties
% 3.89/1.13
% 3.89/1.13
% 3.89/1.13 clauses 102
% 3.89/1.13 conjectures 8
% 3.89/1.13 EPR 25
% 3.89/1.13 Horn 86
% 3.89/1.13 unary 41
% 3.89/1.13 binary 25
% 3.89/1.13 lits 237
% 3.89/1.13 lits eq 41
% 3.89/1.13 fd_pure 0
% 3.89/1.13 fd_pseudo 0
% 3.89/1.13 fd_cond 3
% 3.89/1.13 fd_pseudo_cond 13
% 3.89/1.13 AC symbols 0
% 3.89/1.13
% 3.89/1.13 ------ Schedule dynamic 5 is on
% 3.89/1.13
% 3.89/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.89/1.13
% 3.89/1.13
% 3.89/1.13 ------
% 3.89/1.13 Current options:
% 3.89/1.13 ------
% 3.89/1.13
% 3.89/1.13
% 3.89/1.13
% 3.89/1.13
% 3.89/1.13 ------ Proving...
% 3.89/1.13
% 3.89/1.13
% 3.89/1.13 % SZS status Theorem for theBenchmark.p
% 3.89/1.13
% 3.89/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.23/1.13
% 4.23/1.14
%------------------------------------------------------------------------------