%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU437+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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:57:32 PM UTC 2026
% Result : Theorem 54.89s 12.12s
% Output : CNFRefutation 54.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 177 ( 43 unt; 5 def)
% Number of atoms : 633 ( 10 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 661 ( 292 ~; 312 |; 31 &)
% ( 7 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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 : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 366 ( 0 sgn 351 !; 15 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( r1_tarski(X3,X4)
=> r1_tarski(k8_relset_2(X0,X1,X2,X3),k8_relset_2(X0,X1,X2,X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( r1_tarski(X3,X4)
=> r1_tarski(k8_relset_2(X0,X1,X2,X3),k8_relset_2(X0,X1,X2,X4)) ) ) ) ),
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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,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(f9,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f21,axiom,
! [X0,X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(f30,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f51,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m1_subset_1(X3,X0)
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
=> ( r2_hidden(X3,k8_relset_2(X1,X0,X2,X4))
<=> ! [X5] :
( r2_hidden(X5,X2)
=> r2_hidden(X3,k9_relat_1(X4,k1_tarski(X5))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_2) ).
fof(f52,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f53,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f55,axiom,
! [X0,X1,X2] :
~ ( v1_xboole_0(X2)
& m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f57,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f59,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
<=> r2_hidden(k4_tarski(X1,X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relset_2) ).
fof(f67,plain,
? [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& ? [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& r1_tarski(X3,X4)
& ~ r1_tarski(k8_relset_2(X0,X1,X2,X3),k8_relset_2(X0,X1,X2,X4)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f68,plain,
? [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& ? [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& r1_tarski(X3,X4)
& ~ r1_tarski(k8_relset_2(X0,X1,X2,X3),k8_relset_2(X0,X1,X2,X4)) ) ) ),
inference(flattening,[],[f67]) ).
fof(f71,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(f72,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
inference(flattening,[],[f77]) ).
fof(f90,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| ( r2_hidden(X3,k8_relset_2(X1,X0,X2,X4))
<=> ! [X5] :
( ~ r2_hidden(X5,X2)
| r2_hidden(X3,k9_relat_1(X4,k1_tarski(X5))) ) ) ) ) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f91,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f92,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f97,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
<=> r2_hidden(k4_tarski(X1,X0),X2) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f100,plain,
( m1_subset_1(sK2,k1_zfmisc_1(sK0))
& m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
& m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
& r1_tarski(sK3,sK4)
& ~ r1_tarski(k8_relset_2(sK0,sK1,sK2,sK3),k8_relset_2(sK0,sK1,sK2,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f68]) ).
fof(f101,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,[],[f72]) ).
fof(f102,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,[],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ( r2_hidden(sK5(X0,X1),X0)
& ~ r2_hidden(sK5(X0,X1),X1) )
| r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f102]) ).
fof(f106,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f30]) ).
fof(f115,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| ( ( ~ r2_hidden(X3,k8_relset_2(X1,X0,X2,X4))
| ! [X5] :
( ~ r2_hidden(X5,X2)
| r2_hidden(X3,k9_relat_1(X4,k1_tarski(X5))) ) )
& ( ? [X5] :
( r2_hidden(X5,X2)
& ~ r2_hidden(X3,k9_relat_1(X4,k1_tarski(X5))) )
| r2_hidden(X3,k8_relset_2(X1,X0,X2,X4)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f116,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| ( ( ~ r2_hidden(X3,k8_relset_2(X1,X0,X2,X4))
| ! [X6] :
( ~ r2_hidden(X6,X2)
| r2_hidden(X3,k9_relat_1(X4,k1_tarski(X6))) ) )
& ( ? [X5] :
( r2_hidden(X5,X2)
& ~ r2_hidden(X3,k9_relat_1(X4,k1_tarski(X5))) )
| r2_hidden(X3,k8_relset_2(X1,X0,X2,X4)) ) ) ) ) ) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| ( ( ~ r2_hidden(X3,k8_relset_2(X1,X0,X2,X4))
| ! [X6] :
( ~ r2_hidden(X6,X2)
| r2_hidden(X3,k9_relat_1(X4,k1_tarski(X6))) ) )
& ( ( r2_hidden(sK16(X2,X3,X4),X2)
& ~ r2_hidden(X3,k9_relat_1(X4,k1_tarski(sK16(X2,X3,X4)))) )
| r2_hidden(X3,k8_relset_2(X1,X0,X2,X4)) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X5,sK16(X2,X3,X4))],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) )
& ( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ( ( ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k4_tarski(X1,X0),X2) )
& ( ~ r2_hidden(k4_tarski(X1,X0),X2)
| r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1))) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f120,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f100]) ).
fof(f121,plain,
m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f100]) ).
fof(f122,plain,
m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f100]) ).
fof(f123,plain,
r1_tarski(sK3,sK4),
inference(cnf_transformation,[],[f100]) ).
fof(f124,plain,
~ r1_tarski(k8_relset_2(sK0,sK1,sK2,sK3),k8_relset_2(sK0,sK1,sK2,sK4)),
inference(cnf_transformation,[],[f100]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f128,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f129,plain,
! [X3,X0,X1] :
( ~ r1_tarski(X0,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f130,plain,
! [X0,X1] :
( r2_hidden(sK5(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f131,plain,
! [X0,X1] :
( ~ r2_hidden(sK5(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f133,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f144,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f106]) ).
fof(f173,plain,
! [X2,X3,X0,X1,X6,X4] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,X0)
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| ~ r2_hidden(X3,k8_relset_2(X1,X0,X2,X4))
| ~ r2_hidden(X6,X2)
| r2_hidden(X3,k9_relat_1(X4,k1_tarski(X6))) ),
inference(cnf_transformation,[],[f117]) ).
fof(f174,plain,
! [X2,X3,X0,X1,X4] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,X0)
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| r2_hidden(sK16(X2,X3,X4),X2)
| r2_hidden(X3,k8_relset_2(X1,X0,X2,X4)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f175,plain,
! [X2,X3,X0,X1,X4] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,X0)
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| ~ r2_hidden(X3,k9_relat_1(X4,k1_tarski(sK16(X2,X3,X4))))
| r2_hidden(X3,k8_relset_2(X1,X0,X2,X4)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f176,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f177,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f178,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f182,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k4_tarski(X1,X0),X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(k4_tarski(X1,X0),X2)
| r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1))) ),
inference(cnf_transformation,[],[f119]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),X2)
| r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1))) ),
inference(definition_unfolding,[],[f185,f133]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),X2) ),
inference(definition_unfolding,[],[f184,f133]) ).
tcf(c_49,negated_conjecture,
~ r1_tarski(k8_relset_2(sK0,sK1,sK2,sK3),k8_relset_2(sK0,sK1,sK2,sK4)),
inference(cnf_transformation,[],[f124]) ).
tcf(c_50,negated_conjecture,
r1_tarski(sK3,sK4),
inference(cnf_transformation,[],[f123]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f122]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f121]) ).
tcf(c_53,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f120]) ).
tcf(c_56,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,[],[f127]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( m1_subset_1(k8_relset_2(X1,X2,X3,X0),k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_72,plain,
! [X0: $i] : m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f144]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_xboole_0(X4)
| r2_hidden(X0,k8_relset_2(X3,X4,X2,X1))
| ~ m1_subset_1(X0,X4)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))
| ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(sK16(X2,X0,X1)))) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v1_xboole_0(X2)
| r2_hidden(sK16(X3,X4,X0),X3)
| r2_hidden(X4,k8_relset_2(X1,X2,X3,X0))
| ~ m1_subset_1(X4,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v1_xboole_0(X2)
| r2_hidden(X0,k9_relat_1(X4,k1_tarski(X5)))
| ~ r2_hidden(X5,X3)
| ~ m1_subset_1(X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ r2_hidden(X0,k8_relset_2(X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X2,X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,k9_relat_1(X2,k1_tarski(X0)))
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),X2) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k2_tarski(k2_tarski(X2,X0),k1_tarski(X2)),X1)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2))) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_105]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X2,X1)
| ~ r2_hidden(X2,X0)
| ~ r1_tarski(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_107,c_155]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,X0)
| ~ r1_tarski(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_108,c_155]) ).
tcf(c_693,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k2_tarski(k1_tarski(X2),k2_tarski(X2,X0)),X1)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2))) ),
inference(demodulation,[status(thm)],[c_113,c_57]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,k9_relat_1(X2,k1_tarski(X0)))
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_112,c_57]) ).
tcf(c_1876,definition,
iPr_def_10 = k1_zfmisc_1(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1877,definition,
iPr_def_11 = k2_zfmisc_1(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1878,definition,
iPr_def_12 = k1_zfmisc_1(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1879,definition,
iPr_def_13 = k8_relset_2(sK0,sK1,sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1880,definition,
iPr_def_14 = k8_relset_2(sK0,sK1,sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1881,negated_conjecture,
m1_subset_1(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_53,c_1876]) ).
tcf(c_1882,negated_conjecture,
m1_subset_1(sK3,iPr_def_12),
inference(demodulation,[status(thm)],[c_52,c_1877,c_1878]) ).
tcf(c_1883,negated_conjecture,
m1_subset_1(sK4,iPr_def_12),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_1884,negated_conjecture,
r1_tarski(sK3,sK4),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_1885,negated_conjecture,
~ r1_tarski(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_49,c_1880,c_1879]) ).
tcf(c_3049,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ v1_xboole_0(X0) ),
inference(superposition,[status(thm)],[c_59,c_110]) ).
tcf(c_3061,plain,
~ v1_xboole_0(iPr_def_13),
inference(superposition,[status(thm)],[c_3049,c_1885]) ).
tcf(c_3123,plain,
! [X0: $i] :
( v1_relat_1(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1877,c_56]) ).
tcf(c_3124,plain,
! [X0: $i] :
( v1_relat_1(X0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_3123,c_1878]) ).
tcf(c_3165,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r2_hidden(sK8(X0),X0) ),
inference(superposition,[status(thm)],[c_72,c_104]) ).
tcf(c_3261,plain,
! [X0: $i] :
( r2_hidden(X0,sK4)
| ~ r2_hidden(X0,sK3) ),
inference(superposition,[status(thm)],[c_1884,c_60]) ).
tcf(c_3574,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k2_tarski(k1_tarski(X1),k2_tarski(X1,X0)),sK4)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(superposition,[status(thm)],[c_693,c_3261]) ).
tcf(c_3725,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK4,k1_tarski(X1)))
| ~ v1_relat_1(sK4)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(superposition,[status(thm)],[c_3574,c_703]) ).
tcf(c_3845,plain,
( m1_subset_1(iPr_def_13,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_1879,c_66]) ).
tcf(c_3853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r1_tarski(k8_relset_2(X1,X2,X3,X0),X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(superposition,[status(thm)],[c_66,c_106]) ).
tcf(c_3856,plain,
( m1_subset_1(iPr_def_13,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sK3,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_3845,c_1876,c_1877,c_1878]) ).
tcf(c_3857,plain,
m1_subset_1(iPr_def_13,k1_zfmisc_1(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_3856,c_1882,c_1881]) ).
tcf(c_4035,plain,
! [X0: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,iPr_def_14)
| r2_hidden(sK16(sK2,X0,sK4),sK2)
| ~ m1_subset_1(X0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_1880,c_102]) ).
tcf(c_4047,plain,
! [X0: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,iPr_def_14)
| r2_hidden(sK16(sK2,X0,sK4),sK2)
| ~ m1_subset_1(sK4,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ m1_subset_1(X0,sK1) ),
inference(light_normalisation,[status(thm)],[c_4035,c_1876,c_1877,c_1878]) ).
tcf(c_4048,plain,
! [X0: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,iPr_def_14)
| r2_hidden(sK16(sK2,X0,sK4),sK2)
| ~ m1_subset_1(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4047,c_1883,c_1881]) ).
tcf(c_4165,plain,
r1_tarski(iPr_def_13,sK1),
inference(superposition,[status(thm)],[c_3857,c_106]) ).
tcf(c_4167,plain,
! [X0: $i] :
( r2_hidden(X0,sK1)
| ~ r2_hidden(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4165,c_60]) ).
tcf(c_4345,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_1879,c_103]) ).
tcf(c_4354,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ m1_subset_1(sK3,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1) ),
inference(light_normalisation,[status(thm)],[c_4345,c_1876,c_1877,c_1878]) ).
tcf(c_4355,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4354,c_1882,c_1881]) ).
tcf(c_4785,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ v1_xboole_0(X0) ),
inference(superposition,[status(thm)],[c_59,c_110]) ).
tcf(c_4804,plain,
~ v1_xboole_0(iPr_def_13),
inference(superposition,[status(thm)],[c_4785,c_1885]) ).
tcf(c_4820,plain,
v1_relat_1(sK3),
inference(superposition,[status(thm)],[c_1882,c_3124]) ).
tcf(c_4821,plain,
v1_relat_1(sK4),
inference(superposition,[status(thm)],[c_1883,c_3124]) ).
tcf(c_5805,plain,
( v1_xboole_0(iPr_def_13)
| r2_hidden(sK8(iPr_def_13),sK1) ),
inference(superposition,[status(thm)],[c_3165,c_4167]) ).
tcf(c_5806,plain,
r2_hidden(sK8(iPr_def_13),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_5805,c_3061]) ).
tcf(c_5905,plain,
~ v1_xboole_0(sK1),
inference(superposition,[status(thm)],[c_5806,c_110]) ).
tcf(c_6298,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r2_hidden(sK8(X0),X0) ),
inference(superposition,[status(thm)],[c_72,c_104]) ).
tcf(c_7215,plain,
! [X0: $i] :
( r2_hidden(X0,sK4)
| ~ r2_hidden(X0,sK3) ),
inference(superposition,[status(thm)],[c_1884,c_60]) ).
tcf(c_10173,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k2_tarski(k1_tarski(X1),k2_tarski(X1,X0)),sK4)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(superposition,[status(thm)],[c_693,c_7215]) ).
tcf(c_10906,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k2_tarski(k1_tarski(X1),k2_tarski(X1,X0)),sK4)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_10173,c_3574,c_4820]) ).
tcf(c_10917,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK4,k1_tarski(X1)))
| ~ v1_relat_1(sK4)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(superposition,[status(thm)],[c_10906,c_703]) ).
tcf(c_11312,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK4,k1_tarski(X1)))
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_10917,c_3725,c_4821,c_4820]) ).
tcf(c_11501,plain,
( m1_subset_1(iPr_def_13,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_1879,c_66]) ).
tcf(c_11512,plain,
( m1_subset_1(iPr_def_13,k1_zfmisc_1(sK1))
| ~ m1_subset_1(sK3,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_11501,c_1876,c_1877,c_1878]) ).
tcf(c_11513,plain,
m1_subset_1(iPr_def_13,k1_zfmisc_1(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_11512,c_1882,c_1881]) ).
tcf(c_15528,plain,
r1_tarski(iPr_def_13,sK1),
inference(superposition,[status(thm)],[c_11513,c_106]) ).
tcf(c_15681,plain,
! [X0: $i] :
( r2_hidden(X0,sK1)
| ~ r2_hidden(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_15528,c_60]) ).
tcf(c_16289,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_1879,c_103]) ).
tcf(c_16298,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ m1_subset_1(sK3,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1) ),
inference(light_normalisation,[status(thm)],[c_16289,c_1876,c_1877,c_1878]) ).
tcf(c_16299,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16298,c_1882,c_1881]) ).
tcf(c_17403,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X0,sK1)
| ~ r2_hidden(X0,iPr_def_13)
| ~ r2_hidden(X1,sK2)
| r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_16299,c_4355,c_5905]) ).
tcf(c_17404,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1) ),
inference(renaming,[status(thm)],[c_17403]) ).
tcf(c_17419,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK4,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1) ),
inference(superposition,[status(thm)],[c_17404,c_11312]) ).
tcf(c_17532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| r2_hidden(X3,k8_relset_2(X0,X1,X2,sK4))
| ~ r2_hidden(X3,iPr_def_13)
| ~ m1_subset_1(X3,sK1)
| ~ m1_subset_1(X3,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ r2_hidden(sK16(X2,X3,sK4),sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(superposition,[status(thm)],[c_17419,c_101]) ).
tcf(c_20181,plain,
( v1_xboole_0(iPr_def_13)
| r2_hidden(sK8(iPr_def_13),sK1) ),
inference(superposition,[status(thm)],[c_6298,c_15681]) ).
tcf(c_20182,plain,
r2_hidden(sK8(iPr_def_13),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_20181,c_4804]) ).
tcf(c_20823,plain,
~ v1_xboole_0(sK1),
inference(superposition,[status(thm)],[c_20182,c_110]) ).
tcf(c_29451,plain,
! [X0: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ r2_hidden(sK16(sK2,X0,sK4),sK2) ),
inference(superposition,[status(thm)],[c_1880,c_17532]) ).
tcf(c_29462,plain,
! [X0: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,iPr_def_14)
| ~ m1_subset_1(sK4,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ r2_hidden(sK16(sK2,X0,sK4),sK2) ),
inference(light_normalisation,[status(thm)],[c_29451,c_1876,c_1877,c_1878]) ).
tcf(c_29463,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ r2_hidden(sK16(sK2,X0,sK4),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29462,c_20823,c_1883,c_1881]) ).
tcf(c_29596,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_29463,c_4048,c_5905,c_29463]) ).
tcf(c_47104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ r2_hidden(X0,k8_relset_2(X1,X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_3853,c_326]) ).
tcf(c_47128,plain,
! [X0: $i] :
( m1_subset_1(X0,sK1)
| ~ r2_hidden(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4165,c_326]) ).
tcf(c_48061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ r2_hidden(X0,k8_relset_2(X1,X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_3853,c_327]) ).
tcf(c_99794,plain,
! [X0: $i] :
( r2_hidden(X0,sK4)
| ~ r2_hidden(X0,sK3) ),
inference(superposition,[status(thm)],[c_1884,c_60]) ).
tcf(c_100023,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k2_tarski(k1_tarski(X1),k2_tarski(X1,X0)),sK4)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(superposition,[status(thm)],[c_693,c_99794]) ).
tcf(c_100060,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k2_tarski(k1_tarski(X1),k2_tarski(X1,X0)),sK4)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_100023,c_3574,c_4820]) ).
tcf(c_100071,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK4,k1_tarski(X1)))
| ~ v1_relat_1(sK4)
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(superposition,[status(thm)],[c_100060,c_703]) ).
tcf(c_100119,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK4,k1_tarski(X1)))
| ~ r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_100071,c_3725,c_4821,c_4820]) ).
tcf(c_100577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ r2_hidden(X0,k8_relset_2(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| r2_hidden(X0,k9_relat_1(X4,k1_tarski(X5))) ),
inference(global_subsumption_just,[status(thm)],[c_103,c_103,c_47104,c_48061]) ).
tcf(c_100578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r2_hidden(X0,k9_relat_1(X4,k1_tarski(X5)))
| ~ r2_hidden(X5,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ r2_hidden(X0,k8_relset_2(X1,X2,X3,X4)) ),
inference(renaming,[status(thm)],[c_100577]) ).
tcf(c_100593,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_1879,c_100578]) ).
tcf(c_100600,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ m1_subset_1(sK3,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_100593,c_1876,c_1877,c_1878]) ).
tcf(c_100601,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK3,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100600,c_1882,c_1881]) ).
tcf(c_100760,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k9_relat_1(sK4,k1_tarski(X1)))
| ~ r2_hidden(X1,sK2)
| ~ r2_hidden(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_100601,c_100119]) ).
tcf(c_100974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| r2_hidden(X3,k8_relset_2(X0,X1,X2,sK4))
| ~ r2_hidden(X3,iPr_def_13)
| ~ m1_subset_1(X3,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ r2_hidden(sK16(X2,X3,sK4),sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(superposition,[status(thm)],[c_100760,c_101]) ).
tcf(c_103510,plain,
! [X0: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ r2_hidden(sK16(sK2,X0,sK4),sK2) ),
inference(superposition,[status(thm)],[c_1880,c_100974]) ).
tcf(c_103521,plain,
! [X0: $i] :
( v1_xboole_0(sK1)
| r2_hidden(X0,iPr_def_14)
| ~ m1_subset_1(sK4,iPr_def_12)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ r2_hidden(sK16(sK2,X0,sK4),sK2) ),
inference(light_normalisation,[status(thm)],[c_103510,c_1876,c_1877,c_1878]) ).
tcf(c_103522,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X0,iPr_def_13)
| ~ m1_subset_1(X0,sK1)
| ~ r2_hidden(sK16(sK2,X0,sK4),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_103521,c_20823,c_1883,c_1881]) ).
tcf(c_103701,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_103522,c_29596,c_47128]) ).
tcf(c_103708,plain,
! [X0: $i] :
( r1_tarski(iPr_def_13,X0)
| r2_hidden(sK5(iPr_def_13,X0),iPr_def_14) ),
inference(superposition,[status(thm)],[c_59,c_103701]) ).
tcf(c_103753,plain,
r1_tarski(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_103708,c_58]) ).
tcf(c_103756,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_103753,c_1885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU437+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Thu Sep 24 14:18:11 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 0.16/0.50
% 0.16/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.50
% 0.16/0.51 % Detected problem language: tptp
% 0.25/0.52 % Proving...
% 54.89/12.12 % SZS status Started for theBenchmark.p
% 54.89/12.12 % SZS status Theorem for theBenchmark.p
% 54.89/12.12
% 54.89/12.12 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 54.89/12.12
% 54.89/12.12 % ------ iProver source info
% 54.89/12.12
% 54.89/12.12 % git: date: 2026-07-19 20:42:38 +0200
% 54.89/12.12 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 54.89/12.12 % git: non_committed_changes: false
% 54.89/12.12
% 54.89/12.12 % ------ Parsing...
% 54.89/12.12 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 54.89/12.12
% 54.89/12.12 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 54.89/12.12
% 54.89/12.12 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 54.89/12.12
% 54.89/12.12 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 54.89/12.12 % ------ Proving...
% 54.89/12.12 % ------ Problem Properties
% 54.89/12.12
% 54.89/12.12 %
% 54.89/12.12 % clauses 64
% 54.89/12.12 % conjectures 5
% 54.89/12.12 % EPR 23
% 54.89/12.12 % Horn 57
% 54.89/12.12 % unary 32
% 54.89/12.12 % binary 18
% 54.89/12.12 % lits 120
% 54.89/12.12 % lits eq 12
% 54.89/12.12 % fd_pure 0
% 54.89/12.12 % fd_pseudo 0
% 54.89/12.12 % fd_cond 1
% 54.89/12.12 % fd_pseudo_cond 1
% 54.89/12.12 % AC symbols 0
% 54.89/12.12
% 54.89/12.12 % ------ Schedule dynamic 5 is on
% 54.89/12.12
% 54.89/12.12 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 54.89/12.12
% 54.89/12.12
% 54.89/12.12 % ------
% 54.89/12.12 % Current options:
% 54.89/12.12 % ------
% 54.89/12.12
% 54.89/12.12
% 54.89/12.12 %
% 54.89/12.12
% 54.89/12.12 % ------ Proving...
% 54.89/12.12 % Proof_search_loop: time out after: 4570 full_loop iterations
% 54.89/12.12
% 54.89/12.12 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 54.89/12.12
% 54.89/12.12
% 54.89/12.12 % ------
% 54.89/12.12 % Current options:
% 54.89/12.12 % ------
% 54.89/12.12
% 54.89/12.12
% 54.89/12.12 %
% 54.89/12.12
% 54.89/12.12 % ------ Proving...
% 54.89/12.12 %
% 54.89/12.12
% 54.89/12.12 % SZS status Theorem for theBenchmark.p
% 54.89/12.12
% 54.89/12.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 54.89/12.13
% 54.89/12.13
%------------------------------------------------------------------------------