%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU192+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 : n002.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 02:55:50 PM UTC 2026
% Result : Theorem 3.74s 11.44s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 8 unt; 0 def)
% Number of atoms : 320 ( 31 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 425 ( 176 ~; 183 |; 47 &)
% ( 10 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 216 ( 0 sgn 193 !; 23 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f21,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(f27,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(f56,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f117,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(f165,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f173,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f174,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f173]) ).
fof(f197,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,[],[f9]) ).
fof(f202,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f219,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f266,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,[],[f117]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(flattening,[],[f266]) ).
fof(f318,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<~> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f174]) ).
fof(f333,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,[],[f197]) ).
fof(f334,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,[],[f333]) ).
fof(f335,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,[],[f334]) ).
fof(f336,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(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ( in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0)
& in(sK2(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0)
| ~ in(sK2(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2))],[f335]) ).
fof(f371,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,[],[f202]) ).
fof(f372,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,[],[f371]) ).
fof(f373,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK24(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK22(X0,X1),X1)
| in(ordered_pair(sK22(X0,X1),sK23(X0,X1)),X0) )
& ( ~ in(sK22(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK22(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24]),skolemize(X2,sK22(X0,X1)),skolemize(X4,sK23(X0,X1)),skolemize(X7,sK24(X0,X5))],[f372]) ).
fof(f430,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f318]) ).
fof(f431,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) ) ),
inference(flattening,[],[f430]) ).
fof(f432,plain,
( relation(sK55)
& ( in(sK53,relation_dom(relation_dom_restriction(sK55,sK54)))
| ( in(sK53,relation_dom(sK55))
& in(sK53,sK54) ) )
& ( ~ in(sK53,relation_dom(relation_dom_restriction(sK55,sK54)))
| ~ in(sK53,relation_dom(sK55))
| ~ in(sK53,sK54) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55)],[f431]) ).
fof(f449,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,[],[f336]) ).
fof(f450,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,[],[f336]) ).
fof(f451,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,[],[f336]) ).
fof(f509,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK24(X0,X5)),X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f531,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f559,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f219]) ).
fof(f641,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f267]) ).
fof(f709,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f165]) ).
fof(f721,plain,
relation(sK55),
inference(cnf_transformation,[],[f432]) ).
fof(f722,plain,
( in(sK53,relation_dom(relation_dom_restriction(sK55,sK54)))
| in(sK53,relation_dom(sK55)) ),
inference(cnf_transformation,[],[f432]) ).
fof(f723,plain,
( in(sK53,relation_dom(relation_dom_restriction(sK55,sK54)))
| in(sK53,sK54) ),
inference(cnf_transformation,[],[f432]) ).
fof(f724,plain,
( ~ in(sK53,relation_dom(relation_dom_restriction(sK55,sK54)))
| ~ in(sK53,relation_dom(sK55))
| ~ in(sK53,sK54) ),
inference(cnf_transformation,[],[f432]) ).
fof(f735,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f531,f709]) ).
fof(f746,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2) ),
inference(definition_unfolding,[],[f451,f735,f735]) ).
fof(f747,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(X5,X1) ),
inference(definition_unfolding,[],[f450,f735]) ).
fof(f748,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f449,f735,f735]) ).
fof(f768,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK24(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f509,f735]) ).
fof(f807,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,[],[f641,f735]) ).
fof(f839,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1)) ),
inference(equality_resolution,[],[f746]) ).
fof(f840,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| in(X5,X1) ),
inference(equality_resolution,[],[f747]) ).
fof(f841,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f748]) ).
fof(f872,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK24(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f768]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f839]) ).
tcf(c_68,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),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f840]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f841]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK24(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f872]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f559]) ).
tcf(c_254,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,[],[f807]) ).
tcf(c_333,negated_conjecture,
( ~ in(sK53,sK54)
| ~ in(sK53,relation_dom(sK55))
| ~ in(sK53,relation_dom(relation_dom_restriction(sK55,sK54))) ),
inference(cnf_transformation,[],[f724]) ).
tcf(c_334,negated_conjecture,
( in(sK53,sK54)
| in(sK53,relation_dom(relation_dom_restriction(sK55,sK54))) ),
inference(cnf_transformation,[],[f723]) ).
tcf(c_335,negated_conjecture,
( in(sK53,relation_dom(sK55))
| in(sK53,relation_dom(relation_dom_restriction(sK55,sK54))) ),
inference(cnf_transformation,[],[f722]) ).
tcf(c_336,negated_conjecture,
relation(sK55),
inference(cnf_transformation,[],[f721]) ).
tcf(c_496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68,c_173]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_127,c_496]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69,c_173]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK24(relation_dom_restriction(X1,X2),X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_127,c_512]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67,c_173]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(superposition,[status(thm)],[c_529,c_254]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_506,c_173]) ).
tcf(c_631,plain,
( in(sK53,sK54)
| ~ relation(sK55) ),
inference(superposition,[status(thm)],[c_334,c_619]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK24(relation_dom_restriction(X1,X2),X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_522,c_173]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_653,c_254]) ).
tcf(c_725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_544,c_173]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_127,c_725]) ).
tcf(c_978,plain,
( in(sK53,relation_dom(sK55))
| ~ relation(sK55) ),
inference(superposition,[status(thm)],[c_335,c_665]) ).
tcf(c_1259,plain,
( ~ relation(sK55)
| ~ in(sK53,sK54)
| ~ in(sK53,relation_dom(sK55)) ),
inference(superposition,[status(thm)],[c_739,c_333]) ).
tcf(c_1265,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1259,c_978,c_631,c_336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU192+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.61 % Computer : n002.cluster.edu
% 0.12/10.61 % Model : x86_64 x86_64
% 0.12/10.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.61 % Memory : 8046.5625MB
% 0.12/10.61 % OS : Linux 6.8.0-71-generic
% 0.12/10.61 % CPULimit : 300
% 0.12/10.61 % WCLimit : 300
% 0.12/10.61 % DateTime : Thu Sep 24 13:10:31 UTC 2026
% 0.12/10.61 % CPUTime :
% 0.12/10.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.65 Running first-order theorem proving
% 0.12/10.65 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
% 0.12/10.66
% 0.12/10.66 % ======== iProver multi-core TPTP/SMT =========
% 0.12/10.66
% 0.12/10.66 % Detected problem language: tptp
% 0.12/10.67 % Proving...
% 3.74/11.44 % SZS status Started for theBenchmark.p
% 3.74/11.44 % SZS status Theorem for theBenchmark.p
% 3.74/11.44
% 3.74/11.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.74/11.44
% 3.74/11.44 % ------ iProver source info
% 3.74/11.44
% 3.74/11.44 % git: date: 2026-07-19 20:42:38 +0200
% 3.74/11.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.74/11.44 % git: non_committed_changes: false
% 3.74/11.44
% 3.74/11.44 % ------ Parsing...
% 3.74/11.44 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.74/11.44 % ------ Proving...
% 3.74/11.44 % ------ Problem Properties
% 3.74/11.44
% 3.74/11.44 %
% 3.74/11.44 % clauses 298
% 3.74/11.44 % conjectures 4
% 3.74/11.44 % EPR 37
% 3.74/11.44 % Horn 238
% 3.74/11.44 % unary 58
% 3.74/11.44 % binary 102
% 3.74/11.44 % lits 748
% 3.74/11.44 % lits eq 155
% 3.74/11.44 % fd_pure 0
% 3.74/11.44 % fd_pseudo 0
% 3.74/11.44 % fd_cond 13
% 3.74/11.44 % fd_pseudo_cond 58
% 3.74/11.44 % AC symbols 0
% 3.74/11.44
% 3.74/11.44 % ------ Input Options Time Limit: Unbounded
% 3.74/11.44
% 3.74/11.44
% 3.74/11.44 % ------
% 3.74/11.44 % Current options:
% 3.74/11.44 % ------
% 3.74/11.44
% 3.74/11.44
% 3.74/11.44 %
% 3.74/11.44
% 3.74/11.44 % ------ Proving...
% 3.74/11.44 %
% 3.74/11.44
% 3.74/11.44 % SZS status Theorem for theBenchmark.p
% 3.74/11.44
% 3.74/11.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.74/11.45
% 3.74/11.45
%------------------------------------------------------------------------------