%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU190+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 : n016.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 02:55:49 PM UTC 2026
% Result : Theorem 9.78s 2.26s
% Output : CNFRefutation 9.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 127 ( 21 unt; 3 def)
% Number of atoms : 537 ( 130 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 528 ( 225 ~; 241 |; 44 &)
% ( 13 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 1 con; 0-2 aty)
% Number of variables : 277 ( 0 sgn 252 !; 25 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f7,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] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f32,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f34,conjecture,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f40,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f32]) ).
fof(f54,plain,
? [X0] :
( relation_rng(identity_relation(X0)) != X0
| relation_dom(identity_relation(X0)) != X0 ),
inference(ennf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f58,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ( sK0(X0,X1) = sK1(X0,X1)
& in(sK0(X0,X1),X0) ) )
& ( ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK4(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0) )
& ( ~ in(sK2(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK2(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK7(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK5(X0,X1),X1)
| in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) )
& ( ~ in(sK5(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X7,sK7(X0,X5))],[f65]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f52]) ).
fof(f73,plain,
! [X0,X1] :
( ( ( in(sK13(X0,X1),X0)
| in(sK13(X0,X1),X1) )
& ( ~ in(sK13(X0,X1),X0)
| ~ in(sK13(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f72]) ).
fof(f74,plain,
( sK14 != relation_rng(identity_relation(sK14))
| sK14 != relation_dom(identity_relation(sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f54]) ).
fof(f77,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f78,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f60]) ).
fof(f79,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f80,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK4(X0,X5)),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f85,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f88,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK7(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f89,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f92,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f93,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f115,plain,
! [X0,X1] :
( in(sK13(X0,X1),X0)
| in(sK13(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f116,plain,
! [X0,X1] :
( ~ in(sK13(X0,X1),X0)
| ~ in(sK13(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f118,plain,
( sK14 != relation_rng(identity_relation(sK14))
| sK14 != relation_dom(identity_relation(sK14)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f124,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1) ),
inference(definition_unfolding,[],[f80,f92]) ).
fof(f125,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| in(X4,X0) ),
inference(definition_unfolding,[],[f79,f92]) ).
fof(f126,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| X4 = X5 ),
inference(definition_unfolding,[],[f78,f92]) ).
fof(f129,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f85,f92]) ).
fof(f130,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK4(X0,X5)),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f84,f92]) ).
fof(f133,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f89,f92]) ).
fof(f134,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0) ),
inference(definition_unfolding,[],[f88,f92]) ).
fof(f136,plain,
! [X0,X1,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),X1) ),
inference(equality_resolution,[],[f124]) ).
fof(f137,plain,
! [X0,X5] :
( ~ relation(identity_relation(X0))
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),identity_relation(X0)) ),
inference(equality_resolution,[],[f136]) ).
fof(f138,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),identity_relation(X0))
| in(X4,X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f139,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),identity_relation(X0))
| X4 = X5 ),
inference(equality_resolution,[],[f126]) ).
fof(f140,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f129]) ).
fof(f141,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK4(X0,X5)),singleton(X5)),X0) ),
inference(equality_resolution,[],[f130]) ).
fof(f142,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f133]) ).
fof(f143,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0) ),
inference(equality_resolution,[],[f134]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f77]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK4(X1,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK7(X1,X0),X0),singleton(sK7(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_66,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f93]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| in(sK13(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_91,negated_conjecture,
( ( relation_rng(identity_relation(sK14)) != sK14 )
| ( relation_dom(identity_relation(sK14)) != sK14 ) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_66]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_66]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_66]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),identity_relation(X2)) ),
inference(demodulation,[status(thm)],[c_138,c_51]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_137,c_51]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),identity_relation(X2)) ),
inference(demodulation,[status(thm)],[c_139,c_51]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_64,c_51]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_61,c_51]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK7(X1,X0)),unordered_pair(X0,sK7(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(demodulation,[status(thm)],[c_65,c_51]) ).
tcf(c_2895,definition,
iPr_def_10 = identity_relation(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2896,definition,
iPr_def_11 = relation_dom(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2897,definition,
iPr_def_12 = relation_rng(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2898,negated_conjecture,
( ( iPr_def_12 != sK14 )
| ( iPr_def_11 != sK14 ) ),
inference(demodulation,[status(thm)],[c_91,c_2897,c_2895,c_2896]) ).
tcf(c_2899,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2901,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3828,plain,
( ( iPr_def_11 = sK14 )
| ~ in(sK13(iPr_def_11,sK14),iPr_def_11)
| ~ in(sK13(iPr_def_11,sK14),sK14) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_4902,plain,
! [X0: $i,X1: $i] :
( ( sK14 = X0 )
| ( sK14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2901]) ).
tcf(c_7845,plain,
! [X0: $i] :
( ( sK14 = X0 )
| ( sK14 != sK14 )
| ( X0 != sK14 ) ),
inference(instantiation,[status(thm)],[c_4902]) ).
tcf(c_7846,plain,
sK14 = sK14,
inference(instantiation,[status(thm)],[c_2899]) ).
tcf(c_14871,plain,
( ( sK14 = iPr_def_11 )
| ( iPr_def_11 != sK14 )
| ( sK14 != sK14 ) ),
inference(instantiation,[status(thm)],[c_7845]) ).
tcf(c_21470,plain,
relation(iPr_def_10),
inference(superposition,[status(thm)],[c_2895,c_66]) ).
tcf(c_21829,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2895,c_396]) ).
tcf(c_21854,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(identity_relation(X1)))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_389,c_419]) ).
tcf(c_21857,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(identity_relation(X1)))
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21854,c_66]) ).
tcf(c_21869,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(identity_relation(X1)))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_389,c_429]) ).
tcf(c_21870,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_51,c_429]) ).
tcf(c_21872,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(identity_relation(X1)))
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21869,c_66]) ).
tcf(c_21898,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_51,c_21829]) ).
tcf(c_21921,plain,
! [X0: $i] :
( in(X0,relation_rng(iPr_def_10))
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_2895,c_21857]) ).
tcf(c_21929,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,sK14) ),
inference(light_normalisation,[status(thm)],[c_21921,c_2897]) ).
tcf(c_21959,plain,
! [X0: $i] :
( in(sK13(sK14,X0),iPr_def_12)
| in(sK13(sK14,X0),X0)
| ( X0 = sK14 ) ),
inference(superposition,[status(thm)],[c_89,c_21929]) ).
tcf(c_21990,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_2895,c_21872]) ).
tcf(c_21998,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,sK14) ),
inference(light_normalisation,[status(thm)],[c_21990,c_2896]) ).
tcf(c_22027,plain,
! [X0: $i] :
( in(sK13(X0,sK14),iPr_def_11)
| in(sK13(X0,sK14),X0)
| ( X0 = sK14 ) ),
inference(superposition,[status(thm)],[c_89,c_21998]) ).
tcf(c_22065,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ relation(identity_relation(X1))
| ~ in(X0,relation_dom(identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_439,c_382]) ).
tcf(c_22077,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,relation_dom(identity_relation(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22065,c_66]) ).
tcf(c_22112,plain,
! [X0: $i] :
( ( sK7(iPr_def_10,X0) = X0 )
| ~ relation(iPr_def_10)
| ~ in(X0,relation_rng(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_449,c_21898]) ).
tcf(c_22119,plain,
! [X0: $i] :
( ( sK7(iPr_def_10,X0) = X0 )
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_22112,c_2897]) ).
tcf(c_22120,plain,
! [X0: $i] :
( ( sK7(iPr_def_10,X0) = X0 )
| ~ in(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22119,c_21470]) ).
tcf(c_22346,plain,
! [X0: $i] :
( in(X0,sK14)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_2895,c_22077]) ).
tcf(c_22347,plain,
! [X0: $i] :
( in(X0,sK14)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_22346,c_2896]) ).
tcf(c_23836,plain,
( in(sK13(sK14,iPr_def_12),iPr_def_12)
| ( sK14 = iPr_def_12 ) ),
inference(equality_factoring,[status(thm)],[c_21959]) ).
tcf(c_24098,plain,
( ( sK14 = iPr_def_12 )
| ~ in(sK13(sK14,iPr_def_12),sK14) ),
inference(superposition,[status(thm)],[c_23836,c_88]) ).
tcf(c_34437,plain,
( in(sK13(iPr_def_11,sK14),iPr_def_11)
| ( sK14 = iPr_def_11 ) ),
inference(equality_factoring,[status(thm)],[c_22027]) ).
tcf(c_36564,plain,
( in(sK13(iPr_def_11,sK14),sK14)
| ( sK14 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_34437,c_22347]) ).
tcf(c_36571,plain,
sK14 = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_36564,c_3828,c_7846,c_14871,c_34437,c_36564]) ).
tcf(c_36576,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ in(sK13(iPr_def_11,iPr_def_12),iPr_def_11) ),
inference(demodulation,[status(thm)],[c_24098,c_36571]) ).
tcf(c_36581,plain,
( in(sK13(iPr_def_11,iPr_def_12),iPr_def_12)
| ( iPr_def_11 = iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_23836,c_36571]) ).
tcf(c_36636,plain,
( ( iPr_def_11 != iPr_def_12 )
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_2898,c_36571]) ).
tcf(c_36651,plain,
iPr_def_11 != iPr_def_12,
inference(equality_resolution_simp,[status(thm)],[c_36636]) ).
tcf(c_36653,plain,
in(sK13(iPr_def_11,iPr_def_12),iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_36581,c_36651]) ).
tcf(c_36658,plain,
~ in(sK13(iPr_def_11,iPr_def_12),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_36576,c_36651]) ).
tcf(c_36682,plain,
sK7(iPr_def_10,sK13(iPr_def_11,iPr_def_12)) = sK13(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_36653,c_22120]) ).
tcf(c_38342,plain,
( in(unordered_pair(singleton(sK13(iPr_def_11,iPr_def_12)),unordered_pair(sK13(iPr_def_11,iPr_def_12),sK13(iPr_def_11,iPr_def_12))),iPr_def_10)
| ~ relation(iPr_def_10)
| ~ in(sK13(iPr_def_11,iPr_def_12),relation_rng(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_36682,c_449]) ).
tcf(c_38343,plain,
( in(unordered_pair(singleton(sK13(iPr_def_11,iPr_def_12)),unordered_pair(sK13(iPr_def_11,iPr_def_12),sK13(iPr_def_11,iPr_def_12))),iPr_def_10)
| ~ relation(iPr_def_10)
| ~ in(sK13(iPr_def_11,iPr_def_12),iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_38342,c_2897]) ).
tcf(c_38344,plain,
in(unordered_pair(singleton(sK13(iPr_def_11,iPr_def_12)),unordered_pair(sK13(iPr_def_11,iPr_def_12),sK13(iPr_def_11,iPr_def_12))),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_38343,c_21470,c_36653]) ).
tcf(c_38525,plain,
( in(sK13(iPr_def_11,iPr_def_12),relation_dom(iPr_def_10))
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_38344,c_21870]) ).
tcf(c_38529,plain,
( in(sK13(iPr_def_11,iPr_def_12),iPr_def_11)
| ~ relation(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_38525,c_2896]) ).
tcf(c_38530,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_38529,c_36658,c_21470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU190+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 : n016.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 13:11:42 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
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 9.78/2.26 % SZS status Started for theBenchmark.p
% 9.78/2.26 % SZS status Theorem for theBenchmark.p
% 9.78/2.26
% 9.78/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.78/2.26
% 9.78/2.26 % ------ iProver source info
% 9.78/2.26
% 9.78/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 9.78/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.78/2.26 % git: non_committed_changes: false
% 9.78/2.26
% 9.78/2.26 % ------ Parsing...
% 9.78/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.78/2.26
% 9.78/2.26 % ------ 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 %
% 9.78/2.26
% 9.78/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.78/2.26
% 9.78/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.78/2.26 % ------ Proving...
% 9.78/2.26 % ------ Problem Properties
% 9.78/2.26
% 9.78/2.26 %
% 9.78/2.26 % clauses 44
% 9.78/2.26 % conjectures 1
% 9.78/2.26 % EPR 14
% 9.78/2.26 % Horn 38
% 9.78/2.26 % unary 15
% 9.78/2.26 % binary 13
% 9.78/2.26 % lits 97
% 9.78/2.26 % lits eq 20
% 9.78/2.26 % fd_pure 0
% 9.78/2.26 % fd_pseudo 0
% 9.78/2.26 % fd_cond 1
% 9.78/2.26 % fd_pseudo_cond 11
% 9.78/2.26 % AC symbols 0
% 9.78/2.26
% 9.78/2.26 % ------ Schedule dynamic 5 is on
% 9.78/2.26
% 9.78/2.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.78/2.26
% 9.78/2.26
% 9.78/2.26 % ------
% 9.78/2.26 % Current options:
% 9.78/2.26 % ------
% 9.78/2.26
% 9.78/2.26
% 9.78/2.26 %
% 9.78/2.26
% 9.78/2.26 % ------ Proving...
% 9.78/2.26 %
% 9.78/2.26
% 9.78/2.26 % SZS status Theorem for theBenchmark.p
% 9.78/2.26
% 9.78/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.78/2.26
% 9.78/2.26
%------------------------------------------------------------------------------