%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU181+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 : 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 02:55:47 PM UTC 2026
% Result : Theorem 12.69s 23.44s
% Output : CNFRefutation 12.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 135 ( 24 unt; 5 def)
% Number of atoms : 547 ( 75 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 521 ( 224 ~; 231 |; 42 &)
% ( 15 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 1 con; 0-2 aty)
% Number of variables : 262 ( 0 sgn 239 !; 23 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
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(f8,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(f15,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f44,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(f45,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(f46,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,[],[f8]) ).
fof(f47,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f48,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(ennf_transformation,[],[f24]) ).
fof(f53,plain,
? [X0] :
( relation(X0)
& ( relation_dom(X0) != relation_rng(relation_inverse(X0))
| relation_rng(X0) != relation_dom(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f60,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f61,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f63]) ).
fof(f65,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,[],[f44]) ).
fof(f66,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,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK3(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK1(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f66]) ).
fof(f68,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,[],[f45]) ).
fof(f69,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,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK6(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK4(X0,X1),X1)
| in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0) )
& ( ~ in(sK4(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f69]) ).
fof(f71,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,[],[f46]) ).
fof(f72,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,[],[f71]) ).
fof(f73,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(sK7(X0,X1),sK8(X0,X1)),X1)
| in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0) )
& ( ~ in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X1)
| ~ in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1))],[f72]) ).
fof(f80,plain,
( relation(sK15)
& ( relation_dom(sK15) != relation_rng(relation_inverse(sK15))
| relation_rng(sK15) != relation_dom(relation_inverse(sK15)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f53]) ).
fof(f83,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f86,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f88,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f90,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK3(X0,X5)),X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f91,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f94,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK6(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f98,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f99,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,[],[f73]) ).
fof(f103,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f110,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f48]) ).
fof(f122,plain,
relation(sK15),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
( relation_dom(sK15) != relation_rng(relation_inverse(sK15))
| relation_rng(sK15) != relation_dom(relation_inverse(sK15)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f133,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,[],[f91,f98]) ).
fof(f134,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f90,f98]) ).
fof(f137,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,[],[f95,f98]) ).
fof(f138,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0) ),
inference(definition_unfolding,[],[f94,f98]) ).
fof(f142,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f99,f98,f98]) ).
fof(f146,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f133]) ).
fof(f147,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f148,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f137]) ).
fof(f149,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0) ),
inference(equality_resolution,[],[f138]) ).
fof(f151,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),relation_inverse(X0))
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0) ),
inference(equality_resolution,[],[f142]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f83]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_59,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,[],[f146]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK3(X1,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_63,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,[],[f148]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK6(X1,X0),X0),singleton(sK6(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),X2)
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_inverse(X2)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_69,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_76,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_88,negated_conjecture,
( ( relation_rng(relation_inverse(sK15)) != relation_dom(sK15) )
| ( relation_dom(relation_inverse(sK15)) != relation_rng(sK15) ) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_89,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f122]) ).
tcf(c_148,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_inverse(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_148]) ).
tcf(c_550,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_63,c_50]) ).
tcf(c_560,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_59,c_50]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_60,c_50]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK6(X1,X0)),unordered_pair(X0,sK6(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(demodulation,[status(thm)],[c_64,c_50]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_inverse(X2)) ),
inference(demodulation,[status(thm)],[c_288,c_50]) ).
tcf(c_1469,definition,
iPr_def_10 = relation_inverse(sK15),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1470,definition,
iPr_def_11 = relation_dom(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1471,definition,
iPr_def_12 = relation_rng(sK15),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1472,definition,
iPr_def_13 = relation_rng(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1473,definition,
iPr_def_14 = relation_dom(sK15),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1474,negated_conjecture,
relation(sK15),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_1475,negated_conjecture,
( ( iPr_def_13 != iPr_def_14 )
| ( iPr_def_11 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_88,c_1473,c_1472,c_1471,c_1469,c_1470]) ).
tcf(c_29510,plain,
( relation(iPr_def_10)
| ~ relation(sK15) ),
inference(superposition,[status(thm)],[c_1469,c_69]) ).
tcf(c_29511,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_29510,c_1474]) ).
tcf(c_29609,plain,
relation_inverse(relation_inverse(sK15)) = sK15,
inference(superposition,[status(thm)],[c_1474,c_76]) ).
tcf(c_29612,plain,
relation_inverse(iPr_def_10) = sK15,
inference(light_normalisation,[status(thm)],[c_29609,c_1469]) ).
tcf(c_29790,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_50,c_550]) ).
tcf(c_30076,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK15)
| ~ relation(sK15)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_1469,c_600]) ).
tcf(c_30077,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),iPr_def_10)
| ~ relation(iPr_def_10)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK15) ),
inference(superposition,[status(thm)],[c_29612,c_600]) ).
tcf(c_30079,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),iPr_def_10)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK15) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30077,c_29511]) ).
tcf(c_30082,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK15)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30076,c_1474]) ).
tcf(c_30232,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(iPr_def_10,X0)),unordered_pair(sK3(iPr_def_10,X0),X0)),sK15)
| ~ relation(iPr_def_10)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_570,c_30082]) ).
tcf(c_30233,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK15)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_30082]) ).
tcf(c_30237,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(iPr_def_10,X0)),unordered_pair(sK3(iPr_def_10,X0),X0)),sK15)
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_30232,c_1470]) ).
tcf(c_30238,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(iPr_def_10,X0)),unordered_pair(sK3(iPr_def_10,X0),X0)),sK15)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30237,c_29511]) ).
tcf(c_30905,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(iPr_def_10,X0)),unordered_pair(X0,sK3(iPr_def_10,X0))),sK15)
| ~ in(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_30238,c_50]) ).
tcf(c_30917,plain,
! [X0: $i] :
( in(X0,relation_rng(sK15))
| ~ relation(sK15)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_30905,c_29790]) ).
tcf(c_30918,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ relation(sK15)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_30917,c_1471]) ).
tcf(c_30919,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30918,c_1474]) ).
tcf(c_30939,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| in(sK0(iPr_def_11,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_55,c_30919]) ).
tcf(c_31099,plain,
subset(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_30939,c_54]) ).
tcf(c_31128,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ subset(iPr_def_12,iPr_def_11) ),
inference(superposition,[status(thm)],[c_31099,c_51]) ).
tcf(c_31469,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(sK15,X0)),unordered_pair(sK3(sK15,X0),X0)),iPr_def_10)
| ~ relation(sK15)
| ~ in(X0,relation_dom(sK15)) ),
inference(superposition,[status(thm)],[c_570,c_30079]) ).
tcf(c_31472,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),iPr_def_10)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK15) ),
inference(superposition,[status(thm)],[c_50,c_30079]) ).
tcf(c_31476,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(sK15,X0)),unordered_pair(sK3(sK15,X0),X0)),iPr_def_10)
| ~ relation(sK15)
| ~ in(X0,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_31469,c_1473]) ).
tcf(c_31477,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(sK15,X0)),unordered_pair(sK3(sK15,X0),X0)),iPr_def_10)
| ~ in(X0,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31476,c_1474]) ).
tcf(c_31491,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK3(sK15,X0)),unordered_pair(X0,sK3(sK15,X0))),iPr_def_10)
| ~ in(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_31477,c_50]) ).
tcf(c_31503,plain,
! [X0: $i] :
( in(X0,relation_rng(iPr_def_10))
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_31491,c_29790]) ).
tcf(c_31506,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_31503,c_1472]) ).
tcf(c_31507,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31506,c_29511]) ).
tcf(c_32252,plain,
! [X0: $i] :
( subset(iPr_def_14,X0)
| in(sK0(iPr_def_14,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_55,c_31507]) ).
tcf(c_35072,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(iPr_def_10,X0))),sK15)
| ~ relation(iPr_def_10)
| ~ in(X0,relation_rng(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_580,c_30233]) ).
tcf(c_35083,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(iPr_def_10,X0))),sK15)
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_35072,c_1472]) ).
tcf(c_35084,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(iPr_def_10,X0))),sK15)
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35083,c_29511]) ).
tcf(c_35429,plain,
! [X0: $i] :
( in(X0,relation_dom(sK15))
| ~ relation(sK15)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_35084,c_560]) ).
tcf(c_35433,plain,
! [X0: $i] :
( in(X0,iPr_def_14)
| ~ relation(sK15)
| ~ in(X0,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_35429,c_1473]) ).
tcf(c_35434,plain,
! [X0: $i] :
( in(X0,iPr_def_14)
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35433,c_1474]) ).
tcf(c_35972,plain,
! [X0: $i] :
( subset(iPr_def_13,X0)
| in(sK0(iPr_def_13,X0),iPr_def_14) ),
inference(superposition,[status(thm)],[c_55,c_35434]) ).
tcf(c_39438,plain,
subset(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_35972,c_54]) ).
tcf(c_45582,plain,
subset(iPr_def_14,iPr_def_13),
inference(superposition,[status(thm)],[c_32252,c_54]) ).
tcf(c_45922,plain,
( ( iPr_def_13 = iPr_def_14 )
| ~ subset(iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_45582,c_51]) ).
tcf(c_45928,plain,
iPr_def_13 = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_45922,c_39438]) ).
tcf(c_45929,plain,
iPr_def_11 != iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_1475,c_45928]) ).
tcf(c_45984,plain,
~ subset(iPr_def_12,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_31128,c_45929]) ).
tcf(c_54420,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(sK15,X0))),iPr_def_10)
| ~ relation(sK15)
| ~ in(X0,relation_rng(sK15)) ),
inference(superposition,[status(thm)],[c_580,c_31472]) ).
tcf(c_54429,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(sK15,X0))),iPr_def_10)
| ~ relation(sK15)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_54420,c_1471]) ).
tcf(c_54430,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(sK15,X0))),iPr_def_10)
| ~ in(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54429,c_1474]) ).
tcf(c_54938,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_54430,c_560]) ).
tcf(c_54944,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_54938,c_1470]) ).
tcf(c_54945,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54944,c_29511]) ).
tcf(c_59031,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| in(sK0(iPr_def_12,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_55,c_54945]) ).
tcf(c_59175,plain,
subset(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_59031,c_54]) ).
tcf(c_59179,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_59175,c_45984]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU181+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/21.07 % Computer : n008.cluster.edu
% 0.16/21.07 % Model : x86_64 x86_64
% 0.16/21.07 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/21.07 % Memory : 8046.5625MB
% 0.16/21.07 % OS : Linux 6.8.0-71-generic
% 0.16/21.07 % CPULimit : 300
% 0.16/21.07 % WCLimit : 300
% 0.16/21.07 % DateTime : Thu Sep 24 13:06:16 UTC 2026
% 0.16/21.07 % CPUTime :
% 0.16/21.07 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/21.11 Running first-order theorem proving
% 0.16/21.11 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
% 0.16/21.12
% 0.16/21.12 % ======== iProver multi-core TPTP/SMT =========
% 0.16/21.12
% 0.16/21.12 % Detected problem language: tptp
% 0.20/21.13 % Proving...
% 12.69/23.44 % SZS status Started for theBenchmark.p
% 12.69/23.44 % SZS status Theorem for theBenchmark.p
% 12.69/23.44
% 12.69/23.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.69/23.44
% 12.69/23.44 % ------ iProver source info
% 12.69/23.44
% 12.69/23.44 % git: date: 2026-07-19 20:42:38 +0200
% 12.69/23.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.69/23.44 % git: non_committed_changes: false
% 12.69/23.44
% 12.69/23.44 % ------ Parsing...
% 12.69/23.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.69/23.44
% 12.69/23.44 % ------ Preprocessing... sup_sim: 12 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 12.69/23.44
% 12.69/23.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.69/23.44
% 12.69/23.44 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 12.69/23.44 % ------ Proving...
% 12.69/23.44 % ------ Problem Properties
% 12.69/23.44
% 12.69/23.44 %
% 12.69/23.44 % clauses 50
% 12.69/23.44 % conjectures 2
% 12.69/23.44 % EPR 18
% 12.69/23.44 % Horn 44
% 12.69/23.44 % unary 19
% 12.69/23.44 % binary 13
% 12.69/23.44 % lits 107
% 12.69/23.44 % lits eq 18
% 12.69/23.44 % fd_pure 0
% 12.69/23.44 % fd_pseudo 0
% 12.69/23.44 % fd_cond 1
% 12.69/23.44 % fd_pseudo_cond 8
% 12.69/23.44 % AC symbols 0
% 12.69/23.44
% 12.69/23.44 % ------ Schedule dynamic 5 is on
% 12.69/23.44
% 12.69/23.44 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 12.69/23.44
% 12.69/23.44
% 12.69/23.44 % ------
% 12.69/23.44 % Current options:
% 12.69/23.44 % ------
% 12.69/23.44
% 12.69/23.44
% 12.69/23.44 %
% 12.69/23.44
% 12.69/23.44 % ------ Proving...
% 12.69/23.44 %
% 12.69/23.44
% 12.69/23.44 % SZS status Theorem for theBenchmark.p
% 12.69/23.44
% 12.69/23.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.69/23.45
% 12.69/23.45
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