%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU246+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 02:56:20 PM UTC 2026
% Result : Theorem 43.12s 7.50s
% Output : CNFRefutation 32.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 105 ( 7 unt; 0 def)
% Number of atoms : 470 ( 46 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 629 ( 264 ~; 283 |; 61 &)
% ( 11 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 292 ( 0 sgn 278 !; 14 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f7,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f9,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f14,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f25,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f33,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f34,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
fof(f35,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f49,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f55,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f58,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f59,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
? [X0,X1] :
( relation(X1)
& relation_restriction(X1,X0) != relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f68,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f69,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
& in(sK0(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| ~ in(sK0(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f73,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ( in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X1)
& in(sK3(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2))],[f74]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
( relation(sK13)
& relation_restriction(sK13,sK12) != relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f61]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| in(sK0(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| ~ in(sK0(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f102,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X6,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f112,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f114,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f116,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f123,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f140,plain,
relation(sK13),
inference(cnf_transformation,[],[f89]) ).
fof(f141,plain,
relation_restriction(sK13,sK12) != relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
| ~ in(sK0(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f101,f112,f112]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| in(sK0(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f100,f112]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f99,f112,f112]) ).
fof(f157,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2) ),
inference(definition_unfolding,[],[f104,f112,f112]) ).
fof(f158,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(X6,X0) ),
inference(definition_unfolding,[],[f103,f112]) ).
fof(f159,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1) ),
inference(definition_unfolding,[],[f102,f112,f112]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f136,f112]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f135,f112]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f134,f112]) ).
fof(f171,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f157]) ).
fof(f172,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| in(X6,X0) ),
inference(equality_resolution,[],[f158]) ).
fof(f173,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1) ),
inference(equality_resolution,[],[f159]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X2,X1),X2)
| in(unordered_pair(unordered_pair(sK0(X0,X2,X1),sK1(X0,X2,X1)),singleton(sK0(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK0(X0,X2,X1),sK1(X0,X2,X1)),singleton(sK0(X0,X2,X1))),X1)
| in(unordered_pair(unordered_pair(sK0(X0,X2,X1),sK1(X0,X2,X1)),singleton(sK0(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_restriction(X2,X1))
| ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,cartesian_product2(X2,X2))
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_96,negated_conjecture,
relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12) != relation_restriction(sK13,sK12),
inference(cnf_transformation,[],[f141]) ).
tcf(c_97,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f140]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_78,c_72]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_135]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_135]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_135]) ).
tcf(c_1037,plain,
! [X0: $i] :
( relation(relation_restriction(sK13,X0))
| ~ relation(sK13) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_1486,plain,
( relation(relation_restriction(sK13,sK12))
| ~ relation(sK13) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_2258,plain,
( in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| ( relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12) = relation_restriction(sK13,sK12) )
| ~ relation(relation_restriction(sK13,sK12))
| ~ relation(relation_rng_restriction(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2259,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13))
| ( relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12) = relation_restriction(sK13,sK12) )
| ~ relation(relation_restriction(sK13,sK12))
| ~ relation(relation_rng_restriction(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_2279,plain,
( relation(relation_rng_restriction(sK12,sK13))
| ~ relation(sK13) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_2360,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,X0),sK1(relation_rng_restriction(sK12,sK13),sK12,X0)),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,X0))),sK13)
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,X0),sK1(relation_rng_restriction(sK12,sK13),sK12,X0)),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,X0))),relation_rng_restriction(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_200]) ).
tcf(c_2361,plain,
! [X0: $i] :
( in(sK1(relation_rng_restriction(sK12,sK13),sK12,X0),sK12)
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,X0),sK1(relation_rng_restriction(sK12,sK13),sK12,X0)),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,X0))),relation_rng_restriction(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_199]) ).
tcf(c_2426,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(sK12,sK12))
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_2427,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_2575,plain,
( ( relation_dom_restriction(relation_rng_restriction(sK12,sK13),sK12) = relation_restriction(sK13,sK12) )
| ~ relation(relation_restriction(sK13,sK12))
| ~ relation(relation_rng_restriction(sK12,sK13))
| ~ in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_2582,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),X0),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(sK12,X1))
| ~ in(X0,X1)
| ~ in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_2597,plain,
( in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_2361]) ).
tcf(c_2598,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_2360]) ).
tcf(c_2738,plain,
( in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(sK12,sK12)) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_2739,plain,
( in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(sK12,sK12)) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_2765,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,X0))
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(X0,X0)) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_3305,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK1(relation_rng_restriction(sK12,sK13),sK12,X1)),singleton(X0)),relation_rng_restriction(sK12,X2))
| ~ relation(X2)
| ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,X1),sK12)
| ~ in(unordered_pair(unordered_pair(X0,sK1(relation_rng_restriction(sK12,sK13),sK12,X1)),singleton(X0)),X2) ),
inference(instantiation,[status(thm)],[c_201]) ).
tcf(c_4145,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,X0)),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(sK12,sK12))
| ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,X0),sK12)
| ~ in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12) ),
inference(instantiation,[status(thm)],[c_2582]) ).
tcf(c_4161,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_restriction(sK13,sK12))
| ~ relation(sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(sK12,sK12)) ),
inference(instantiation,[status(thm)],[c_2765]) ).
tcf(c_4241,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,X0),sK1(relation_rng_restriction(sK12,sK13),sK12,X0)),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,X0))),relation_rng_restriction(sK12,sK13))
| ~ relation(sK13)
| ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,X0),sK12)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,X0),sK1(relation_rng_restriction(sK12,sK13),sK12,X0)),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,X0))),sK13) ),
inference(instantiation,[status(thm)],[c_3305]) ).
tcf(c_7649,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),relation_rng_restriction(sK12,sK13))
| ~ relation(sK13)
| ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),sK13) ),
inference(instantiation,[status(thm)],[c_4241]) ).
tcf(c_13097,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12))),singleton(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)))),cartesian_product2(sK12,sK12))
| ~ in(sK1(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12)
| ~ in(sK0(relation_rng_restriction(sK12,sK13),sK12,relation_restriction(sK13,sK12)),sK12) ),
inference(instantiation,[status(thm)],[c_4145]) ).
tcf(c_13103,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13097,c_7649,c_4161,c_2738,c_2739,c_2597,c_2598,c_2575,c_2426,c_2427,c_2279,c_2259,c_2258,c_1486,c_96,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU246+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:23:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.46 % Proving...
% 43.12/7.50 % SZS status Started for theBenchmark.p
% 43.12/7.50 % SZS status Theorem for theBenchmark.p
% 43.12/7.50
% 43.12/7.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 43.12/7.50
% 43.12/7.50 % ------ iProver source info
% 43.12/7.50
% 43.12/7.50 % git: date: 2026-07-19 20:42:38 +0200
% 43.12/7.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 43.12/7.50 % git: non_committed_changes: false
% 43.12/7.50
% 43.12/7.50 % ------ Parsing...
% 43.12/7.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 43.12/7.50
% 43.12/7.50 % ------ Preprocessing...%
% 43.12/7.50
% 43.12/7.50 % ------ Preprocessing...%
% 43.12/7.50
% 43.12/7.50 % ------ Preprocessing...
% 43.12/7.50 % ------ Proving...
% 43.12/7.50 % ------ Problem Properties
% 43.12/7.50
% 43.12/7.50 %
% 43.12/7.50 % clauses 51
% 43.12/7.50 % conjectures 2
% 43.12/7.50 % EPR 18
% 43.12/7.50 % Horn 45
% 43.12/7.50 % unary 18
% 43.12/7.50 % binary 11
% 43.12/7.50 % lits 127
% 43.12/7.50 % lits eq 16
% 43.12/7.50 % fd_pure 0
% 43.12/7.50 % fd_pseudo 0
% 43.12/7.50 % fd_cond 1
% 43.12/7.50 % fd_pseudo_cond 9
% 43.12/7.50 % AC symbols 0
% 43.12/7.50
% 43.12/7.50 % ------ Input Options Time Limit: Unbounded
% 43.12/7.50
% 43.12/7.50
% 43.12/7.50 % ------
% 43.12/7.50 % Current options:
% 43.12/7.50 % ------
% 43.12/7.50
% 43.12/7.50
% 43.12/7.50 %
% 43.12/7.50
% 43.12/7.50 % ------ Proving...
% 43.12/7.50 %
% 43.12/7.50
% 43.12/7.50 % SZS status Theorem for theBenchmark.p
% 43.12/7.50
% 43.12/7.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.42/7.50
% 32.42/7.50
%------------------------------------------------------------------------------