%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 02:57:28 PM UTC 2026
% Result : Theorem 5.52s 1.77s
% Output : CNFRefutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 94 ( 19 unt; 0 def)
% Number of atoms : 303 ( 99 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 360 ( 151 ~; 148 |; 36 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 170 ( 1 sgn 164 !; 6 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( m2_relset_1(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
& v1_funct_2(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
& v1_funct_1(k5_relset_2(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( m2_relset_1(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
& v1_funct_2(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
& v1_funct_1(k5_relset_2(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> ( ( X1 = k1_xboole_0
=> ( ( v1_funct_2(X2,X0,X1)
<=> X2 = k1_xboole_0 )
| X0 = k1_xboole_0 ) )
& ( ( X1 = k1_xboole_0
=> X0 = k1_xboole_0 )
=> ( v1_funct_2(X2,X0,X1)
<=> X0 = k4_relset_1(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f7,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_relat_1(X2) )
=> ( X2 = k5_relset_2(X0,X1)
<=> ( ! [X3] :
( r1_tarski(X3,X0)
=> k1_funct_1(X2,X3) = k9_relat_1(X1,X3) )
& k1_relat_1(X2) = k1_zfmisc_1(X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relset_2) ).
fof(f15,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ( v1_funct_1(k5_relset_2(X0,X1))
& v1_relat_1(k5_relset_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
fof(f24,axiom,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f26,axiom,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f38,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> k4_relset_1(X0,X1,X2) = k1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f39,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f40,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f41,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( ( r1_tarski(k2_relat_1(X2),X1)
& r1_tarski(k1_relat_1(X2),X0) )
=> m2_relset_1(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> r1_tarski(k2_relat_1(k5_relset_2(X0,X2)),k1_zfmisc_1(k2_relat_1(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relset_2) ).
fof(f51,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f40]) ).
fof(f54,plain,
? [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& ( ~ m2_relset_1(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
| ~ v1_funct_2(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
| ~ v1_funct_1(k5_relset_2(X0,X2)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X2,X0,X1)
| ( ( k1_xboole_0 != X1
| ( v1_funct_2(X2,X0,X1)
<=> X2 = k1_xboole_0 )
| X0 = k1_xboole_0 )
& ( ( X1 = k1_xboole_0
& k1_xboole_0 != X0 )
| ( v1_funct_2(X2,X0,X1)
<=> X0 = k4_relset_1(X0,X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X2,X0,X1)
| ( ( k1_xboole_0 != X1
| ( v1_funct_2(X2,X0,X1)
<=> X2 = k1_xboole_0 )
| X0 = k1_xboole_0 )
& ( ( X1 = k1_xboole_0
& k1_xboole_0 != X0 )
| ( v1_funct_2(X2,X0,X1)
<=> X0 = k4_relset_1(X0,X1,X2) ) ) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ( X2 = k5_relset_2(X0,X1)
<=> ( ! [X3] :
( ~ r1_tarski(X3,X0)
| k1_funct_1(X2,X3) = k9_relat_1(X1,X3) )
& k1_relat_1(X2) = k1_zfmisc_1(X0) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f61,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ( X2 = k5_relset_2(X0,X1)
<=> ( ! [X3] :
( ~ r1_tarski(X3,X0)
| k1_funct_1(X2,X3) = k9_relat_1(X1,X3) )
& k1_relat_1(X2) = k1_zfmisc_1(X0) ) ) ) ),
inference(flattening,[],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ( v1_funct_1(k5_relset_2(X0,X1))
& v1_relat_1(k5_relset_2(X0,X1)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ m1_relset_1(X2,X0,X1)
| k4_relset_1(X0,X1,X2) = k1_relat_1(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(k2_relat_1(X2),X1)
| ~ r1_tarski(k1_relat_1(X2),X0)
| m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(k2_relat_1(X2),X1)
| ~ r1_tarski(k1_relat_1(X2),X0)
| m2_relset_1(X2,X0,X1) ),
inference(flattening,[],[f75]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| r1_tarski(k2_relat_1(k5_relset_2(X0,X2)),k1_zfmisc_1(k2_relat_1(X2))) ),
inference(ennf_transformation,[],[f43]) ).
fof(f87,plain,
( m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
& ( ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_funct_1(k5_relset_2(sK0,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f54]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X2,X0,X1)
| ( ( k1_xboole_0 != X1
| ( ( ~ v1_funct_2(X2,X0,X1)
| X2 = k1_xboole_0 )
& ( k1_xboole_0 != X2
| v1_funct_2(X2,X0,X1) ) )
| X0 = k1_xboole_0 )
& ( ( X1 = k1_xboole_0
& k1_xboole_0 != X0 )
| ( ( ~ v1_funct_2(X2,X0,X1)
| X0 = k4_relset_1(X0,X1,X2) )
& ( k4_relset_1(X0,X1,X2) != X0
| v1_funct_2(X2,X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f89,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ( ( k5_relset_2(X0,X1) != X2
| ( ! [X3] :
( ~ r1_tarski(X3,X0)
| k1_funct_1(X2,X3) = k9_relat_1(X1,X3) )
& k1_relat_1(X2) = k1_zfmisc_1(X0) ) )
& ( ? [X3] :
( r1_tarski(X3,X0)
& k1_funct_1(X2,X3) != k9_relat_1(X1,X3) )
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| X2 = k5_relset_2(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f90,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ( ( k5_relset_2(X0,X1) != X2
| ( ! [X3] :
( ~ r1_tarski(X3,X0)
| k1_funct_1(X2,X3) = k9_relat_1(X1,X3) )
& k1_relat_1(X2) = k1_zfmisc_1(X0) ) )
& ( ? [X3] :
( r1_tarski(X3,X0)
& k1_funct_1(X2,X3) != k9_relat_1(X1,X3) )
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| X2 = k5_relset_2(X0,X1) ) ) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ( ( k5_relset_2(X0,X1) != X2
| ( ! [X4] :
( ~ r1_tarski(X4,X0)
| k1_funct_1(X2,X4) = k9_relat_1(X1,X4) )
& k1_relat_1(X2) = k1_zfmisc_1(X0) ) )
& ( ? [X3] :
( r1_tarski(X3,X0)
& k1_funct_1(X2,X3) != k9_relat_1(X1,X3) )
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| X2 = k5_relset_2(X0,X1) ) ) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ! [X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ( ( k5_relset_2(X0,X1) != X2
| ( ! [X4] :
( ~ r1_tarski(X4,X0)
| k1_funct_1(X2,X4) = k9_relat_1(X1,X4) )
& k1_relat_1(X2) = k1_zfmisc_1(X0) ) )
& ( ( r1_tarski(sK3(X0,X1,X2),X0)
& k1_funct_1(X2,sK3(X0,X1,X2)) != k9_relat_1(X1,sK3(X0,X1,X2)) )
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| X2 = k5_relset_2(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f91]) ).
fof(f102,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,[],[f39]) ).
fof(f104,plain,
m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f87]) ).
fof(f105,plain,
( ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_funct_1(k5_relset_2(sK0,sK2)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k1_xboole_0 = X1
| k4_relset_1(X0,X1,X2) != X0
| v1_funct_2(X2,X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| k5_relset_2(X0,X1) != X2
| k1_zfmisc_1(X0) = k1_relat_1(X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f120,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| v1_funct_1(k5_relset_2(X0,X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f121,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| v1_relat_1(k5_relset_2(X0,X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f128,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f131,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f26]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| k4_relset_1(X0,X1,X2) = k1_relat_1(X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f154,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f51]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(k2_relat_1(X2),X1)
| ~ r1_tarski(k1_relat_1(X2),X0)
| m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| r1_tarski(k2_relat_1(k5_relset_2(X0,X2)),k1_zfmisc_1(k2_relat_1(X2))) ),
inference(cnf_transformation,[],[f78]) ).
fof(f171,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_funct_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(k5_relset_2(X0,X1))
| k1_zfmisc_1(X0) = k1_relat_1(k5_relset_2(X0,X1)) ),
inference(equality_resolution,[],[f116]) ).
tcf(c_49,negated_conjecture,
( ~ v1_funct_1(k5_relset_2(sK0,sK2))
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_50,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f104]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_relat_1(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_funct_2(X2,X0,X1)
| ( X1 = k1_xboole_0 )
| ~ m2_relset_1(X2,X0,X1)
| ( k4_relset_1(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(k5_relset_2(X0,X1)) = k1_zfmisc_1(X0) )
| ~ v1_relat_1(X1)
| ~ v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_funct_1(k5_relset_2(X0,X1)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_73,plain,
! [X0: $i] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f128]) ).
tcf(c_75,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f131]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k4_relset_1(X1,X2,X0) = k1_relat_1(X0) )
| ~ m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_99,plain,
! [X0: $i] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( m2_relset_1(X0,X2,X1)
| ~ v1_relat_1(X0)
| ~ r1_tarski(k1_relat_1(X0),X2)
| ~ r1_tarski(k2_relat_1(X0),X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_tarski(k2_relat_1(k5_relset_2(X1,X0)),k1_zfmisc_1(k2_relat_1(X0)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(k5_relset_2(X1,X0))
| ~ v1_relat_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(k5_relset_2(X0,X1)) = k1_zfmisc_1(X0) )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(k5_relset_2(X0,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_182]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(k5_relset_2(X1,X0)) = k1_zfmisc_1(X1) )
| ~ v1_relat_1(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_415,c_184]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = k1_xboole_0 )
| ~ v1_funct_1(k5_relset_2(sK0,sK2))
| ~ m2_relset_1(X2,X0,X1)
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ( k1_zfmisc_1(sK0) != X0 )
| ( k1_zfmisc_1(k2_relat_1(sK2)) != X1 )
| ( k5_relset_2(sK0,sK2) != X2 )
| ( k4_relset_1(X0,X1,X2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_55]) ).
tcf(c_905,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ~ v1_funct_1(k5_relset_2(sK0,sK2))
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ( k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) != k1_zfmisc_1(sK0) ) ),
inference(unflattening,[status(thm)],[c_904]) ).
tcf(c_1758,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(k5_relset_2(X1,X0)) = k1_zfmisc_1(X1) )
| ~ v1_relat_1(X0) ),
inference(prop_impl_just,[status(thm)],[c_424]) ).
tcf(c_4002,plain,
( v1_funct_1(k5_relset_2(sK0,sK2))
| ~ v1_relat_1(sK2) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_4008,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(sK2)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_4016,plain,
( v1_relat_1(sK2)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_4008]) ).
tcf(c_4221,plain,
( v1_relat_1(k5_relset_2(sK0,sK2))
| ~ v1_relat_1(sK2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_4564,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ( k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) != k1_zfmisc_1(sK0) )
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_905,c_50,c_905,c_4002,c_4016]) ).
tcf(c_4565,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ( k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) != k1_zfmisc_1(sK0) ) ),
inference(renaming,[status(thm)],[c_4564]) ).
tcf(c_5499,plain,
r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2))),
inference(superposition,[status(thm)],[c_50,c_102]) ).
tcf(c_6089,plain,
! [X0: $i] :
( m2_relset_1(k5_relset_2(sK0,sK2),X0,k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_relat_1(k5_relset_2(sK0,sK2))
| ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),X0) ),
inference(superposition,[status(thm)],[c_5499,c_100]) ).
tcf(c_11494,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ( k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) != k1_zfmisc_1(sK0) )
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_905,c_4565]) ).
tcf(c_11495,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ( k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) != k1_zfmisc_1(sK0) ) ),
inference(renaming,[status(thm)],[c_11494]) ).
tcf(c_11521,plain,
v1_relat_1(sK2),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_11618,plain,
! [X0: $i] : k1_relat_1(k5_relset_2(X0,sK2)) = k1_zfmisc_1(X0),
inference(superposition,[status(thm)],[c_11521,c_1758]) ).
tcf(c_11667,plain,
r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2))),
inference(superposition,[status(thm)],[c_50,c_102]) ).
tcf(c_11706,plain,
! [X0: $i] :
( m2_relset_1(k5_relset_2(sK0,sK2),X0,k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_relat_1(k5_relset_2(sK0,sK2))
| ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),X0) ),
inference(superposition,[status(thm)],[c_11667,c_100]) ).
tcf(c_11723,plain,
! [X0: $i] :
( m2_relset_1(k5_relset_2(sK0,sK2),X0,k1_zfmisc_1(k2_relat_1(sK2)))
| ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_11706,c_50,c_4016,c_4221,c_6089]) ).
tcf(c_11725,plain,
! [X0: $i] :
( m1_relset_1(k5_relset_2(sK0,sK2),X0,k1_zfmisc_1(k2_relat_1(sK2)))
| ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),X0) ),
inference(superposition,[status(thm)],[c_11723,c_98]) ).
tcf(c_11789,plain,
! [X0: $i] :
( ( k4_relset_1(X0,k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) = k1_relat_1(k5_relset_2(sK0,sK2)) )
| ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),X0) ),
inference(superposition,[status(thm)],[c_11725,c_96]) ).
tcf(c_12598,plain,
! [X0: $i] :
( ( k4_relset_1(X0,k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) = k1_relat_1(k5_relset_2(sK0,sK2)) )
| ~ r1_tarski(k1_zfmisc_1(sK0),X0) ),
inference(superposition,[status(thm)],[c_11618,c_11789]) ).
tcf(c_12608,plain,
k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) = k1_relat_1(k5_relset_2(sK0,sK2)),
inference(superposition,[status(thm)],[c_99,c_12598]) ).
tcf(c_12629,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ( k1_relat_1(k5_relset_2(sK0,sK2)) != k1_zfmisc_1(sK0) ) ),
inference(superposition,[status(thm)],[c_12608,c_11495]) ).
tcf(c_12669,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) ),
inference(superposition,[status(thm)],[c_11618,c_12629]) ).
tcf(c_12670,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(sK0)) ),
inference(superposition,[status(thm)],[c_11723,c_12669]) ).
tcf(c_13341,plain,
( ( k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0 )
| ~ r1_tarski(k1_zfmisc_1(sK0),k1_zfmisc_1(sK0)) ),
inference(superposition,[status(thm)],[c_11618,c_12670]) ).
tcf(c_13342,plain,
k1_zfmisc_1(k2_relat_1(sK2)) = k1_xboole_0,
inference(superposition,[status(thm)],[c_99,c_13341]) ).
tcf(c_13447,plain,
~ v1_xboole_0(k1_xboole_0),
inference(superposition,[status(thm)],[c_13342,c_73]) ).
tcf(c_13448,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13447,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 14:09:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 5.52/1.77 % SZS status Started for theBenchmark.p
% 5.52/1.77 % SZS status Theorem for theBenchmark.p
% 5.52/1.77
% 5.52/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.52/1.77
% 5.52/1.77 % ------ iProver source info
% 5.52/1.77
% 5.52/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 5.52/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.52/1.77 % git: non_committed_changes: false
% 5.52/1.77
% 5.52/1.77 % ------ Parsing...
% 5.52/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.52/1.77
% 5.52/1.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 5.52/1.77
% 5.52/1.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.52/1.77
% 5.52/1.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.52/1.77 % ------ Proving...
% 5.52/1.77 % ------ Problem Properties
% 5.52/1.77
% 5.52/1.77 %
% 5.52/1.77 % clauses 56
% 5.52/1.77 % conjectures 1
% 5.52/1.77 % EPR 19
% 5.52/1.77 % Horn 52
% 5.52/1.77 % unary 19
% 5.52/1.77 % binary 23
% 5.52/1.77 % lits 120
% 5.52/1.77 % lits eq 17
% 5.52/1.77 % fd_pure 0
% 5.52/1.77 % fd_pseudo 0
% 5.52/1.77 % fd_cond 1
% 5.52/1.77 % fd_pseudo_cond 3
% 5.52/1.77 % AC symbols 0
% 5.52/1.77
% 5.52/1.77 % ------ Input Options Time Limit: Unbounded
% 5.52/1.77
% 5.52/1.77
% 5.52/1.77 % ------
% 5.52/1.77 % Current options:
% 5.52/1.77 % ------
% 5.52/1.77
% 5.52/1.77
% 5.52/1.77 %
% 5.52/1.77
% 5.52/1.77 % ------ Proving...
% 5.52/1.77 %
% 5.52/1.77
% 5.52/1.77 % SZS status Theorem for theBenchmark.p
% 5.52/1.77
% 5.52/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.52/1.77
% 5.52/1.77
%------------------------------------------------------------------------------