%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP622+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 : Fri Sep 25 01:34:53 PM UTC 2026
% Result : Theorem 8.62s 1.74s
% Output : CNFRefutation 8.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 118 ( 25 unt; 3 def)
% Number of atoms : 430 ( 24 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 445 ( 181 ~; 195 |; 49 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 4 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 225 ( 0 sgn 221 !; 4 ?; 110 :)
% 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,[status(cth)],[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] :
( 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(ennf_transformation,[],[f2]) ).
fof(f78,plain,
? [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(flattening,[],[f77]) ).
fof(f82,plain,
! [X0] :
( ~ v1_fraenkel(X0)
| ! [X1] :
( ~ m1_subset_1(X1,X0)
| ( v1_funct_1(X1)
& v1_relat_1(X1) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f95,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f99,plain,
! [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)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f100,plain,
! [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)) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f103,plain,
! [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) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f104,plain,
! [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) ) ) ),
inference(flattening,[],[f103]) ).
fof(f112,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f113,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f112]) ).
fof(f118,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| k1_fraenkel(X0,X1) = k1_funct_2(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
! [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)) ),
inference(ennf_transformation,[],[f62]) ).
fof(f122,plain,
! [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)) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f132,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0)
& ~ r1_tarski(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f78]) ).
fof(f133,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f134,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ( r2_hidden(sK1(X0,X1),X0)
& ~ r2_hidden(sK1(X0,X1),X1) )
| r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f134]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ( ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2) )
& ( ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f160,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f132]) ).
fof(f161,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f132]) ).
fof(f162,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f132]) ).
fof(f163,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f132]) ).
fof(f164,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f132]) ).
fof(f165,plain,
~ r1_tarski(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),
inference(cnf_transformation,[],[f132]) ).
fof(f168,plain,
! [X0,X1] :
( ~ v1_fraenkel(X0)
| ~ m1_subset_1(X1,X0)
| v1_funct_1(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f185,plain,
! [X0,X1] :
( r2_hidden(sK1(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f186,plain,
! [X0,X1] :
( ~ r2_hidden(sK1(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f190,plain,
! [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)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f191,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_fraenkel(X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f194,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_2(X3,X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_1(X3) ),
inference(cnf_transformation,[],[f104]) ).
fof(f212,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f252,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| k1_fraenkel(X0,X1) = k1_funct_2(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f254,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
fof(f258,plain,
! [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)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f259,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_49,negated_conjecture,
~ r1_tarski(k4_autgroup(sK0),k1_fraenkel(u1_struct_0(sK0),u1_struct_0(sK0))),
inference(cnf_transformation,[],[f165]) ).
tcf(c_50,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f164]) ).
tcf(c_51,negated_conjecture,
v1_group_1(sK0),
inference(cnf_transformation,[],[f163]) ).
tcf(c_52,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f162]) ).
tcf(c_53,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f161]) ).
tcf(c_54,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| ~ v1_fraenkel(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_71,plain,
! [X0: $i] :
( v3_struct_0(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) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_72,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_fraenkel(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_1(X0)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_2(X0,X1,X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_relset_1(X0,X1,X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_93,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| ( k1_fraenkel(X0,X1) = k1_funct_2(X0,X1) ) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_fraenkel(X3,X1,X2,X0)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k1_funct_2(X1,X1))
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X0,X1,X1)
| ~ v1_funct_2(X0,X1,X1) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_198,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_217,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_fraenkel(X0,X1,X2)
| v1_fraenkel(X0) ),
inference(prop_impl_just,[status(thm)],[c_74]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_fraenkel(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_233]) ).
tcf(c_1134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_funct_1(X4)
| ~ m1_subset_1(X4,X1)
| ~ m1_fraenkel(X0,X2,X3)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_234,c_58]) ).
tcf(c_1135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_funct_1(X3)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_1134]) ).
tcf(c_1173,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_71]) ).
tcf(c_1174,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_1173]) ).
tcf(c_1175,plain,
m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_1174,c_54,c_53,c_52,c_51,c_50,c_198]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v1_xboole_0(u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_217,c_93]) ).
tcf(c_1268,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1267]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( v1_xboole_0(X5)
| v1_xboole_0(X4)
| m2_relset_1(X0,X2,X4)
| ~ m1_subset_1(X1,X7)
| ~ m1_fraenkel(X7,X3,X5)
| ~ m1_fraenkel(X6,X2,X4)
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_134]) ).
tcf(c_1568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_relset_1(X3,X1,X2)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_1567]) ).
tcf(c_1582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( v1_xboole_0(X5)
| v1_xboole_0(X4)
| v1_funct_2(X0,X2,X4)
| ~ m1_subset_1(X1,X7)
| ~ m1_fraenkel(X7,X3,X5)
| ~ m1_fraenkel(X6,X2,X4)
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_134]) ).
tcf(c_1583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_2(X3,X1,X2)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_1582]) ).
tcf(c_1597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( v1_xboole_0(X5)
| v1_xboole_0(X4)
| v1_funct_1(X0)
| ~ m1_subset_1(X1,X7)
| ~ m1_fraenkel(X7,X3,X5)
| ~ m1_fraenkel(X6,X2,X4)
| ( X6 != X7 )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_134]) ).
tcf(c_1598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| v1_funct_1(X3)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_1597]) ).
tcf(c_1599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ m1_fraenkel(X0,X1,X2)
| ~ m1_subset_1(X3,X0)
| v1_funct_1(X3) ),
inference(global_subsumption_just,[status(thm)],[c_1598,c_1135]) ).
tcf(c_1600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_funct_1(X3)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_1599]) ).
tcf(c_17182,definition,
iPr_def_10 = k4_autgroup(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_17183,definition,
iPr_def_11 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_17184,definition,
iPr_def_12 = k1_fraenkel(iPr_def_11,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_17185,plain,
m1_fraenkel(iPr_def_10,iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_1175,c_17183,c_17182]) ).
tcf(c_17186,negated_conjecture,
l1_group_1(sK0),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_17188,negated_conjecture,
~ v3_struct_0(sK0),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_17189,negated_conjecture,
~ r1_tarski(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_49,c_17184]) ).
tcf(c_18777,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| m1_subset_1(sK1(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_66,c_140]) ).
tcf(c_19452,plain,
( v3_struct_0(sK0)
| ~ v1_xboole_0(iPr_def_11)
| ~ l1_group_1(sK0) ),
inference(superposition,[status(thm)],[c_17183,c_1268]) ).
tcf(c_19453,plain,
~ v1_xboole_0(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_19452,c_17188,c_17186]) ).
tcf(c_19460,plain,
! [X0: $i] : k1_fraenkel(X0,iPr_def_11) = k1_funct_2(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_133,c_19453]) ).
tcf(c_19461,plain,
k1_funct_2(iPr_def_11,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_17184,c_19460]) ).
tcf(c_19469,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_12)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X0,iPr_def_11,iPr_def_11)
| ~ v1_funct_2(X0,iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_19461,c_139]) ).
tcf(c_20934,plain,
! [X0: $i] :
( v1_funct_1(X0)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_17185,c_1600]) ).
tcf(c_24734,plain,
! [X0: $i] :
( v1_xboole_0(iPr_def_11)
| m2_relset_1(X0,iPr_def_11,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_17185,c_1568]) ).
tcf(c_24774,plain,
! [X0: $i] :
( m2_relset_1(X0,iPr_def_11,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24734,c_19453]) ).
tcf(c_34845,plain,
! [X0: $i] :
( v1_xboole_0(iPr_def_11)
| v1_funct_2(X0,iPr_def_11,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_17185,c_1583]) ).
tcf(c_34888,plain,
! [X0: $i] :
( v1_funct_2(X0,iPr_def_11,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34845,c_19453]) ).
tcf(c_35762,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_12)
| ~ v1_funct_1(X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m2_relset_1(X0,iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_34888,c_19469]) ).
tcf(c_36571,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_35762,c_20934,c_24774,c_35762]) ).
tcf(c_36580,plain,
! [X0: $i] :
( r1_tarski(iPr_def_10,X0)
| r2_hidden(sK1(iPr_def_10,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_18777,c_36571]) ).
tcf(c_36751,plain,
r1_tarski(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_36580,c_65]) ).
tcf(c_36752,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_36751,c_17189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP622+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 15:16:30 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 8.62/1.74 % SZS status Started for theBenchmark.p
% 8.62/1.74 % SZS status Theorem for theBenchmark.p
% 8.62/1.74
% 8.62/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.62/1.74
% 8.62/1.74 % ------ iProver source info
% 8.62/1.74
% 8.62/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 8.62/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.62/1.74 % git: non_committed_changes: false
% 8.62/1.74
% 8.62/1.74 % ------ Parsing...
% 8.62/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.62/1.74
% 8.62/1.74 % ------ 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 %
% 8.62/1.74
% 8.62/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.62/1.74
% 8.62/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.62/1.74 % ------ Proving...
% 8.62/1.74 % ------ Problem Properties
% 8.62/1.74
% 8.62/1.74 %
% 8.62/1.74 % clauses 90
% 8.62/1.74 % conjectures 4
% 8.62/1.74 % EPR 44
% 8.62/1.74 % Horn 77
% 8.62/1.74 % unary 43
% 8.62/1.74 % binary 24
% 8.62/1.74 % lits 173
% 8.62/1.74 % lits eq 11
% 8.62/1.74 % fd_pure 0
% 8.62/1.74 % fd_pseudo 0
% 8.62/1.74 % fd_cond 1
% 8.62/1.74 % fd_pseudo_cond 3
% 8.62/1.74 % AC symbols 0
% 8.62/1.74
% 8.62/1.74 % ------ Schedule dynamic 5 is on
% 8.62/1.74
% 8.62/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.62/1.74
% 8.62/1.74
% 8.62/1.74 % ------
% 8.62/1.74 % Current options:
% 8.62/1.74 % ------
% 8.62/1.74
% 8.62/1.74
% 8.62/1.74 %
% 8.62/1.74
% 8.62/1.74 % ------ Proving...
% 8.62/1.74 %
% 8.62/1.74
% 8.62/1.74 % SZS status Theorem for theBenchmark.p
% 8.62/1.74
% 8.62/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.62/1.74
% 8.62/1.74
%------------------------------------------------------------------------------