%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU202+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:55:52 PM UTC 2026
% Result : Theorem 1.33s 1.75s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 99 ( 10 unt; 0 def)
% Number of atoms : 466 ( 58 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 649 ( 282 ~; 305 |; 46 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 303 ( 0 sgn 288 !; 15 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,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/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f5,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/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f12,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f25,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f34,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,[],[f4]) ).
fof(f35,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,[],[f5]) ).
fof(f37,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f38,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f39,plain,
? [X0,X1,X2] :
( relation(X2)
& relation_dom_restriction(relation_rng_restriction(X0,X2),X1) != relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f46,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,[],[f34]) ).
fof(f47,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,[],[f46]) ).
fof(f48,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,[],[f47]) ).
fof(f49,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))],[f48]) ).
fof(f50,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,[],[f35]) ).
fof(f51,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,[],[f50]) ).
fof(f52,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,[],[f51]) ).
fof(f53,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))],[f52]) ).
fof(f62,plain,
( relation(sK13)
& relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) != relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f39]) ).
fof(f65,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f66,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f67,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X5,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f68,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f69,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,[],[f49]) ).
fof(f70,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,[],[f49]) ).
fof(f71,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,[],[f49]) ).
fof(f72,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,[],[f53]) ).
fof(f73,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,[],[f53]) ).
fof(f74,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,[],[f53]) ).
fof(f82,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f83,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f84,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f98,plain,
relation(sK13),
inference(cnf_transformation,[],[f62]) ).
fof(f99,plain,
relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) != relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)),
inference(cnf_transformation,[],[f62]) ).
fof(f105,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,[],[f71,f82,f82]) ).
fof(f106,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,[],[f70,f82]) ).
fof(f107,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,[],[f69,f82,f82]) ).
fof(f108,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2) ),
inference(definition_unfolding,[],[f68,f82,f82]) ).
fof(f109,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(X5,X1) ),
inference(definition_unfolding,[],[f67,f82]) ).
fof(f110,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f66,f82,f82]) ).
fof(f114,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,[],[f74,f82,f82]) ).
fof(f115,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,[],[f73,f82]) ).
fof(f116,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,[],[f72,f82,f82]) ).
fof(f122,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1)) ),
inference(equality_resolution,[],[f108]) ).
fof(f123,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(X5,X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f124,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f125,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,[],[f114]) ).
fof(f126,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,[],[f115]) ).
fof(f127,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,[],[f116]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f65]) ).
tcf(c_52,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,[],[f105]) ).
tcf(c_53,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,[],[f106]) ).
tcf(c_54,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,[],[f107]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_61,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,[],[f125]) ).
tcf(c_62,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,[],[f126]) ).
tcf(c_63,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,[],[f127]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_83,negated_conjecture,
relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) != relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)),
inference(cnf_transformation,[],[f99]) ).
tcf(c_84,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f98]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_68]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_68]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_68]) ).
tcf(c_158,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_62,c_69]) ).
tcf(c_159,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_63,c_69]) ).
tcf(c_160,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_61,c_69]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_rng_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_158,c_51]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_149,c_51]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_rng_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_159,c_51]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_150,c_51]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_160,c_51]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_151,c_51]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X2,X1),X2)
| in(unordered_pair(singleton(sK0(X0,X2,X1)),unordered_pair(sK0(X0,X2,X1),sK1(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_53,c_51]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(sK0(X0,X2,X1)),unordered_pair(sK0(X0,X2,X1),sK1(X0,X2,X1))),X1)
| in(unordered_pair(singleton(sK0(X0,X2,X1)),unordered_pair(sK0(X0,X2,X1),sK1(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_54,c_51]) ).
tcf(c_328,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(singleton(sK0(X0,X1,X2)),unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2))),X2)
| ~ in(unordered_pair(singleton(sK0(X0,X1,X2)),unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2))),X0) ),
inference(demodulation,[status(thm)],[c_52,c_51]) ).
tcf(c_1051,plain,
( ( relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) = relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)) )
| ~ relation(relation_rng_restriction(sK11,sK13))
| ~ relation(relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))
| ~ in(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK12)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,sK13))
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_328]) ).
tcf(c_1052,plain,
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,sK13))
| in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))
| ( relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) = relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)) )
| ~ relation(relation_rng_restriction(sK11,sK13))
| ~ relation(relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_326]) ).
tcf(c_1053,plain,
( in(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK12)
| in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))
| ( relation_dom_restriction(relation_rng_restriction(sK11,sK13),sK12) = relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)) )
| ~ relation(relation_rng_restriction(sK11,sK13))
| ~ relation(relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_1138,plain,
( relation(relation_rng_restriction(sK11,sK13))
| ~ relation(sK13) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1148,plain,
( relation(relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))
| ~ relation(relation_dom_restriction(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1250,plain,
( relation(relation_dom_restriction(sK13,sK12))
| ~ relation(sK13) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1358,plain,
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_dom_restriction(sK13,sK12))
| ~ relation(relation_dom_restriction(sK13,sK12))
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_317]) ).
tcf(c_1359,plain,
( in(sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK11)
| ~ relation(relation_dom_restriction(sK13,sK12))
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_315]) ).
tcf(c_2279,plain,
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),sK13)
| ~ relation(sK13)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,sK13)) ),
inference(instantiation,[status(thm)],[c_317]) ).
tcf(c_2280,plain,
( in(sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK11)
| ~ relation(sK13)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,sK13)) ),
inference(instantiation,[status(thm)],[c_315]) ).
tcf(c_3449,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),X0)),relation_dom_restriction(X1,sK12))
| ~ relation(X1)
| ~ in(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK12)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),X0)),X1) ),
inference(instantiation,[status(thm)],[c_320]) ).
tcf(c_3677,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,X1))
| ~ relation(X1)
| ~ in(sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),X1) ),
inference(instantiation,[status(thm)],[c_319]) ).
tcf(c_3723,plain,
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),sK13)
| ~ relation(sK13)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_dom_restriction(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_318]) ).
tcf(c_3724,plain,
( in(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK12)
| ~ relation(sK13)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_dom_restriction(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_6475,plain,
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))
| ~ relation(relation_dom_restriction(sK13,sK12))
| ~ in(sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK11)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_dom_restriction(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_3677]) ).
tcf(c_7093,plain,
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_dom_restriction(sK13,sK12))
| ~ relation(sK13)
| ~ in(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK12)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),sK13) ),
inference(instantiation,[status(thm)],[c_3449]) ).
tcf(c_7095,plain,
( in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),relation_rng_restriction(sK11,sK13))
| ~ relation(sK13)
| ~ in(sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK11)
| ~ in(unordered_pair(singleton(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12)))),unordered_pair(sK0(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))),sK1(relation_rng_restriction(sK11,sK13),sK12,relation_rng_restriction(sK11,relation_dom_restriction(sK13,sK12))))),sK13) ),
inference(instantiation,[status(thm)],[c_3677]) ).
tcf(c_7142,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7095,c_7093,c_6475,c_3723,c_3724,c_2279,c_2280,c_1358,c_1359,c_1250,c_1148,c_1138,c_1052,c_1053,c_1051,c_83,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 13:10:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.33/1.75 % SZS status Started for theBenchmark.p
% 1.33/1.75 % SZS status Theorem for theBenchmark.p
% 1.33/1.75
% 1.33/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.33/1.75
% 1.33/1.75 % ------ iProver source info
% 1.33/1.75
% 1.33/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 1.33/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.33/1.75 % git: non_committed_changes: false
% 1.33/1.75
% 1.33/1.75 % ------ Parsing...
% 1.33/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.33/1.75
% 1.33/1.75 % ------ Preprocessing... sup_sim: 14 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 %
% 1.33/1.75
% 1.33/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.33/1.75
% 1.33/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.33/1.75 % ------ Proving...
% 1.33/1.75 % ------ Problem Properties
% 1.33/1.75
% 1.33/1.75 %
% 1.33/1.75 % clauses 35
% 1.33/1.75 % conjectures 2
% 1.33/1.75 % EPR 14
% 1.33/1.75 % Horn 29
% 1.33/1.75 % unary 13
% 1.33/1.75 % binary 7
% 1.33/1.75 % lits 92
% 1.33/1.75 % lits eq 12
% 1.33/1.75 % fd_pure 0
% 1.33/1.75 % fd_pseudo 0
% 1.33/1.75 % fd_cond 1
% 1.33/1.75 % fd_pseudo_cond 9
% 1.33/1.75 % AC symbols 0
% 1.33/1.75
% 1.33/1.75 % ------ Input Options Time Limit: Unbounded
% 1.33/1.75
% 1.33/1.75
% 1.33/1.75 % ------
% 1.33/1.75 % Current options:
% 1.33/1.75 % ------
% 1.33/1.75
% 1.33/1.75
% 1.33/1.75 %
% 1.33/1.75
% 1.33/1.75 % ------ Proving...
% 1.33/1.75 %
% 1.33/1.75
% 1.33/1.75 % SZS status Theorem for theBenchmark.p
% 1.33/1.75
% 1.33/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.33/1.76
% 1.33/1.76
%------------------------------------------------------------------------------