%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU227+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 : n004.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 02:56:14 PM UTC 2026
% Result : Theorem 5.89s 12.62s
% Output : CNFRefutation 5.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 14 unt; 0 def)
% Number of atoms : 389 ( 39 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 495 ( 203 ~; 208 |; 59 &)
% ( 15 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 2 con; 0-3 aty)
% Number of variables : 269 ( 0 sgn 239 !; 30 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,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(f10,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(f41,conjecture,
! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f44,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f45,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f47,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
? [X0,X1] :
( relation(X1)
& subset(X0,relation_dom(X1))
& ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(ennf_transformation,[],[f42]) ).
fof(f70,plain,
? [X0,X1] :
( relation(X1)
& subset(X0,relation_dom(X1))
& ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f73,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f81]) ).
fof(f83,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK5(X0,X1,X6),X1)
& in(ordered_pair(X6,sK5(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| ( in(sK4(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f84]) ).
fof(f86,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,[],[f63]) ).
fof(f87,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,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK6(X0,X1),X0)
& ~ in(sK6(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f87]) ).
fof(f89,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,[],[f64]) ).
fof(f90,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,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK9(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK7(X0,X1),X1)
| in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) )
& ( ~ in(sK7(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f90]) ).
fof(f103,plain,
( relation(sK22)
& subset(sK21,relation_dom(sK22))
& ~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X0,sK21),skolemize(X1,sK22)],[f70]) ).
fof(f104,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f110,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f113,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f119,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f124,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f125,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f126,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK9(X0,X5)),X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f130,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f163,plain,
relation(sK22),
inference(cnf_transformation,[],[f103]) ).
fof(f164,plain,
subset(sK21,relation_dom(sK22)),
inference(cnf_transformation,[],[f103]) ).
fof(f165,plain,
~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f177,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f113,f130]) ).
fof(f181,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f119,f130]) ).
fof(f186,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f126,f130]) ).
fof(f188,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f177]) ).
fof(f191,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f181]) ).
fof(f195,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0) ),
inference(equality_resolution,[],[f186]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f110]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK9(X1,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_104,negated_conjecture,
~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(cnf_transformation,[],[f165]) ).
tcf(c_105,negated_conjecture,
subset(sK21,relation_dom(sK22)),
inference(cnf_transformation,[],[f164]) ).
tcf(c_106,negated_conjecture,
relation(sK22),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_109]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_185]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_111,c_147]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_112,c_147]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_71,c_52]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_62,c_52]) ).
tcf(c_564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_56,c_52]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1),X0)
| ( X0 != sK21 )
| ( relation_inverse_image(sK22,relation_image(sK22,sK21)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_186,c_104]) ).
tcf(c_837,plain,
in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21),
inference(unflattening,[status(thm)],[c_836]) ).
tcf(c_841,plain,
! [X0: $i,X1: $i] :
( ~ in(sK6(X0,X1),X1)
| ( X0 != sK21 )
| ( relation_inverse_image(sK22,relation_image(sK22,sK21)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_175,c_104]) ).
tcf(c_842,plain,
~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(unflattening,[status(thm)],[c_841]) ).
tcf(c_6673,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK22))
| ~ in(X0,sK21)
| ~ subset(sK21,relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_293]) ).
tcf(c_6674,plain,
! [X0: $i] :
( empty(relation_dom(sK22))
| in(X0,relation_dom(sK22))
| ~ element(X0,relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_6721,plain,
( ~ empty(relation_dom(sK22))
| ~ subset(sK21,relation_dom(sK22))
| ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21) ),
inference(instantiation,[status(thm)],[c_6673]) ).
tcf(c_6789,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_image(sK22,sK21))
| ~ relation(sK22)
| ~ in(X0,sK21)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22) ),
inference(instantiation,[status(thm)],[c_564]) ).
tcf(c_6956,plain,
! [X0: $i] :
( element(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),X0)
| ~ subset(sK21,X0)
| ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21) ),
inference(instantiation,[status(thm)],[c_292]) ).
tcf(c_7193,plain,
! [X0: $i] :
( in(sK9(sK22,X0),relation_image(sK22,sK21))
| ~ relation(sK22)
| ~ in(X0,sK21)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,X0))),sK22) ),
inference(instantiation,[status(thm)],[c_6789]) ).
tcf(c_7618,plain,
( element(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22))
| ~ subset(sK21,relation_dom(sK22))
| ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21) ),
inference(instantiation,[status(thm)],[c_6956]) ).
tcf(c_8512,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_inverse_image(X2,relation_image(sK22,sK21)))
| ~ relation(X2)
| ~ in(X1,relation_image(sK22,sK21))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(instantiation,[status(thm)],[c_563]) ).
tcf(c_8528,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,X0))),sK22)
| ~ relation(sK22)
| ~ in(X0,relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_561]) ).
tcf(c_9291,plain,
( empty(relation_dom(sK22))
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22))
| ~ element(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_6674]) ).
tcf(c_21751,plain,
( in(unordered_pair(singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))))),sK22)
| ~ relation(sK22)
| ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_8528]) ).
tcf(c_25189,plain,
( in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,relation_image(sK22,sK21)))
| ~ relation(sK22)
| ~ in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),relation_image(sK22,sK21))
| ~ in(unordered_pair(singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))))),sK22) ),
inference(instantiation,[status(thm)],[c_8512]) ).
tcf(c_25203,plain,
( in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),relation_image(sK22,sK21))
| ~ relation(sK22)
| ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21)
| ~ in(unordered_pair(singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))))),sK22) ),
inference(instantiation,[status(thm)],[c_7193]) ).
tcf(c_25205,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_25203,c_25189,c_21751,c_9291,c_7618,c_6721,c_842,c_837,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU227+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n004.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 13:17:33 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 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
% 0.15/10.43
% 0.15/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43
% 0.15/10.43 % Detected problem language: tptp
% 0.15/10.44 % Proving...
% 5.89/12.62 % SZS status Started for theBenchmark.p
% 5.89/12.62 % SZS status Theorem for theBenchmark.p
% 5.89/12.62
% 5.89/12.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.89/12.62
% 5.89/12.62 % ------ iProver source info
% 5.89/12.62
% 5.89/12.62 % git: date: 2026-07-19 20:42:38 +0200
% 5.89/12.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.89/12.62 % git: non_committed_changes: false
% 5.89/12.62
% 5.89/12.62 % ------ Parsing...
% 5.89/12.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.89/12.62
% 5.89/12.62 % ------ Preprocessing... sup_sim: 12 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 5.89/12.62
% 5.89/12.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.89/12.62
% 5.89/12.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.89/12.62 % ------ Proving...
% 5.89/12.62 % ------ Problem Properties
% 5.89/12.62
% 5.89/12.62 %
% 5.89/12.62 % clauses 59
% 5.89/12.62 % conjectures 3
% 5.89/12.62 % EPR 25
% 5.89/12.62 % Horn 51
% 5.89/12.62 % unary 24
% 5.89/12.62 % binary 13
% 5.89/12.62 % lits 128
% 5.89/12.62 % lits eq 11
% 5.89/12.62 % fd_pure 0
% 5.89/12.62 % fd_pseudo 0
% 5.89/12.62 % fd_cond 1
% 5.89/12.62 % fd_pseudo_cond 9
% 5.89/12.62 % AC symbols 0
% 5.89/12.62
% 5.89/12.62 % ------ Input Options Time Limit: Unbounded
% 5.89/12.62
% 5.89/12.62
% 5.89/12.62 % ------
% 5.89/12.62 % Current options:
% 5.89/12.62 % ------
% 5.89/12.62
% 5.89/12.62
% 5.89/12.62 %
% 5.89/12.62
% 5.89/12.62 % ------ Proving...
% 5.89/12.62 %
% 5.89/12.62
% 5.89/12.62 % SZS status Theorem for theBenchmark.p
% 5.89/12.62
% 5.89/12.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.89/12.62
% 5.89/12.62
%------------------------------------------------------------------------------