%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU181+2 : 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 : n026.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 02:55:47 PM UTC 2026
% Result : Theorem 79.21s 21.67s
% Output : CNFRefutation 79.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 92 ( 8 unt; 0 def)
% Number of atoms : 380 ( 69 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 499 ( 211 ~; 233 |; 34 &)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 15 ( 15 usr; 1 con; 0-2 aty)
% Number of variables : 208 ( 0 sgn 187 !; 21 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f18,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(f22,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(f24,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(f26,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f44,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f102,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f115,conjecture,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f116,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
fof(f143,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f173,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f174,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f177,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f182,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(ennf_transformation,[],[f102]) ).
fof(f224,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(flattening,[],[f223]) ).
fof(f237,plain,
? [X0] :
( relation(X0)
& ( relation_dom(X0) != relation_rng(relation_inverse(X0))
| relation_rng(X0) != relation_dom(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f116]) ).
fof(f307,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,[],[f173]) ).
fof(f308,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,[],[f307]) ).
fof(f309,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK20(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK18(X0,X1),X1)
| in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0) )
& ( ~ in(sK18(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK18(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X2,sK18(X0,X1)),skolemize(X4,sK19(X0,X1)),skolemize(X7,sK20(X0,X5))],[f308]) ).
fof(f317,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,[],[f174]) ).
fof(f318,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,[],[f317]) ).
fof(f319,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK27(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK25(X0,X1),X1)
| in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0) )
& ( ~ in(sK25(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X2,sK25(X0,X1)),skolemize(X4,sK26(X0,X1)),skolemize(X7,sK27(X0,X5))],[f318]) ).
fof(f320,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f177]) ).
fof(f321,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(rectify,[],[f320]) ).
fof(f322,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK28(X0,X1),sK29(X0,X1)),X1)
| in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0) )
& ( ~ in(ordered_pair(sK28(X0,X1),sK29(X0,X1)),X1)
| ~ in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29]),skolemize(X2,sK28(X0,X1)),skolemize(X3,sK29(X0,X1))],[f321]) ).
fof(f346,plain,
( relation(sK40)
& ( relation_dom(sK40) != relation_rng(relation_inverse(sK40))
| relation_rng(sK40) != relation_dom(relation_inverse(sK40)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X0,sK40)],[f237]) ).
fof(f422,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK20(X0,X5)),X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f424,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK18(X0,X1),X1)
| in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f309]) ).
fof(f425,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK18(X0,X1),X1)
| ~ in(ordered_pair(sK18(X0,X1),X3),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f309]) ).
fof(f439,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK27(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f441,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK25(X0,X1),X1)
| in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f319]) ).
fof(f442,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK25(X0,X1),X1)
| ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f319]) ).
fof(f444,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f446,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) ),
inference(cnf_transformation,[],[f322]) ).
fof(f447,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f322]) ).
fof(f460,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f182]) ).
fof(f530,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f224]) ).
fof(f531,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f224]) ).
fof(f548,plain,
relation(sK40),
inference(cnf_transformation,[],[f346]) ).
fof(f549,plain,
( relation_dom(sK40) != relation_rng(relation_inverse(sK40))
| relation_rng(sK40) != relation_dom(relation_inverse(sK40)) ),
inference(cnf_transformation,[],[f346]) ).
fof(f588,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f143]) ).
fof(f605,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f444,f588]) ).
fof(f623,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK18(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK18(X0,X1),X3),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f425,f605]) ).
fof(f624,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK18(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK18(X0,X1),sK19(X0,X1)),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f424,f605]) ).
fof(f626,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f422,f605]) ).
fof(f627,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK25(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(X3,sK25(X0,X1)),unordered_pair(X3,X3)),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f442,f605]) ).
fof(f628,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK25(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f441,f605]) ).
fof(f630,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0) ),
inference(definition_unfolding,[],[f439,f605]) ).
fof(f633,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f447,f605,f605]) ).
fof(f634,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f446,f605,f605]) ).
fof(f659,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_dom(X2)) ),
inference(definition_unfolding,[],[f531,f605]) ).
fof(f660,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_rng(X2)) ),
inference(definition_unfolding,[],[f530,f605]) ).
fof(f713,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f626]) ).
fof(f721,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0) ),
inference(equality_resolution,[],[f630]) ).
fof(f722,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0)) ),
inference(equality_resolution,[],[f633]) ).
fof(f723,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f634]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK18(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK18(X0,X1),X2),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0) ),
inference(cnf_transformation,[],[f623]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( in(sK18(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK18(X0,X1),sK19(X0,X1)),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f624]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK20(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f713]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X1) = X2 )
| ~ relation(X1)
| ~ in(sK25(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X0,sK25(X1,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f627]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f628]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK27(X1,X0),X0),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f721]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2))
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f722]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2)) ),
inference(cnf_transformation,[],[f723]) ).
tcf(c_148,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f460]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f659]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f660]) ).
tcf(c_236,negated_conjecture,
( ( relation_rng(relation_inverse(sK40)) != relation_dom(sK40) )
| ( relation_dom(relation_inverse(sK40)) != relation_rng(sK40) ) ),
inference(cnf_transformation,[],[f549]) ).
tcf(c_237,negated_conjecture,
relation(sK40),
inference(cnf_transformation,[],[f548]) ).
tcf(c_520,plain,
( relation(relation_inverse(sK40))
| ~ relation(sK40) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_748,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(X0,sK20(sK40,X0)),unordered_pair(X0,X0)),sK40)
| ~ relation(sK40)
| ~ in(X0,relation_dom(sK40)) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_792,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK27(sK40,X0),X0),unordered_pair(sK27(sK40,X0),sK27(sK40,X0))),sK40)
| ~ relation(sK40)
| ~ in(X0,relation_rng(sK40)) ),
inference(instantiation,[status(thm)],[c_131]) ).
tcf(c_2490,plain,
( in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40))
| in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40))
| ( relation_dom(relation_inverse(sK40)) = relation_rng(sK40) )
| ~ relation(relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_6675,plain,
! [X0: $i] :
( in(sK25(relation_inverse(sK40),X0),X0)
| in(unordered_pair(unordered_pair(sK26(relation_inverse(sK40),X0),sK25(relation_inverse(sK40),X0)),unordered_pair(sK26(relation_inverse(sK40),X0),sK26(relation_inverse(sK40),X0))),relation_inverse(sK40))
| ( relation_rng(relation_inverse(sK40)) = X0 )
| ~ relation(relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_6948,plain,
( in(unordered_pair(unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40)))),sK40)
| ~ relation(sK40)
| ~ relation(relation_inverse(sK40))
| ~ in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_7571,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(X0,sK27(sK40,X0)),unordered_pair(X0,X0)),relation_inverse(sK40))
| ~ relation(sK40)
| ~ relation(relation_inverse(sK40))
| ~ in(unordered_pair(unordered_pair(sK27(sK40,X0),X0),unordered_pair(sK27(sK40,X0),sK27(sK40,X0))),sK40) ),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_12410,plain,
( in(unordered_pair(unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))))),sK40)
| ~ relation(sK40)
| ~ in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40)) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_20444,plain,
( in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40)))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40))
| ~ relation(sK40)
| ~ relation(relation_inverse(sK40))
| ~ in(unordered_pair(unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))))),sK40) ),
inference(instantiation,[status(thm)],[c_7571]) ).
tcf(c_27245,plain,
( in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40))
| ~ relation(sK40)
| ~ in(unordered_pair(unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40)))),sK40) ),
inference(instantiation,[status(thm)],[c_219]) ).
tcf(c_47952,plain,
( in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| in(unordered_pair(unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40)))),relation_inverse(sK40))
| ( relation_rng(relation_inverse(sK40)) = relation_dom(sK40) )
| ~ relation(relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_6675]) ).
tcf(c_47953,plain,
( in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40)))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40)
| ~ relation(sK40)
| ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40)) ),
inference(instantiation,[status(thm)],[c_748]) ).
tcf(c_74775,plain,
( in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_rng(relation_inverse(sK40)))
| ~ relation(relation_inverse(sK40))
| ~ in(unordered_pair(unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40)))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_219]) ).
tcf(c_74783,plain,
( in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40)
| ~ relation(sK40)
| ~ relation(relation_inverse(sK40))
| ~ in(unordered_pair(unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40)))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_76985,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK40)) = relation_dom(sK40) )
| ~ relation(relation_inverse(sK40))
| ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| ~ in(unordered_pair(unordered_pair(X0,sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(X0,X0)),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_80418,plain,
( in(unordered_pair(unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))))),relation_inverse(sK40))
| ~ relation(sK40)
| ~ relation(relation_inverse(sK40))
| ~ in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40)))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40) ),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_80892,plain,
( in(unordered_pair(unordered_pair(sK27(relation_inverse(sK40),sK25(relation_inverse(sK40),relation_dom(sK40))),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK27(relation_inverse(sK40),sK25(relation_inverse(sK40),relation_dom(sK40))),sK27(relation_inverse(sK40),sK25(relation_inverse(sK40),relation_dom(sK40))))),relation_inverse(sK40))
| ~ relation(relation_inverse(sK40))
| ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_rng(relation_inverse(sK40))) ),
inference(instantiation,[status(thm)],[c_131]) ).
tcf(c_80962,plain,
( in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| ~ relation(sK40)
| ~ in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40) ),
inference(instantiation,[status(thm)],[c_218]) ).
tcf(c_87631,plain,
( ( relation_rng(relation_inverse(sK40)) = relation_dom(sK40) )
| ~ relation(relation_inverse(sK40))
| ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| ~ in(unordered_pair(unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_76985]) ).
tcf(c_88462,plain,
( ( relation_rng(relation_inverse(sK40)) = relation_dom(sK40) )
| ~ relation(relation_inverse(sK40))
| ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| ~ in(unordered_pair(unordered_pair(sK27(relation_inverse(sK40),sK25(relation_inverse(sK40),relation_dom(sK40))),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK27(relation_inverse(sK40),sK25(relation_inverse(sK40),relation_dom(sK40))),sK27(relation_inverse(sK40),sK25(relation_inverse(sK40),relation_dom(sK40))))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_76985]) ).
tcf(c_92913,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK40)) = relation_rng(sK40) )
| ~ relation(relation_inverse(sK40))
| ~ in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40))
| ~ in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),X0),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_124808,plain,
( ( relation_dom(relation_inverse(sK40)) = relation_rng(sK40) )
| ~ relation(relation_inverse(sK40))
| ~ in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40))
| ~ in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40)))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_92913]) ).
tcf(c_124809,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_124808,c_88462,c_87631,c_80962,c_80892,c_80418,c_74783,c_74775,c_47953,c_47952,c_27245,c_20444,c_12410,c_6948,c_2490,c_520,c_236,c_237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU181+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Thu Sep 24 13:07:54 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 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
% 0.14/0.47
% 0.14/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.47
% 0.14/0.47 % Detected problem language: tptp
% 0.14/0.49 % Proving...
% 79.21/21.67 % SZS status Started for theBenchmark.p
% 79.21/21.67 % SZS status Theorem for theBenchmark.p
% 79.21/21.67
% 79.21/21.67 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 79.21/21.67
% 79.21/21.67 % ------ iProver source info
% 79.21/21.67
% 79.21/21.67 % git: date: 2026-07-19 20:42:38 +0200
% 79.21/21.67 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 79.21/21.67 % git: non_committed_changes: false
% 79.21/21.67
% 79.21/21.67 % ------ Parsing...
% 79.21/21.67 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 79.21/21.67
% 79.21/21.67 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 79.21/21.67
% 79.21/21.67 % ------ Preprocessing...%
% 79.21/21.67
% 79.21/21.67 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 79.21/21.67 % ------ Proving...
% 79.21/21.67 % ------ Problem Properties
% 79.21/21.67
% 79.21/21.67 %
% 79.21/21.67 % clauses 223
% 79.21/21.67 % conjectures 2
% 79.21/21.67 % EPR 28
% 79.21/21.67 % Horn 175
% 79.21/21.67 % unary 44
% 79.21/21.67 % binary 85
% 79.21/21.67 % lits 533
% 79.21/21.67 % lits eq 122
% 79.21/21.67 % fd_pure 0
% 79.21/21.67 % fd_pseudo 0
% 79.21/21.67 % fd_cond 10
% 79.21/21.67 % fd_pseudo_cond 47
% 79.21/21.67 % AC symbols 0
% 79.21/21.67
% 79.21/21.67 % ------ Input Options Time Limit: Unbounded
% 79.21/21.67
% 79.21/21.67
% 79.21/21.67 % ------
% 79.21/21.67 % Current options:
% 79.21/21.67 % ------
% 79.21/21.67
% 79.21/21.67
% 79.21/21.67 %
% 79.21/21.67
% 79.21/21.67 % ------ Proving...
% 79.21/21.67 %
% 79.21/21.67
% 79.21/21.67 % SZS status Theorem for theBenchmark.p
% 79.21/21.67
% 79.21/21.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 79.21/21.67
% 79.21/21.67
%------------------------------------------------------------------------------