%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU450+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 : n007.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 02:57:35 PM UTC 2026
% Result : Theorem 8.04s 1.77s
% Output : CNFRefutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 18
% Syntax : Number of formulae : 154 ( 33 unt; 9 def)
% Number of atoms : 871 ( 63 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 673 ( 324 ~; 313 |; 16 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 223 ( 1 sgn 218 !; 5 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ( k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)) = k8_relset_2(X1,X0,k8_relset_2(X0,X1,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)),X4),k6_relset_1(X0,X1,X4))
& k8_relset_2(X0,X1,X2,X4) = k8_relset_2(X0,X1,k8_relset_2(X1,X0,k8_relset_2(X0,X1,X2,X4),k6_relset_1(X0,X1,X4)),X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_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(X1))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ( k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)) = k8_relset_2(X1,X0,k8_relset_2(X0,X1,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)),X4),k6_relset_1(X0,X1,X4))
& k8_relset_2(X0,X1,X2,X4) = k8_relset_2(X0,X1,k8_relset_2(X1,X0,k8_relset_2(X0,X1,X2,X4),k6_relset_1(X0,X1,X4)),X4) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( r1_tarski(X1,X0)
& r1_tarski(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f15,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_1) ).
fof(f18,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/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(f24,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f47,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(f48,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f51,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X0))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( r1_tarski(X2,X3)
=> r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relset_2) ).
fof(f55,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ( r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
<=> r1_tarski(X3,k8_relset_2(X0,X1,X2,X4)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_relset_2) ).
fof(f59,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f48]) ).
fof(f66,plain,
? [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
& ? [X4] :
( m2_relset_1(X4,X0,X1)
& ( k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)) != k8_relset_2(X1,X0,k8_relset_2(X0,X1,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)),X4),k6_relset_1(X0,X1,X4))
| k8_relset_2(X0,X1,X2,X4) != k8_relset_2(X0,X1,k8_relset_2(X1,X0,k8_relset_2(X0,X1,X2,X4),k6_relset_1(X0,X1,X4)),X4) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,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,[],[f18]) ).
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(flattening,[],[f76]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ m2_relset_1(X2,X0,X1)
| m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f24]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X0))
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ r1_tarski(X2,X3)
| r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4)) ) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X0))
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ r1_tarski(X2,X3)
| r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4)) ) ) ),
inference(flattening,[],[f95]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ! [X4] :
( ~ m2_relset_1(X4,X0,X1)
| ( r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
<=> r1_tarski(X3,k8_relset_2(X0,X1,X2,X4)) ) ) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f104,plain,
( m1_subset_1(sK2,k1_zfmisc_1(sK0))
& m1_subset_1(sK3,k1_zfmisc_1(sK1))
& m2_relset_1(sK4,sK0,sK1)
& ( k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)) != k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)),sK4),k6_relset_1(sK0,sK1,sK4))
| k8_relset_2(sK0,sK1,sK2,sK4) != k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,sK2,sK4),k6_relset_1(sK0,sK1,sK4)),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)],[f66]) ).
fof(f105,plain,
! [X0,X1] :
( ( X0 != X1
| ( r1_tarski(X1,X0)
& r1_tarski(X0,X1) ) )
& ( ~ r1_tarski(X1,X0)
| ~ r1_tarski(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f106,plain,
! [X0,X1] :
( ( X0 != X1
| ( r1_tarski(X1,X0)
& r1_tarski(X0,X1) ) )
& ( ~ r1_tarski(X1,X0)
| ~ r1_tarski(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f105]) ).
fof(f117,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,[],[f47]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ! [X4] :
( ~ m2_relset_1(X4,X0,X1)
| ( ( ~ r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
| r1_tarski(X3,k8_relset_2(X0,X1,X2,X4)) )
& ( ~ r1_tarski(X3,k8_relset_2(X0,X1,X2,X4))
| r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4))) ) ) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f120,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f104]) ).
fof(f121,plain,
m1_subset_1(sK3,k1_zfmisc_1(sK1)),
inference(cnf_transformation,[],[f104]) ).
fof(f122,plain,
m2_relset_1(sK4,sK0,sK1),
inference(cnf_transformation,[],[f104]) ).
fof(f123,plain,
( k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)) != k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)),sK4),k6_relset_1(sK0,sK1,sK4))
| k8_relset_2(sK0,sK1,sK2,sK4) != k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,sK2,sK4),k6_relset_1(sK0,sK1,sK4)),sK4) ),
inference(cnf_transformation,[],[f104]) ).
fof(f129,plain,
! [X0,X1] :
( ~ r1_tarski(X1,X0)
| ~ r1_tarski(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f106]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f137,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,[],[f77]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f173,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f59]) ).
fof(f176,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(X0))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ r1_tarski(X2,X3)
| r1_tarski(k8_relset_2(X0,X1,X3,X4),k8_relset_2(X0,X1,X2,X4)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f181,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X0,X1)
| ~ r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
| r1_tarski(X3,k8_relset_2(X0,X1,X2,X4)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f182,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X0,X1)
| ~ r1_tarski(X3,k8_relset_2(X0,X1,X2,X4))
| r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4))) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_49,negated_conjecture,
( ( k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,sK2,sK4),k6_relset_1(sK0,sK1,sK4)),sK4) != k8_relset_2(sK0,sK1,sK2,sK4) )
| ( k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)),sK4),k6_relset_1(sK0,sK1,sK4)) != k8_relset_2(sK1,sK0,sK3,k6_relset_1(sK0,sK1,sK4)) ) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_50,negated_conjecture,
m2_relset_1(sK4,sK0,sK1),
inference(cnf_transformation,[],[f122]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(sK1)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f120]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ r1_tarski(X1,X0)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( m2_relset_1(k6_relset_1(X1,X2,X0),X2,X1)
| ~ m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f135]) ).
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,[],[f137]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( m2_relset_1(X0,X1,X2)
| ~ m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_102,plain,
! [X0: $i] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f173]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r1_tarski(k8_relset_2(X1,X2,X4,X0),k8_relset_2(X1,X2,X3,X0))
| ~ r1_tarski(X3,X4)
| ~ m1_subset_1(X4,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r1_tarski(X3,k8_relset_2(X2,X1,X0,k6_relset_1(X1,X2,X4)))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X2))
| ~ m2_relset_1(X4,X1,X2)
| ~ r1_tarski(X0,k8_relset_2(X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r1_tarski(X3,k8_relset_2(X2,X1,X0,X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X2))
| ~ m2_relset_1(X4,X2,X1)
| ~ r1_tarski(X0,k8_relset_2(X1,X2,X3,k6_relset_1(X2,X1,X4))) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m2_relset_1(X0,X1,X2)
| m1_relset_1(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_101]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_163]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_relset_1(X0,X1,X2)
| m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_100,c_69]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_relset_1(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_209]) ).
tcf(c_939,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X2,X0,X1)
| ( X2 != sK4 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_164]) ).
tcf(c_940,plain,
m1_relset_1(sK4,sK0,sK1),
inference(unflattening,[status(thm)],[c_939]) ).
tcf(c_1234,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_relset_1(X0,X1,X2)
| m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_210]) ).
tcf(c_1235,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_relset_1(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_1234]) ).
tcf(c_2156,definition,
iPr_def_10 = k1_zfmisc_1(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2157,definition,
iPr_def_11 = k1_zfmisc_1(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2158,definition,
iPr_def_12 = k6_relset_1(sK0,sK1,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2159,definition,
iPr_def_13 = k8_relset_2(sK1,sK0,sK3,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2160,definition,
iPr_def_14 = k8_relset_2(sK0,sK1,iPr_def_13,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2161,definition,
iPr_def_15 = k8_relset_2(sK1,sK0,iPr_def_14,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2162,definition,
iPr_def_16 = k8_relset_2(sK0,sK1,sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2163,definition,
iPr_def_17 = k8_relset_2(sK1,sK0,iPr_def_16,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2164,definition,
iPr_def_18 = k8_relset_2(sK0,sK1,iPr_def_17,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_2165,negated_conjecture,
m1_subset_1(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_52,c_2156]) ).
tcf(c_2166,negated_conjecture,
m1_subset_1(sK3,iPr_def_11),
inference(demodulation,[status(thm)],[c_51,c_2157]) ).
tcf(c_2167,negated_conjecture,
m2_relset_1(sK4,sK0,sK1),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_2168,negated_conjecture,
( ( iPr_def_18 != iPr_def_16 )
| ( iPr_def_15 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_49,c_2162,c_2163,c_2164,c_2158,c_2159,c_2160,c_2161]) ).
tcf(c_3624,plain,
m1_relset_1(sK4,sK0,sK1),
inference(superposition,[status(thm)],[c_2167,c_101]) ).
tcf(c_3807,plain,
( m2_relset_1(iPr_def_12,sK1,sK0)
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(superposition,[status(thm)],[c_2158,c_64]) ).
tcf(c_3809,plain,
m2_relset_1(iPr_def_12,sK1,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_3807,c_3624]) ).
tcf(c_3882,plain,
m1_relset_1(iPr_def_12,sK1,sK0),
inference(superposition,[status(thm)],[c_3809,c_101]) ).
tcf(c_4153,plain,
( m1_subset_1(iPr_def_16,k1_zfmisc_1(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_2162,c_66]) ).
tcf(c_4154,plain,
( m1_subset_1(iPr_def_13,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(sK1))
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_2159,c_66]) ).
tcf(c_4155,plain,
( m1_subset_1(iPr_def_14,k1_zfmisc_1(sK1))
| ~ m1_subset_1(iPr_def_13,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_2160,c_66]) ).
tcf(c_4157,plain,
( m1_subset_1(iPr_def_17,k1_zfmisc_1(sK0))
| ~ m1_subset_1(iPr_def_16,k1_zfmisc_1(sK1))
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_2163,c_66]) ).
tcf(c_4170,plain,
( m1_subset_1(iPr_def_17,iPr_def_10)
| ~ m1_subset_1(iPr_def_16,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(light_normalisation,[status(thm)],[c_4157,c_2156,c_2157]) ).
tcf(c_4178,plain,
( m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(light_normalisation,[status(thm)],[c_4155,c_2156,c_2157]) ).
tcf(c_4182,plain,
( m1_subset_1(iPr_def_13,iPr_def_10)
| ~ m1_subset_1(sK3,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(light_normalisation,[status(thm)],[c_4154,c_2156,c_2157]) ).
tcf(c_4183,plain,
( m1_subset_1(iPr_def_13,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4182,c_2166]) ).
tcf(c_4186,plain,
( m1_subset_1(iPr_def_16,iPr_def_11)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(light_normalisation,[status(thm)],[c_4153,c_2156,c_2157]) ).
tcf(c_4187,plain,
( m1_subset_1(iPr_def_16,iPr_def_11)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4186,c_2165]) ).
tcf(c_4329,plain,
! [X0: $i] :
( r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_16)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_2162,c_105]) ).
tcf(c_4330,plain,
! [X0: $i] :
( r1_tarski(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_13)
| ~ r1_tarski(sK3,X0)
| ~ m1_subset_1(sK3,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK1))
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_2159,c_105]) ).
tcf(c_4360,plain,
! [X0: $i] :
( r1_tarski(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_13)
| ~ m1_subset_1(sK3,iPr_def_11)
| ~ r1_tarski(sK3,X0)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(light_normalisation,[status(thm)],[c_4330,c_2157]) ).
tcf(c_4361,plain,
! [X0: $i] :
( r1_tarski(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_13)
| ~ r1_tarski(sK3,X0)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4360,c_2166]) ).
tcf(c_4366,plain,
! [X0: $i] :
( r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_16)
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(light_normalisation,[status(thm)],[c_4329,c_2156]) ).
tcf(c_4367,plain,
! [X0: $i] :
( r1_tarski(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_16)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4366,c_2165]) ).
tcf(c_4489,plain,
( r1_tarski(iPr_def_15,iPr_def_13)
| ~ r1_tarski(sK3,iPr_def_14)
| ~ m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_2161,c_4361]) ).
tcf(c_4491,plain,
! [X0: $i] :
( ( k8_relset_2(sK1,sK0,X0,iPr_def_12) = iPr_def_13 )
| ~ r1_tarski(sK3,X0)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(iPr_def_13,k8_relset_2(sK1,sK0,X0,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_4361,c_56]) ).
tcf(c_4517,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,X0,sK4) = iPr_def_16 )
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,X0,sK4)) ),
inference(superposition,[status(thm)],[c_4367,c_56]) ).
tcf(c_4619,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m2_relset_1(sK4,sK0,sK1)
| ~ m1_subset_1(X1,k1_zfmisc_1(sK0))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK1))
| ~ r1_tarski(X0,k8_relset_2(sK0,sK1,X1,sK4)) ),
inference(superposition,[status(thm)],[c_2158,c_110]) ).
tcf(c_4635,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m1_subset_1(X1,iPr_def_10)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ m2_relset_1(sK4,sK0,sK1)
| ~ r1_tarski(X0,k8_relset_2(sK0,sK1,X1,sK4)) ),
inference(light_normalisation,[status(thm)],[c_4619,c_2156,c_2157]) ).
tcf(c_4636,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m1_subset_1(X1,iPr_def_10)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ r1_tarski(X0,k8_relset_2(sK0,sK1,X1,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4635,c_2167]) ).
tcf(c_4718,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m2_relset_1(sK4,sK0,sK1)
| ~ m1_subset_1(X1,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| ~ r1_tarski(X0,k8_relset_2(sK1,sK0,X1,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_2158,c_111]) ).
tcf(c_4737,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X1,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m2_relset_1(sK4,sK0,sK1)
| ~ r1_tarski(X0,k8_relset_2(sK1,sK0,X1,iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_4718,c_2156,c_2157]) ).
tcf(c_4738,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X1,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ r1_tarski(X0,k8_relset_2(sK1,sK0,X1,iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4737,c_2167]) ).
tcf(c_4891,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12))
| ~ m1_subset_1(X1,iPr_def_10)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(sK0))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11) ),
inference(superposition,[status(thm)],[c_105,c_4636]) ).
tcf(c_4896,plain,
! [X0: $i] :
( r1_tarski(sK2,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r1_tarski(X0,iPr_def_16)
| ~ m1_subset_1(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2162,c_4636]) ).
tcf(c_4897,plain,
! [X0: $i] :
( r1_tarski(iPr_def_13,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ r1_tarski(X0,iPr_def_14)
| ~ m1_subset_1(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2160,c_4636]) ).
tcf(c_4910,plain,
! [X0: $i] :
( r1_tarski(sK2,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ r1_tarski(X0,iPr_def_16)
| ~ m1_subset_1(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4896,c_2165]) ).
tcf(c_4930,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12))
| ~ m1_subset_1(X1,iPr_def_10)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_4891,c_2156]) ).
tcf(c_4976,plain,
( r1_tarski(sK2,iPr_def_17)
| ~ r1_tarski(iPr_def_16,iPr_def_16)
| ~ m1_subset_1(iPr_def_16,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2163,c_4910]) ).
tcf(c_4978,plain,
( r1_tarski(sK2,iPr_def_17)
| ~ m1_subset_1(iPr_def_16,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4976,c_102]) ).
tcf(c_4995,plain,
( m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_1235]) ).
tcf(c_5011,plain,
! [X0: $i] :
( r1_tarski(X0,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,X0,iPr_def_12),sK4))
| ~ m1_subset_1(X0,iPr_def_11)
| ~ m1_subset_1(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_102,c_4738]) ).
tcf(c_5012,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,X0,iPr_def_12),sK4))
| ~ m1_subset_1(X1,iPr_def_11)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK1))
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ m1_subset_1(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_105,c_4738]) ).
tcf(c_5018,plain,
! [X0: $i] :
( r1_tarski(sK3,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(sK3,iPr_def_11)
| ~ r1_tarski(X0,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2159,c_4738]) ).
tcf(c_5020,plain,
! [X0: $i] :
( r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(iPr_def_16,iPr_def_11)
| ~ r1_tarski(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2163,c_4738]) ).
tcf(c_5032,plain,
! [X0: $i] :
( r1_tarski(sK3,k8_relset_2(sK0,sK1,X0,sK4))
| ~ r1_tarski(X0,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5018,c_2166]) ).
tcf(c_5053,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,X0,iPr_def_12),sK4))
| ~ m1_subset_1(X1,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ m1_subset_1(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_5012,c_2157]) ).
tcf(c_5087,plain,
( r1_tarski(sK3,iPr_def_14)
| ~ r1_tarski(iPr_def_13,iPr_def_13)
| ~ m1_subset_1(iPr_def_13,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2160,c_5032]) ).
tcf(c_5094,plain,
( r1_tarski(sK3,iPr_def_14)
| ~ m1_subset_1(iPr_def_13,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5087,c_102]) ).
tcf(c_5245,plain,
( r1_tarski(iPr_def_15,iPr_def_13)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_4489,c_940,c_4183,c_4178,c_4489,c_4995,c_5094]) ).
tcf(c_5374,plain,
r1_tarski(sK2,iPr_def_17),
inference(global_subsumption_just,[status(thm)],[c_4978,c_940,c_4187,c_4978,c_4995]) ).
tcf(c_5426,plain,
! [X0: $i] :
( ( k8_relset_2(sK1,sK0,X0,iPr_def_12) = iPr_def_13 )
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ r1_tarski(X0,iPr_def_14)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ r1_tarski(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_13) ),
inference(superposition,[status(thm)],[c_4897,c_56]) ).
tcf(c_5522,plain,
! [X0: $i] :
( r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(X0,iPr_def_10)
| ~ r1_tarski(X0,iPr_def_17) ),
inference(global_subsumption_just,[status(thm)],[c_5020,c_940,c_4187,c_4995,c_5020]) ).
tcf(c_5523,plain,
! [X0: $i] :
( r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,X0,sK4))
| ~ r1_tarski(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(renaming,[status(thm)],[c_5522]) ).
tcf(c_6068,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,X0,sK4) = iPr_def_16 )
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,X0,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_4517,c_940,c_4517,c_4995]) ).
tcf(c_6079,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,X0,sK4) = iPr_def_16 )
| ~ r1_tarski(sK2,X0)
| ~ r1_tarski(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5523,c_6068]) ).
tcf(c_6858,plain,
( ( k8_relset_2(sK0,sK1,iPr_def_17,sK4) = iPr_def_16 )
| ~ r1_tarski(sK2,iPr_def_17)
| ~ m1_subset_1(iPr_def_17,iPr_def_10) ),
inference(superposition,[status(thm)],[c_102,c_6079]) ).
tcf(c_6863,plain,
( ( iPr_def_16 = iPr_def_18 )
| ~ r1_tarski(sK2,iPr_def_17)
| ~ m1_subset_1(iPr_def_17,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_6858,c_2164]) ).
tcf(c_6864,plain,
( ( iPr_def_16 = iPr_def_18 )
| ~ m1_subset_1(iPr_def_17,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6863,c_5374]) ).
tcf(c_7099,plain,
( ( k8_relset_2(sK1,sK0,iPr_def_14,iPr_def_12) = iPr_def_13 )
| ~ r1_tarski(iPr_def_15,iPr_def_13)
| ~ r1_tarski(iPr_def_14,iPr_def_14)
| ~ m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_13,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2161,c_5426]) ).
tcf(c_7107,plain,
( ( iPr_def_13 = iPr_def_15 )
| ~ r1_tarski(iPr_def_15,iPr_def_13)
| ~ r1_tarski(iPr_def_14,iPr_def_14)
| ~ m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_13,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_7099,c_2161]) ).
tcf(c_7108,plain,
( ( iPr_def_13 = iPr_def_15 )
| ~ r1_tarski(iPr_def_15,iPr_def_13)
| ~ m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_13,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7107,c_102]) ).
tcf(c_7564,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12))
| ~ m1_subset_1(X1,iPr_def_10)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ r1_tarski(X1,X0)
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_4930,c_940,c_4930,c_4995]) ).
tcf(c_7581,plain,
! [X0: $i] :
( ( k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12) = iPr_def_13 )
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ r1_tarski(iPr_def_13,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(sK3,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11) ),
inference(superposition,[status(thm)],[c_7564,c_4491]) ).
tcf(c_7878,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,X0,iPr_def_12),sK4) = iPr_def_16 )
| ~ m1_subset_1(iPr_def_16,iPr_def_11)
| ~ r1_tarski(iPr_def_16,X0)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(sK2,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m1_subset_1(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5053,c_6068]) ).
tcf(c_9470,plain,
! [X0: $i] :
( ( k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12) = iPr_def_13 )
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11)
| ~ r1_tarski(sK3,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ m1_subset_1(X0,iPr_def_10)
| ~ r1_tarski(iPr_def_13,X0) ),
inference(global_subsumption_just,[status(thm)],[c_7581,c_4183,c_7581]) ).
tcf(c_9471,plain,
! [X0: $i] :
( ( k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12) = iPr_def_13 )
| ~ r1_tarski(iPr_def_13,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(sK3,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11) ),
inference(renaming,[status(thm)],[c_9470]) ).
tcf(c_9485,plain,
( ( k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,sK3,iPr_def_12),sK4),iPr_def_12) = iPr_def_13 )
| ~ m1_subset_1(sK3,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(iPr_def_13,k8_relset_2(sK1,sK0,sK3,iPr_def_12))
| ~ m1_subset_1(k8_relset_2(sK1,sK0,sK3,iPr_def_12),iPr_def_10)
| ~ m1_subset_1(k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,sK3,iPr_def_12),sK4),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5011,c_9471]) ).
tcf(c_9535,plain,
( ( iPr_def_13 = iPr_def_15 )
| ~ r1_tarski(iPr_def_13,iPr_def_13)
| ~ m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ m1_subset_1(sK3,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(light_normalisation,[status(thm)],[c_9485,c_2159,c_2160,c_2161]) ).
tcf(c_9536,plain,
( ( iPr_def_13 = iPr_def_15 )
| ~ m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9535,c_102,c_2166]) ).
tcf(c_9583,plain,
( ( iPr_def_13 = iPr_def_15 )
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_9536,c_940,c_4183,c_4178,c_4995,c_5245,c_7108]) ).
tcf(c_9876,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,X0,iPr_def_12),sK4) = iPr_def_16 )
| ~ m1_subset_1(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_10)
| ~ r1_tarski(sK2,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ m1_subset_1(X0,iPr_def_11)
| ~ r1_tarski(iPr_def_16,X0) ),
inference(global_subsumption_just,[status(thm)],[c_7878,c_940,c_4187,c_4995,c_7878]) ).
tcf(c_9877,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,X0,iPr_def_12),sK4) = iPr_def_16 )
| ~ r1_tarski(iPr_def_16,X0)
| ~ m1_subset_1(X0,iPr_def_11)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(sK2,k8_relset_2(sK1,sK0,X0,iPr_def_12))
| ~ m1_subset_1(k8_relset_2(sK1,sK0,X0,iPr_def_12),iPr_def_10) ),
inference(renaming,[status(thm)],[c_9876]) ).
tcf(c_9892,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12),sK4) = iPr_def_16 )
| ~ m1_subset_1(sK2,iPr_def_10)
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11)
| ~ m1_subset_1(k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7564,c_9877]) ).
tcf(c_9944,plain,
! [X0: $i] :
( ( k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12),sK4) = iPr_def_16 )
| ~ r1_tarski(sK2,X0)
| ~ m1_subset_1(X0,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,X0,sK4))
| ~ m1_subset_1(k8_relset_2(sK0,sK1,X0,sK4),iPr_def_11)
| ~ m1_subset_1(k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,X0,sK4),iPr_def_12),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9892,c_2165]) ).
tcf(c_10082,plain,
( ( k8_relset_2(sK0,sK1,k8_relset_2(sK1,sK0,k8_relset_2(sK0,sK1,iPr_def_13,sK4),iPr_def_12),sK4) = iPr_def_16 )
| ~ r1_tarski(sK2,iPr_def_13)
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0)))
| ~ r1_tarski(iPr_def_16,k8_relset_2(sK0,sK1,iPr_def_13,sK4))
| ~ m1_subset_1(k8_relset_2(sK1,sK0,iPr_def_14,iPr_def_12),iPr_def_10)
| ~ m1_subset_1(k8_relset_2(sK0,sK1,iPr_def_13,sK4),iPr_def_11) ),
inference(superposition,[status(thm)],[c_2160,c_9944]) ).
tcf(c_10092,plain,
( ( k8_relset_2(sK0,sK1,iPr_def_15,sK4) = iPr_def_16 )
| ~ r1_tarski(iPr_def_16,iPr_def_14)
| ~ r1_tarski(sK2,iPr_def_13)
| ~ m1_subset_1(iPr_def_15,iPr_def_10)
| ~ m1_subset_1(iPr_def_14,iPr_def_11)
| ~ m1_subset_1(iPr_def_13,iPr_def_10)
| ~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))) ),
inference(light_normalisation,[status(thm)],[c_10082,c_2160,c_2161]) ).
tcf(c_10857,plain,
( ( iPr_def_13 = iPr_def_15 )
| ~ m1_relset_1(iPr_def_12,sK1,sK0) ),
inference(superposition,[status(thm)],[c_1235,c_9583]) ).
tcf(c_10871,plain,
iPr_def_13 = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_10857,c_3882]) ).
tcf(c_10967,plain,
( ( iPr_def_16 != iPr_def_18 )
| ( iPr_def_13 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_2168,c_10871]) ).
tcf(c_10968,plain,
iPr_def_16 != iPr_def_18,
inference(equality_resolution_simp,[status(thm)],[c_10967]) ).
tcf(c_10969,plain,
~ m1_subset_1(iPr_def_17,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_6864,c_10968]) ).
tcf(c_11347,plain,
~ m1_subset_1(iPr_def_12,k1_zfmisc_1(k2_zfmisc_1(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_10092,c_940,c_4187,c_4170,c_4995,c_10969]) ).
tcf(c_11349,plain,
~ m1_relset_1(iPr_def_12,sK1,sK0),
inference(superposition,[status(thm)],[c_1235,c_11347]) ).
tcf(c_11351,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11349,c_3882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU450+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 14:18:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 8.04/1.77 % SZS status Started for theBenchmark.p
% 8.04/1.77 % SZS status Theorem for theBenchmark.p
% 8.04/1.77
% 8.04/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.04/1.77
% 8.04/1.77 % ------ iProver source info
% 8.04/1.77
% 8.04/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 8.04/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.04/1.77 % git: non_committed_changes: false
% 8.04/1.77
% 8.04/1.77 % ------ Parsing...
% 8.04/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.04/1.77
% 8.04/1.77 % ------ 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 %
% 8.04/1.77
% 8.04/1.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.04/1.77
% 8.04/1.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.04/1.77 % ------ Proving...
% 8.04/1.77 % ------ Problem Properties
% 8.04/1.77
% 8.04/1.77 %
% 8.04/1.77 % clauses 70
% 8.04/1.77 % conjectures 4
% 8.04/1.77 % EPR 24
% 8.04/1.77 % Horn 67
% 8.04/1.77 % unary 31
% 8.04/1.77 % binary 27
% 8.04/1.77 % lits 127
% 8.04/1.77 % lits eq 21
% 8.04/1.77 % fd_pure 0
% 8.04/1.77 % fd_pseudo 0
% 8.04/1.77 % fd_cond 1
% 8.04/1.77 % fd_pseudo_cond 2
% 8.04/1.77 % AC symbols 0
% 8.04/1.77
% 8.04/1.77 % ------ Schedule dynamic 5 is on
% 8.04/1.77
% 8.04/1.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.04/1.77
% 8.04/1.77
% 8.04/1.77 % ------
% 8.04/1.77 % Current options:
% 8.04/1.77 % ------
% 8.04/1.77
% 8.04/1.77
% 8.04/1.77 %
% 8.04/1.77
% 8.04/1.77 % ------ Proving...
% 8.04/1.77 %
% 8.04/1.77
% 8.04/1.77 % SZS status Theorem for theBenchmark.p
% 8.04/1.77
% 8.04/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.04/1.78
% 8.04/1.78
%------------------------------------------------------------------------------