TSTP Solution File: GRP622+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRP622+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 : Thu Aug 31 01:00:47 EDT 2023
% Result : Theorem 9.74s 2.16s
% Output : CNFRefutation 9.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 130 ( 15 unt; 0 def)
% Number of atoms : 446 ( 39 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 536 ( 220 ~; 233 |; 61 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 266 ( 21 sgn; 113 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> r1_tarski(k4_autgroup(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> r1_tarski(k4_autgroup(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ),
inference(negated_conjecture,[],[f1]) ).
fof(f5,axiom,
! [X0] :
( v1_fraenkel(X0)
=> ! [X1] :
( m1_subset_1(X1,X0)
=> ( v1_funct_1(X1)
& v1_relat_1(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_fraenkel) ).
fof(f13,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f20,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(f21,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f23,axiom,
! [X0,X1,X2] :
( m1_fraenkel(X2,X0,X1)
=> ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( m1_fraenkel(X2,X0,X1)
& ~ v1_xboole_0(X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
=> ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(f40,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f58,axiom,
! [X0,X1] :
( ~ v1_xboole_0(X1)
=> k1_fraenkel(X0,X1) = k1_funct_2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_fraenkel) ).
fof(f59,axiom,
! [X0,X1,X2] :
( ( m1_fraenkel(X2,X0,X1)
& ~ v1_xboole_0(X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f62,axiom,
! [X0,X1] :
( ( m2_relset_1(X1,X0,X0)
& v1_funct_2(X1,X0,X0)
& v1_funct_1(X1) )
=> r2_hidden(X1,k1_funct_2(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).
fof(f63,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f77,plain,
? [X0] :
( ~ r1_tarski(k4_autgroup(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f78,plain,
? [X0] :
( ~ r1_tarski(k4_autgroup(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) ),
inference(flattening,[],[f77]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( v1_funct_1(X1)
& v1_relat_1(X1) )
| ~ m1_subset_1(X1,X0) )
| ~ v1_fraenkel(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f95,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f99,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f100,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) )
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( m2_relset_1(X3,X0,X1)
& v1_funct_2(X3,X0,X1)
& v1_funct_1(X3) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f103]) ).
fof(f112,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f113,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f112]) ).
fof(f118,plain,
! [X0,X1] :
( k1_fraenkel(X0,X1) = k1_funct_2(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( r2_hidden(X1,k1_funct_2(X0,X0))
| ~ m2_relset_1(X1,X0,X0)
| ~ v1_funct_2(X1,X0,X0)
| ~ v1_funct_1(X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f122,plain,
! [X0,X1] :
( r2_hidden(X1,k1_funct_2(X0,X0))
| ~ m2_relset_1(X1,X0,X0)
| ~ v1_funct_2(X1,X0,X0)
| ~ v1_funct_1(X1) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f132,plain,
( ? [X0] :
( ~ r1_tarski(k4_autgroup(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
& l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ( ~ r1_tarski(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
( ~ r1_tarski(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f78,f132]) ).
fof(f134,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f135,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) )
=> ( ~ r2_hidden(sK1(X0,X1),X1)
& r2_hidden(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK1(X0,X1),X1)
& r2_hidden(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f135,f136]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( m2_fraenkel(X3,X0,X1,X2)
| ~ m1_subset_1(X3,X2) )
& ( m1_subset_1(X3,X2)
| ~ m2_fraenkel(X3,X0,X1,X2) ) )
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(nnf_transformation,[],[f120]) ).
fof(f183,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f184,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f185,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f186,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f187,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f188,plain,
~ r1_tarski(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),
inference(cnf_transformation,[],[f133]) ).
fof(f192,plain,
! [X0,X1] :
( v1_funct_1(X1)
| ~ m1_subset_1(X1,X0)
| ~ v1_fraenkel(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f208,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| r2_hidden(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f209,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f213,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f214,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f216,plain,
! [X2,X0,X1] :
( v1_fraenkel(X2)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( v1_funct_1(X3)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f218,plain,
! [X2,X3,X0,X1] :
( v1_funct_2(X3,X0,X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( m2_relset_1(X3,X0,X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f235,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f275,plain,
! [X0,X1] :
( k1_fraenkel(X0,X1) = k1_funct_2(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( m2_fraenkel(X3,X0,X1,X2)
| ~ m1_subset_1(X3,X2)
| ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f281,plain,
! [X0,X1] :
( r2_hidden(X1,k1_funct_2(X0,X0))
| ~ m2_relset_1(X1,X0,X0)
| ~ v1_funct_2(X1,X0,X0)
| ~ v1_funct_1(X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f282,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_49,negated_conjecture,
~ r1_tarski(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),
inference(cnf_transformation,[],[f188]) ).
cnf(c_50,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f187]) ).
cnf(c_51,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f186]) ).
cnf(c_52,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f185]) ).
cnf(c_53,negated_conjecture,
v1_group_1(sK0),
inference(cnf_transformation,[],[f184]) ).
cnf(c_54,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f183]) ).
cnf(c_57,plain,
( ~ m1_subset_1(X0,X1)
| ~ v1_fraenkel(X1)
| v1_funct_1(X0) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_65,plain,
( ~ r2_hidden(sK1(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_66,plain,
( r2_hidden(sK1(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_71,plain,
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_72,plain,
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_73,plain,
( ~ m1_fraenkel(X0,X1,X2)
| v1_fraenkel(X0) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_75,plain,
( ~ m2_fraenkel(X0,X1,X2,X3)
| ~ m1_fraenkel(X3,X1,X2)
| m2_relset_1(X0,X1,X2)
| v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_76,plain,
( ~ m2_fraenkel(X0,X1,X2,X3)
| ~ m1_fraenkel(X3,X1,X2)
| v1_funct_2(X0,X1,X2)
| v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f218]) ).
cnf(c_77,plain,
( ~ m2_fraenkel(X0,X1,X2,X3)
| ~ m1_fraenkel(X3,X1,X2)
| v1_funct_1(X0)
| v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f217]) ).
cnf(c_93,plain,
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f235]) ).
cnf(c_133,plain,
( k1_fraenkel(X0,X1) = k1_funct_2(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f275]) ).
cnf(c_134,plain,
( ~ m1_fraenkel(X0,X1,X2)
| ~ m1_subset_1(X3,X0)
| m2_fraenkel(X3,X1,X2,X0)
| v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f277]) ).
cnf(c_139,plain,
( ~ v1_funct_2(X0,X1,X1)
| ~ m2_relset_1(X0,X1,X1)
| ~ v1_funct_1(X0)
| r2_hidden(X0,k1_funct_2(X1,X1)) ),
inference(cnf_transformation,[],[f281]) ).
cnf(c_140,plain,
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f282]) ).
cnf(c_157,plain,
( ~ l1_group_1(sK0)
| l1_struct_0(sK0) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_178,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ l1_struct_0(sK0)
| v3_struct_0(sK0) ),
inference(instantiation,[status(thm)],[c_93]) ).
cnf(c_198,plain,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v3_struct_0(sK0) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_233,plain,
( v1_fraenkel(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
cnf(c_234,plain,
( ~ m1_fraenkel(X0,X1,X2)
| v1_fraenkel(X0) ),
inference(renaming,[status(thm)],[c_233]) ).
cnf(c_251,plain,
( ~ r2_hidden(sK1(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
cnf(c_255,plain,
( r1_tarski(X0,X1)
| r2_hidden(sK1(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
cnf(c_256,plain,
( r2_hidden(sK1(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(renaming,[status(thm)],[c_255]) ).
cnf(c_842,plain,
( X0 != X1
| ~ m1_fraenkel(X0,X2,X3)
| ~ m1_subset_1(X4,X1)
| v1_funct_1(X4) ),
inference(resolution_lifted,[status(thm)],[c_234,c_57]) ).
cnf(c_843,plain,
( ~ m1_fraenkel(X0,X1,X2)
| ~ m1_subset_1(X3,X0)
| v1_funct_1(X3) ),
inference(unflattening,[status(thm)],[c_842]) ).
cnf(c_1165,plain,
( k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) != X0
| k4_autgroup(sK0) != X1
| r2_hidden(sK1(X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_49,c_256]) ).
cnf(c_1166,plain,
r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0)),
inference(unflattening,[status(thm)],[c_1165]) ).
cnf(c_1170,plain,
( k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) != X0
| k4_autgroup(sK0) != X1
| ~ r2_hidden(sK1(X1,X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_49,c_251]) ).
cnf(c_1171,plain,
~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),
inference(unflattening,[status(thm)],[c_1170]) ).
cnf(c_1275,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| X6 != X7
| ~ m1_fraenkel(X6,X2,X4)
| ~ m1_fraenkel(X7,X3,X5)
| ~ m1_subset_1(X1,X7)
| v1_funct_1(X0)
| v1_xboole_0(X4)
| v1_xboole_0(X5) ),
inference(resolution_lifted,[status(thm)],[c_77,c_134]) ).
cnf(c_1276,plain,
( ~ m1_fraenkel(X0,X1,X2)
| ~ m1_subset_1(X3,X0)
| v1_funct_1(X3)
| v1_xboole_0(X2) ),
inference(unflattening,[status(thm)],[c_1275]) ).
cnf(c_1277,plain,
( v1_funct_1(X3)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_1276,c_843]) ).
cnf(c_1278,plain,
( ~ m1_fraenkel(X0,X1,X2)
| ~ m1_subset_1(X3,X0)
| v1_funct_1(X3) ),
inference(renaming,[status(thm)],[c_1277]) ).
cnf(c_1288,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| X6 != X7
| ~ m1_fraenkel(X6,X2,X4)
| ~ m1_fraenkel(X7,X3,X5)
| ~ m1_subset_1(X1,X7)
| v1_funct_2(X0,X2,X4)
| v1_xboole_0(X4)
| v1_xboole_0(X5) ),
inference(resolution_lifted,[status(thm)],[c_76,c_134]) ).
cnf(c_1289,plain,
( ~ m1_fraenkel(X0,X1,X2)
| ~ m1_subset_1(X3,X0)
| v1_funct_2(X3,X1,X2)
| v1_xboole_0(X2) ),
inference(unflattening,[status(thm)],[c_1288]) ).
cnf(c_1303,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| X6 != X7
| ~ m1_fraenkel(X6,X2,X4)
| ~ m1_fraenkel(X7,X3,X5)
| ~ m1_subset_1(X1,X7)
| m2_relset_1(X0,X2,X4)
| v1_xboole_0(X4)
| v1_xboole_0(X5) ),
inference(resolution_lifted,[status(thm)],[c_75,c_134]) ).
cnf(c_1304,plain,
( ~ m1_fraenkel(X0,X1,X2)
| ~ m1_subset_1(X3,X0)
| m2_relset_1(X3,X1,X2)
| v1_xboole_0(X2) ),
inference(unflattening,[status(thm)],[c_1303]) ).
cnf(c_16383,plain,
( X0 != X1
| X2 != X3
| ~ r2_hidden(X1,X3)
| r2_hidden(X0,X2) ),
theory(equality) ).
cnf(c_17902,plain,
( ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0))
| m1_subset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_18203,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| v1_funct_2(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(instantiation,[status(thm)],[c_1289]) ).
cnf(c_18204,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| m2_relset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(instantiation,[status(thm)],[c_1304]) ).
cnf(c_18205,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| v1_funct_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))) ),
inference(instantiation,[status(thm)],[c_1278]) ).
cnf(c_18211,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| m2_relset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_18204,c_1166,c_17902,c_18204]) ).
cnf(c_18215,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| v1_funct_2(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_18203,c_1166,c_17902,c_18203]) ).
cnf(c_18893,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| v1_funct_2(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(instantiation,[status(thm)],[c_1289]) ).
cnf(c_18894,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| m2_relset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(instantiation,[status(thm)],[c_1304]) ).
cnf(c_18895,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| v1_funct_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))) ),
inference(instantiation,[status(thm)],[c_1278]) ).
cnf(c_18896,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| v1_funct_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))) ),
inference(global_subsumption_just,[status(thm)],[c_18895,c_1166,c_17902,c_18205]) ).
cnf(c_18898,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| m2_relset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_18894,c_18211]) ).
cnf(c_18900,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),X0,X1)
| v1_funct_2(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0,X1)
| v1_xboole_0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_18893,c_18215]) ).
cnf(c_18927,plain,
( X0 != sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))
| X1 != X2
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X2)
| r2_hidden(X0,X1) ),
inference(instantiation,[status(thm)],[c_16383]) ).
cnf(c_19302,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_funct_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))) ),
inference(instantiation,[status(thm)],[c_18896]) ).
cnf(c_19305,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| m2_relset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_18898]) ).
cnf(c_19308,plain,
( ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_funct_2(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_18900]) ).
cnf(c_19402,plain,
( sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))) != sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))
| X0 != X1
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X1)
| r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0) ),
inference(instantiation,[status(thm)],[c_18927]) ).
cnf(c_19403,plain,
( X0 != X1
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X1)
| r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0) ),
inference(equality_resolution_simp,[status(thm)],[c_19402]) ).
cnf(c_21275,plain,
( ~ v1_funct_2(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m2_relset_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v1_funct_1(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))))
| r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k1_funct_2(u1_struct_0(sK0),u1_struct_0(sK0))) ),
inference(instantiation,[status(thm)],[c_139]) ).
cnf(c_21440,plain,
( k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) != X0
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0)
| r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))) ),
inference(instantiation,[status(thm)],[c_19403]) ).
cnf(c_21770,plain,
( X0 != sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))
| X1 != X2
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X2)
| r2_hidden(X0,X1) ),
inference(instantiation,[status(thm)],[c_16383]) ).
cnf(c_22225,plain,
( sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))) != sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)))
| X0 != X1
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X1)
| r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0) ),
inference(instantiation,[status(thm)],[c_21770]) ).
cnf(c_22226,plain,
( X0 != X1
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X1)
| r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0) ),
inference(equality_resolution_simp,[status(thm)],[c_22225]) ).
cnf(c_23649,plain,
( k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) != X0
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0)
| r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))) ),
inference(instantiation,[status(thm)],[c_22226]) ).
cnf(c_23650,plain,
( ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0)
| k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) != X0 ),
inference(global_subsumption_just,[status(thm)],[c_23649,c_1171,c_21440]) ).
cnf(c_23651,plain,
( k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) != X0
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),X0) ),
inference(renaming,[status(thm)],[c_23650]) ).
cnf(c_23819,plain,
( k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) = k1_funct_2(u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_133]) ).
cnf(c_27323,plain,
( k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0)) != k1_funct_2(u1_struct_0(sK0),u1_struct_0(sK0))
| ~ r2_hidden(sK1(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),k1_funct_2(u1_struct_0(sK0),u1_struct_0(sK0))) ),
inference(instantiation,[status(thm)],[c_23651]) ).
cnf(c_27324,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_27323,c_23819,c_21275,c_19308,c_19305,c_19302,c_198,c_178,c_157,c_54,c_50,c_51,c_52,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP622+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.16/0.34 % Computer : n010.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 00:33:19 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.74/2.16 % SZS status Started for theBenchmark.p
% 9.74/2.16 % SZS status Theorem for theBenchmark.p
% 9.74/2.16
% 9.74/2.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.74/2.16
% 9.74/2.16 ------ iProver source info
% 9.74/2.16
% 9.74/2.16 git: date: 2023-05-31 18:12:56 +0000
% 9.74/2.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.74/2.16 git: non_committed_changes: false
% 9.74/2.16 git: last_make_outside_of_git: false
% 9.74/2.16
% 9.74/2.16 ------ Parsing...
% 9.74/2.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.74/2.16
% 9.74/2.16 ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e
% 9.74/2.16
% 9.74/2.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.74/2.16
% 9.74/2.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.74/2.16 ------ Proving...
% 9.74/2.16 ------ Problem Properties
% 9.74/2.16
% 9.74/2.16
% 9.74/2.16 clauses 87
% 9.74/2.16 conjectures 4
% 9.74/2.16 EPR 42
% 9.74/2.16 Horn 74
% 9.74/2.16 unary 40
% 9.74/2.16 binary 24
% 9.74/2.16 lits 170
% 9.74/2.16 lits eq 8
% 9.74/2.16 fd_pure 0
% 9.74/2.16 fd_pseudo 0
% 9.74/2.16 fd_cond 1
% 9.74/2.16 fd_pseudo_cond 3
% 9.74/2.16 AC symbols 0
% 9.74/2.16
% 9.74/2.16 ------ Input Options Time Limit: Unbounded
% 9.74/2.16
% 9.74/2.16
% 9.74/2.16 ------
% 9.74/2.16 Current options:
% 9.74/2.16 ------
% 9.74/2.16
% 9.74/2.16
% 9.74/2.16
% 9.74/2.16
% 9.74/2.16 ------ Proving...
% 9.74/2.16
% 9.74/2.16
% 9.74/2.16 % SZS status Theorem for theBenchmark.p
% 9.74/2.16
% 9.74/2.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.74/2.16
% 9.74/2.17
%------------------------------------------------------------------------------