%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU061+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:55:11 PM UTC 2026
% Result : Theorem 48.19s 14.92s
% Output : CNFRefutation 48.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 36
% Syntax : Number of formulae : 229 ( 71 unt; 0 def)
% Number of atoms : 619 ( 114 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 675 ( 285 ~; 285 |; 75 &)
% ( 14 <=>; 15 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 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; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-3 aty)
% Number of variables : 411 ( 1 sgn 371 !; 40 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
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_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(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f9,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(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(f11,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f13,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f16,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f17,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f18,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f19,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f20,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f23,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f24,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f25,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f26,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f27,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f28,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f29,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f30,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f31,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f31]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f36]) ).
fof(f44,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f30]) ).
fof(f47,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f29]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f49,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f50,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f53,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,[],[f6]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f55,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f56,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f58,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f59,plain,
? [X0,X1] :
( relation(X1)
& ( in(X0,relation_rng(X1))
<~> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f60,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f61,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f62,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f67,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f39]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f70,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,[],[f53]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(X6,sK2(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_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))],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f74,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| sK3(X0,X1) = X0 )
& ( ~ in(sK3(X0,X1),X1)
| sK3(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f74]) ).
fof(f76,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f77,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK4(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f77]) ).
fof(f79,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,[],[f54]) ).
fof(f80,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,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK7(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK5(X0,X1),X1)
| in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) )
& ( ~ in(sK5(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X7,sK7(X0,X5))],[f80]) ).
fof(f82,plain,
! [X0] : element(sK8(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f11]) ).
fof(f83,plain,
( function(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f21]) ).
fof(f84,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f22]) ).
fof(f85,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f58]) ).
fof(f86,plain,
empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f24]) ).
fof(f87,plain,
( function(sK13)
& empty(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f25]) ).
fof(f88,plain,
( relation(sK14)
& ~ empty(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f26]) ).
fof(f89,plain,
! [X0] :
( empty(sK15(X0))
& element(sK15(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f27]) ).
fof(f90,plain,
~ empty(sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f28]) ).
fof(f91,plain,
( function(sK17)
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f47]) ).
fof(f92,plain,
relation(sK18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X0,sK18)],[f44]) ).
fof(f93,plain,
? [X0,X1] :
( relation(X1)
& ( in(X0,relation_rng(X1))
| relation_inverse_image(X1,singleton(X0)) != empty_set )
& ( ~ in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0)) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f94,plain,
? [X0,X1] :
( relation(X1)
& ( in(X0,relation_rng(X1))
| relation_inverse_image(X1,singleton(X0)) != empty_set )
& ( ~ in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0)) ) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
( relation(sK20)
& ( in(sK19,relation_rng(sK20))
| empty_set != relation_inverse_image(sK20,singleton(sK19)) )
& ( ~ in(sK19,relation_rng(sK20))
| empty_set = relation_inverse_image(sK20,singleton(sK19)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X0,sK19),skolemize(X1,sK20)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f97,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f98,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f101,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f102,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f103,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK2(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f104,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,[],[f72]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),X4),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f108,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f75]) ).
fof(f109,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f110,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| sK3(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f111,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| sK3(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f112,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
! [X0] :
( in(sK4(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK7(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f115,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f116,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f117,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK5(X0,X1),X1)
| ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f118,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f119,plain,
! [X0] : element(sK8(X0),X0),
inference(cnf_transformation,[],[f82]) ).
fof(f122,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f125,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f126,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f127,plain,
relation(empty_set),
inference(cnf_transformation,[],[f18]) ).
fof(f128,plain,
empty(empty_set),
inference(cnf_transformation,[],[f18]) ).
fof(f129,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f130,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_rng(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f131,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f132,plain,
function(sK9),
inference(cnf_transformation,[],[f83]) ).
fof(f133,plain,
relation(sK9),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
relation(sK10),
inference(cnf_transformation,[],[f84]) ).
fof(f135,plain,
empty(sK10),
inference(cnf_transformation,[],[f84]) ).
fof(f136,plain,
! [X0] :
( empty(X0)
| ~ empty(sK11(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f137,plain,
! [X0] :
( empty(X0)
| element(sK11(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f138,plain,
empty(sK12),
inference(cnf_transformation,[],[f86]) ).
fof(f139,plain,
function(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f140,plain,
empty(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f141,plain,
relation(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f142,plain,
relation(sK14),
inference(cnf_transformation,[],[f88]) ).
fof(f143,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f88]) ).
fof(f144,plain,
! [X0] : empty(sK15(X0)),
inference(cnf_transformation,[],[f89]) ).
fof(f145,plain,
! [X0] : element(sK15(X0),powerset(X0)),
inference(cnf_transformation,[],[f89]) ).
fof(f146,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f90]) ).
fof(f147,plain,
function(sK17),
inference(cnf_transformation,[],[f91]) ).
fof(f148,plain,
relation(sK17),
inference(cnf_transformation,[],[f91]) ).
fof(f149,plain,
relation(sK18),
inference(cnf_transformation,[],[f92]) ).
fof(f150,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f151,plain,
relation(sK20),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
( in(sK19,relation_rng(sK20))
| empty_set != relation_inverse_image(sK20,singleton(sK19)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
( ~ in(sK19,relation_rng(sK20))
| empty_set = relation_inverse_image(sK20,singleton(sK19)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f155,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f156,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f159,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f67]) ).
fof(f160,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f161,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f162,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),X4),singleton(sK0(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f107,f118]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f106,f118]) ).
fof(f164,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,[],[f104,f118]) ).
fof(f165,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0) ),
inference(definition_unfolding,[],[f103,f118]) ).
fof(f166,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK5(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(X3,sK5(X0,X1)),singleton(X3)),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f117,f118]) ).
fof(f167,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK6(X0,X1),sK5(X0,X1)),singleton(sK6(X0,X1))),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f116,f118]) ).
fof(f168,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,[],[f115,f118]) ).
fof(f169,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0) ),
inference(definition_unfolding,[],[f114,f118]) ).
fof(f171,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,[],[f164]) ).
fof(f172,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0) ),
inference(equality_resolution,[],[f165]) ).
fof(f173,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK2(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f102]) ).
fof(f174,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f175,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f174]) ).
fof(f176,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f108]) ).
fof(f177,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f112]) ).
fof(f178,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f168]) ).
fof(f179,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0) ),
inference(equality_resolution,[],[f169]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_50,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_51,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f101]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1,X2),X3),singleton(sK0(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_56,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,[],[f171]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK2(X1,X2,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = X1 )
| ~ in(sK3(X0,X1),X1)
| ( sK3(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| ( singleton(X0) = X1 )
| ( sK3(X0,X1) = X0 ) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_61,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f175]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_63,plain,
! [X0: $i] :
( in(sK4(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_64,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f177]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X1) = X2 )
| ~ relation(X1)
| ~ in(sK5(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X0,sK5(X1,X2)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK6(X0,X1),sK5(X0,X1)),singleton(sK6(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_67,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,[],[f178]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK7(X1,X0),X0),singleton(sK7(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_69,plain,
! [X0: $i] : element(sK8(X0),X0),
inference(cnf_transformation,[],[f119]) ).
tcf(c_72,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_75,plain,
! [X0: $i] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f125]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f126]) ).
tcf(c_77,plain,
empty(empty_set),
inference(cnf_transformation,[],[f128]) ).
tcf(c_78,plain,
relation(empty_set),
inference(cnf_transformation,[],[f127]) ).
tcf(c_79,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_80,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_81,plain,
! [X0: $i] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_82,plain,
relation(sK9),
inference(cnf_transformation,[],[f133]) ).
tcf(c_83,plain,
function(sK9),
inference(cnf_transformation,[],[f132]) ).
tcf(c_84,plain,
empty(sK10),
inference(cnf_transformation,[],[f135]) ).
tcf(c_85,plain,
relation(sK10),
inference(cnf_transformation,[],[f134]) ).
tcf(c_86,plain,
! [X0: $i] :
( empty(X0)
| element(sK11(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_87,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK11(X0)) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_88,plain,
empty(sK12),
inference(cnf_transformation,[],[f138]) ).
tcf(c_89,plain,
relation(sK13),
inference(cnf_transformation,[],[f141]) ).
tcf(c_90,plain,
empty(sK13),
inference(cnf_transformation,[],[f140]) ).
tcf(c_91,plain,
function(sK13),
inference(cnf_transformation,[],[f139]) ).
tcf(c_92,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f143]) ).
tcf(c_93,plain,
relation(sK14),
inference(cnf_transformation,[],[f142]) ).
tcf(c_94,plain,
! [X0: $i] : element(sK15(X0),powerset(X0)),
inference(cnf_transformation,[],[f145]) ).
tcf(c_95,plain,
! [X0: $i] : empty(sK15(X0)),
inference(cnf_transformation,[],[f144]) ).
tcf(c_96,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f146]) ).
tcf(c_97,plain,
relation(sK17),
inference(cnf_transformation,[],[f148]) ).
tcf(c_98,plain,
function(sK17),
inference(cnf_transformation,[],[f147]) ).
tcf(c_99,plain,
relation(sK18),
inference(cnf_transformation,[],[f149]) ).
tcf(c_100,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f150]) ).
tcf(c_101,negated_conjecture,
( ( relation_inverse_image(sK20,singleton(sK19)) = empty_set )
| ~ in(sK19,relation_rng(sK20)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_102,negated_conjecture,
( in(sK19,relation_rng(sK20))
| ( relation_inverse_image(sK20,singleton(sK19)) != empty_set ) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_103,negated_conjecture,
relation(sK20),
inference(cnf_transformation,[],[f151]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_109,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_11851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),relation_inverse_image(X0,X3))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ in(sK1(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_54,c_56]) ).
tcf(c_11852,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X0,X1),X1)
| in(sK6(X0,X1),relation_inverse_image(X0,X2))
| ( relation_rng(X0) = X1 )
| ~ relation(X0)
| ~ in(sK5(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_66,c_56]) ).
tcf(c_16245,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,relation_inverse_image(X0,X2)),relation_inverse_image(X0,X2))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X0,X2) )
| ~ relation(X0)
| ~ in(sK1(X0,X1,relation_inverse_image(X0,X2)),X2) ),
inference(equality_factoring,[status(thm)],[c_11851]) ).
tcf(c_28383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X2) = X3 )
| ~ relation(X0)
| ~ in(sK0(X0,X2,X3),X3)
| ~ in(sK0(X0,X2,X3),relation_inverse_image(X0,X1))
| ~ in(sK2(X0,X1,sK0(X0,X2,X3)),X2) ),
inference(superposition,[status(thm)],[c_57,c_53]) ).
tcf(c_28384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_inverse_image(X0,X3))
| ~ relation(X0)
| ~ in(X2,relation_inverse_image(X0,X1))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_57,c_56]) ).
tcf(c_39440,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_28384,c_28383,c_16245,c_11852,c_11851,c_111,c_110,c_109,c_108,c_107,c_106,c_105,c_104,c_103,c_102,c_101,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_79,c_76,c_75,c_72,c_78,c_77,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU061+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:40:33 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 48.19/14.92 % SZS status Started for theBenchmark.p
% 48.19/14.92 % SZS status Theorem for theBenchmark.p
% 48.19/14.92
% 48.19/14.92 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 48.19/14.92
% 48.19/14.92 % ------ iProver source info
% 48.19/14.92
% 48.19/14.92 % git: date: 2026-07-19 20:42:38 +0200
% 48.19/14.92 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 48.19/14.92 % git: non_committed_changes: false
% 48.19/14.92
% 48.19/14.92 % ------ Parsing...
% 48.19/14.92 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 48.19/14.92
% 48.19/14.92 % ------ Preprocessing...%
% 48.19/14.92
% 48.19/14.92 % ------ Preprocessing...%
% 48.19/14.92
% 48.19/14.92 % ------ Preprocessing...
% 48.19/14.92 % ------ Proving...
% 48.19/14.92 % ------ Problem Properties
% 48.19/14.92
% 48.19/14.92 %
% 48.19/14.92 % clauses 59
% 48.19/14.92 % conjectures 3
% 48.19/14.92 % EPR 27
% 48.19/14.92 % Horn 52
% 48.19/14.92 % unary 27
% 48.19/14.92 % binary 15
% 48.19/14.92 % lits 115
% 48.19/14.92 % lits eq 16
% 48.19/14.92 % fd_pure 0
% 48.19/14.92 % fd_pseudo 0
% 48.19/14.92 % fd_cond 2
% 48.19/14.92 % fd_pseudo_cond 8
% 48.19/14.92 % AC symbols 0
% 48.19/14.92
% 48.19/14.92 % ------ Input Options Time Limit: Unbounded
% 48.19/14.92
% 48.19/14.92
% 48.19/14.92 % ------
% 48.19/14.92 % Current options:
% 48.19/14.92 % ------
% 48.19/14.92
% 48.19/14.92
% 48.19/14.92 %
% 48.19/14.92
% 48.19/14.92 % ------ Proving...
% 48.19/14.92 %
% 48.19/14.92
% 48.19/14.92 % SZS status Theorem for theBenchmark.p
% 48.19/14.92
% 48.19/14.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 48.19/14.92
% 48.19/14.92
%------------------------------------------------------------------------------