%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU184+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 : n007.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 57.11s 14.88s
% Output : CNFRefutation 57.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 94 ( 14 unt; 0 def)
% Number of atoms : 400 ( 52 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 520 ( 214 ~; 220 |; 56 &)
% ( 15 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 2 con; 0-4 aty)
% Number of variables : 261 ( 0 sgn 229 !; 32 ?; 53 :)
% 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)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f16,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f34,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
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)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f48,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f47]) ).
fof(f53,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f54,plain,
? [X0] :
( relation(X0)
& ? [X1] :
( relation(X1)
& subset(relation_rng(X0),relation_dom(X1))
& relation_dom(X0) != relation_dom(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f55,plain,
? [X0] :
( relation(X0)
& ? [X1] :
( relation(X1)
& subset(relation_rng(X0),relation_dom(X1))
& relation_dom(X0) != relation_dom(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f54]) ).
fof(f62,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f63,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f62]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f66,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))],[f65]) ).
fof(f67,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(f68,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,[],[f67]) ).
fof(f69,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))],[f68]) ).
fof(f70,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(f71,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,[],[f70]) ).
fof(f72,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))],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ( in(ordered_pair(sK10(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK10(X0,X1,X7,X8)),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ( ( in(ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)),X2)
| ( in(ordered_pair(sK9(X0,X1,X2),sK8(X0,X1,X2)),X1)
& in(ordered_pair(sK7(X0,X1,X2),sK9(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK8(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK7(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X4,sK8(X0,X1,X2)),skolemize(X6,sK9(X0,X1,X2)),skolemize(X10,sK10(X0,X1,X7,X8))],[f74]) ).
fof(f83,plain,
( relation(sK17)
& relation(sK18)
& subset(relation_rng(sK17),relation_dom(sK18))
& relation_dom(sK17) != relation_dom(relation_composition(sK17,sK18)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f55]) ).
fof(f85,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f88,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f63]) ).
fof(f89,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f90,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f91,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f92,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK3(X0,X5)),X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f93,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f97,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f100,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f103,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f107,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f127,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f128,plain,
relation(sK17),
inference(cnf_transformation,[],[f83]) ).
fof(f129,plain,
relation(sK18),
inference(cnf_transformation,[],[f83]) ).
fof(f130,plain,
subset(relation_rng(sK17),relation_dom(sK18)),
inference(cnf_transformation,[],[f83]) ).
fof(f131,plain,
relation_dom(sK17) != relation_dom(relation_composition(sK17,sK18)),
inference(cnf_transformation,[],[f83]) ).
fof(f139,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,[],[f93,f100]) ).
fof(f140,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,[],[f92,f100]) ).
fof(f143,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,[],[f97,f100]) ).
fof(f148,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2) ),
inference(definition_unfolding,[],[f103,f100,f100,f100]) ).
fof(f154,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f139]) ).
fof(f155,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,[],[f140]) ).
fof(f156,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f143]) ).
fof(f158,plain,
! [X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f148]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f85]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
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,[],[f154]) ).
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,[],[f155]) ).
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,[],[f156]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(X1,X0)),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_92,negated_conjecture,
relation_dom(relation_composition(sK17,sK18)) != relation_dom(sK17),
inference(cnf_transformation,[],[f131]) ).
tcf(c_93,negated_conjecture,
subset(relation_rng(sK17),relation_dom(sK18)),
inference(cnf_transformation,[],[f130]) ).
tcf(c_94,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f129]) ).
tcf(c_95,negated_conjecture,
relation(sK17),
inference(cnf_transformation,[],[f128]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_71]) ).
tcf(c_592,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_602,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_612,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_710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_346,c_50]) ).
tcf(c_2562,plain,
( ( relation_dom(relation_composition(sK17,sK18)) = relation_dom(sK17) )
| ~ subset(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))
| ~ subset(relation_dom(relation_composition(sK17,sK18)),relation_dom(sK17)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_2703,plain,
( subset(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))
| in(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),relation_dom(sK17)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_2704,plain,
( subset(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))
| ~ in(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),relation_dom(relation_composition(sK17,sK18))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2722,plain,
( relation(relation_composition(sK17,sK18))
| ~ relation(sK18)
| ~ relation(sK17) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_3446,plain,
( subset(relation_dom(relation_composition(sK17,sK18)),relation_dom(sK17))
| ~ relation(sK18)
| ~ relation(sK17) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_5300,plain,
( in(unordered_pair(singleton(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),unordered_pair(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))))),sK17)
| ~ relation(sK17)
| ~ in(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),relation_dom(sK17)) ),
inference(instantiation,[status(thm)],[c_612]) ).
tcf(c_13561,plain,
( in(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),relation_rng(sK17))
| ~ relation(sK17)
| ~ in(unordered_pair(singleton(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),unordered_pair(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))))),sK17) ),
inference(instantiation,[status(thm)],[c_592]) ).
tcf(c_63581,plain,
! [X0: $i] :
( in(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),X0)
| ~ subset(relation_rng(sK17),X0)
| ~ in(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),relation_rng(sK17)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_67995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,sK3(X1,X0))),relation_composition(X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK3(X1,X0))),X1) ),
inference(instantiation,[status(thm)],[c_710]) ).
tcf(c_69498,plain,
( in(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),relation_dom(sK18))
| ~ subset(relation_rng(sK17),relation_dom(sK18))
| ~ in(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),relation_rng(sK17)) ),
inference(instantiation,[status(thm)],[c_63581]) ).
tcf(c_71019,plain,
( in(unordered_pair(singleton(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))),unordered_pair(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),sK3(sK18,sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))))),sK18)
| ~ relation(sK18)
| ~ in(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),relation_dom(sK18)) ),
inference(instantiation,[status(thm)],[c_612]) ).
tcf(c_73919,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK3(sK18,sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))))),relation_composition(X1,sK18))
| ~ relation(sK18)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))))),X1)
| ~ in(unordered_pair(singleton(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))),unordered_pair(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),sK3(sK18,sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))))),sK18) ),
inference(instantiation,[status(thm)],[c_67995]) ).
tcf(c_78583,plain,
( in(unordered_pair(singleton(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),unordered_pair(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),sK3(sK18,sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))))),relation_composition(sK17,sK18))
| ~ relation(sK18)
| ~ relation(sK17)
| ~ in(unordered_pair(singleton(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),unordered_pair(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))))),sK17)
| ~ in(unordered_pair(singleton(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))),unordered_pair(sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),sK3(sK18,sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))))),sK18) ),
inference(instantiation,[status(thm)],[c_73919]) ).
tcf(c_85186,plain,
( in(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),relation_dom(relation_composition(sK17,sK18)))
| ~ relation(relation_composition(sK17,sK18))
| ~ in(unordered_pair(singleton(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18)))),unordered_pair(sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))),sK3(sK18,sK3(sK17,sK0(relation_dom(sK17),relation_dom(relation_composition(sK17,sK18))))))),relation_composition(sK17,sK18)) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_85188,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_85186,c_78583,c_71019,c_69498,c_13561,c_5300,c_3446,c_2722,c_2703,c_2704,c_2562,c_92,c_93,c_94,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU184+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n007.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 13:03:28 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 57.11/14.88 % SZS status Started for theBenchmark.p
% 57.11/14.88 % SZS status Theorem for theBenchmark.p
% 57.11/14.88
% 57.11/14.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 57.11/14.88
% 57.11/14.88 % ------ iProver source info
% 57.11/14.88
% 57.11/14.88 % git: date: 2026-07-19 20:42:38 +0200
% 57.11/14.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 57.11/14.88 % git: non_committed_changes: false
% 57.11/14.88
% 57.11/14.88 % ------ Parsing...
% 57.11/14.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 57.11/14.88
% 57.11/14.88 % ------ Preprocessing... sup_sim: 14 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 %
% 57.11/14.88
% 57.11/14.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 57.11/14.88
% 57.11/14.88 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 57.11/14.88 % ------ Proving...
% 57.11/14.88 % ------ Problem Properties
% 57.11/14.88
% 57.11/14.88 %
% 57.11/14.88 % clauses 49
% 57.11/14.88 % conjectures 4
% 57.11/14.88 % EPR 18
% 57.11/14.88 % Horn 42
% 57.11/14.88 % unary 17
% 57.11/14.88 % binary 10
% 57.11/14.88 % lits 121
% 57.11/14.88 % lits eq 12
% 57.11/14.88 % fd_pure 0
% 57.11/14.88 % fd_pseudo 0
% 57.11/14.88 % fd_cond 1
% 57.11/14.88 % fd_pseudo_cond 9
% 57.11/14.88 % AC symbols 0
% 57.11/14.88
% 57.11/14.88 % ------ Input Options Time Limit: Unbounded
% 57.11/14.88
% 57.11/14.88
% 57.11/14.88 % ------
% 57.11/14.88 % Current options:
% 57.11/14.88 % ------
% 57.11/14.88
% 57.11/14.88
% 57.11/14.88 %
% 57.11/14.88
% 57.11/14.88 % ------ Proving...
% 57.11/14.88 %
% 57.11/14.88
% 57.11/14.88 % SZS status Theorem for theBenchmark.p
% 57.11/14.88
% 57.11/14.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 57.11/14.88
% 57.11/14.88
%------------------------------------------------------------------------------