%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU216+3 : 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 : n010.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 02:55:57 PM UTC 2026
% Result : Theorem 31.54s 5.36s
% Output : CNFRefutation 31.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 20
% Syntax : Number of formulae : 193 ( 46 unt; 3 def)
% Number of atoms : 789 ( 255 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 734 ( 279 ~; 350 |; 75 &)
% ( 15 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 291 ( 0 sgn 269 !; 22 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_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(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f14,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f24,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f33,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f37,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] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f50,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f51]) ).
fof(f59,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f61,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ( X1 = identity_relation(X0)
<~> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f64,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ( X1 = identity_relation(X0)
<~> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f63]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f75,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ( sK0(X0,X1) = sK1(X0,X1)
& in(sK0(X0,X1),X0) ) )
& ( ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f9]) ).
fof(f82,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f59]) ).
fof(f88,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ( X1 = identity_relation(X0)
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( identity_relation(X0) != X1
| ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0 ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f89,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ( X1 = identity_relation(X0)
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( identity_relation(X0) != X1
| ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0 ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ( X1 = identity_relation(X0)
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( identity_relation(X0) != X1
| ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0 ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
( function(sK12)
& relation(sK12)
& ( sK12 = identity_relation(sK11)
| ( ! [X3] :
( ~ in(X3,sK11)
| apply(sK12,X3) = X3 )
& sK11 = relation_dom(sK12) ) )
& ( sK12 != identity_relation(sK11)
| ( in(sK13,sK11)
& sK13 != apply(sK12,sK13) )
| sK11 != relation_dom(sK12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(ordered_pair(X0,X1),X2)
| ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) )
& ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(ordered_pair(X0,X1),X2)
| ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) )
& ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f97,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f100,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f101,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| sK0(X0,X1) = sK1(X0,X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f102,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| in(sK0(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f103,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2 ),
inference(cnf_transformation,[],[f78]) ).
fof(f108,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f109,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f110,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f79]) ).
fof(f116,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f117,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f132,plain,
! [X0] :
( empty(X0)
| ~ empty(sK5(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f133,plain,
! [X0] :
( empty(X0)
| element(sK5(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f143,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f144,plain,
function(sK12),
inference(cnf_transformation,[],[f91]) ).
fof(f145,plain,
relation(sK12),
inference(cnf_transformation,[],[f91]) ).
fof(f146,plain,
! [X3] :
( sK12 = identity_relation(sK11)
| ~ in(X3,sK11)
| apply(sK12,X3) = X3 ),
inference(cnf_transformation,[],[f91]) ).
fof(f147,plain,
( sK12 = identity_relation(sK11)
| sK11 = relation_dom(sK12) ),
inference(cnf_transformation,[],[f91]) ).
fof(f148,plain,
( sK12 != identity_relation(sK11)
| in(sK13,sK11)
| sK11 != relation_dom(sK12) ),
inference(cnf_transformation,[],[f91]) ).
fof(f149,plain,
( sK12 != identity_relation(sK11)
| sK13 != apply(sK12,sK13)
| sK11 != relation_dom(sK12) ),
inference(cnf_transformation,[],[f91]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f155,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f39]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| apply(X2,X0) = X1 ),
inference(cnf_transformation,[],[f93]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f161,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f103,f108]) ).
fof(f162,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| in(sK0(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f102,f108]) ).
fof(f163,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| sK0(X0,X1) = sK1(X0,X1)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f101,f108]) ).
fof(f164,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1) ),
inference(definition_unfolding,[],[f100,f108]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2 ),
inference(definition_unfolding,[],[f107,f108]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0) ),
inference(definition_unfolding,[],[f106,f108]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| in(X0,relation_dom(X2)) ),
inference(definition_unfolding,[],[f159,f108]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| apply(X2,X0) = X1 ),
inference(definition_unfolding,[],[f158,f108]) ).
fof(f173,plain,
! [X0,X1,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),X1) ),
inference(equality_resolution,[],[f164]) ).
fof(f174,plain,
! [X0,X5] :
( ~ relation(identity_relation(X0))
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),identity_relation(X0)) ),
inference(equality_resolution,[],[f173]) ).
fof(f177,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0) ),
inference(equality_resolution,[],[f168]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f97]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( in(sK0(X1,X0),X1)
| in(unordered_pair(unordered_pair(sK0(X1,X0),sK1(X1,X0)),singleton(sK0(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK0(X1,X0),sK1(X1,X0)),singleton(sK0(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK0(X1,X0) = sK1(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ relation(X2)
| ~ function(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,apply(X1,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_63,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f109]) ).
tcf(c_64,plain,
! [X0: $i] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f110]) ).
tcf(c_70,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f117]) ).
tcf(c_71,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f116]) ).
tcf(c_86,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_87,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK5(X0)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_98,negated_conjecture,
( ( relation_dom(sK12) != sK11 )
| ( identity_relation(sK11) != sK12 )
| ( apply(sK12,sK13) != sK13 ) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_99,negated_conjecture,
( in(sK13,sK11)
| ( relation_dom(sK12) != sK11 )
| ( identity_relation(sK11) != sK12 ) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_100,negated_conjecture,
( ( relation_dom(sK12) = sK11 )
| ( identity_relation(sK11) = sK12 ) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_101,negated_conjecture,
! [X0: $i] :
( ( identity_relation(sK11) = sK12 )
| ( apply(sK12,X0) = X0 )
| ~ in(X0,sK11) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_102,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f145]) ).
tcf(c_103,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f144]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_108,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f155]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_114]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_63]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_180,c_52]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_113,c_52]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_154,c_52]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_60,c_52]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i] :
( in(sK0(X1,X0),X1)
| in(unordered_pair(singleton(sK0(X1,X0)),unordered_pair(sK0(X1,X0),sK1(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_54,c_52]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK0(X1,X0)),unordered_pair(sK0(X1,X0),sK1(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK0(X1,X0) = sK1(X1,X0) )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_55,c_52]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X1)
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(demodulation,[status(thm)],[c_53,c_52]) ).
tcf(c_3633,definition,
iPr_def_10 = identity_relation(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3634,definition,
iPr_def_11 = relation_dom(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3635,definition,
iPr_def_12 = apply(sK12,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3636,negated_conjecture,
function(sK12),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_3637,negated_conjecture,
relation(sK12),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_3638,negated_conjecture,
! [X0: $i] :
( ( iPr_def_10 = sK12 )
| ( apply(sK12,X0) = X0 )
| ~ in(X0,sK11) ),
inference(demodulation,[status(thm)],[c_101,c_3633]) ).
tcf(c_3639,negated_conjecture,
( ( iPr_def_11 = sK11 )
| ( iPr_def_10 = sK12 ) ),
inference(demodulation,[status(thm)],[c_100,c_3634]) ).
tcf(c_3640,negated_conjecture,
( in(sK13,sK11)
| ( iPr_def_11 != sK11 )
| ( iPr_def_10 != sK12 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_3641,negated_conjecture,
( ( iPr_def_12 != sK13 )
| ( iPr_def_11 != sK11 )
| ( iPr_def_10 != sK12 ) ),
inference(demodulation,[status(thm)],[c_98,c_3635]) ).
tcf(c_3642,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3644,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4301,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3639,c_3633]) ).
tcf(c_4374,plain,
relation_dom(iPr_def_10) = sK11,
inference(superposition,[status(thm)],[c_3633,c_108]) ).
tcf(c_4375,plain,
( ( sK12 = iPr_def_10 )
| ( relation_dom(iPr_def_10) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4301,c_108]) ).
tcf(c_4395,plain,
( ( sK12 = iPr_def_10 )
| ( sK11 = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_4375,c_4374]) ).
tcf(c_4742,plain,
! [X0: $i] :
( empty(X0)
| in(sK2(X0),X0) ),
inference(superposition,[status(thm)],[c_64,c_97]) ).
tcf(c_4786,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK2(powerset(X1))) ),
inference(superposition,[status(thm)],[c_64,c_105]) ).
tcf(c_4787,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK5(X1)) ),
inference(superposition,[status(thm)],[c_86,c_105]) ).
tcf(c_4806,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK2(powerset(X1))) ),
inference(superposition,[status(thm)],[c_64,c_106]) ).
tcf(c_5052,plain,
! [X0: $i] :
( ( iPr_def_11 = sK11 )
| ( iPr_def_11 != X0 )
| ( sK11 != X0 ) ),
inference(instantiation,[status(thm)],[c_3644]) ).
tcf(c_5184,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_488,c_541]) ).
tcf(c_5189,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5184,c_70,c_71]) ).
tcf(c_6276,plain,
! [X0: $i] :
( empty(sK2(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4742,c_4806]) ).
tcf(c_6988,plain,
! [X0: $i] :
( empty(X0)
| empty(sK5(X0))
| element(sK2(sK5(X0)),X0) ),
inference(superposition,[status(thm)],[c_4742,c_4787]) ).
tcf(c_9738,plain,
! [X0: $i] :
( empty(X0)
| element(sK2(sK5(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_6988,c_87,c_6988]) ).
tcf(c_9745,plain,
! [X0: $i] :
( empty(X0)
| in(sK2(sK5(X0)),X0) ),
inference(superposition,[status(thm)],[c_9738,c_97]) ).
tcf(c_9772,plain,
! [X0: $i] :
( empty(sK2(powerset(X0)))
| element(sK2(sK5(sK2(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_9745,c_4786]) ).
tcf(c_22030,plain,
! [X0: $i] :
( ( iPr_def_12 = sK13 )
| ( iPr_def_12 != X0 )
| ( sK13 != X0 ) ),
inference(instantiation,[status(thm)],[c_3644]) ).
tcf(c_22575,plain,
! [X0: $i] :
( ( iPr_def_10 = sK12 )
| ( iPr_def_10 != X0 )
| ( sK12 != X0 ) ),
inference(instantiation,[status(thm)],[c_3644]) ).
tcf(c_24960,plain,
! [X0: $i] :
( empty(X0)
| empty(sK2(powerset(X0)))
| in(sK2(sK5(sK2(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_9772,c_97]) ).
tcf(c_31475,plain,
! [X0: $i] :
( ( sK12 = iPr_def_10 )
| ( apply(sK12,X0) = X0 )
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3639,c_3638]) ).
tcf(c_31507,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3639,c_3633]) ).
tcf(c_31556,plain,
relation_dom(iPr_def_10) = sK11,
inference(superposition,[status(thm)],[c_3633,c_108]) ).
tcf(c_32481,plain,
! [X0: $i,X1: $i] :
( in(sK0(X1,X0),X1)
| in(sK0(X1,X0),relation_dom(X0))
| ( identity_relation(X1) = X0 )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_567,c_522]) ).
tcf(c_32576,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X1) = X0 )
| ( sK0(X1,X0) = sK1(X1,X0) )
| ( apply(X0,sK0(X1,X0)) = sK1(X1,X0) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_580,c_541]) ).
tcf(c_43296,plain,
( ( iPr_def_10 = sK12 )
| ( iPr_def_10 != iPr_def_10 )
| ( sK12 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_22575]) ).
tcf(c_43297,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_3642]) ).
tcf(c_46657,plain,
( ( iPr_def_12 = sK13 )
| ( iPr_def_12 != iPr_def_12 )
| ( sK13 != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_22030]) ).
tcf(c_46658,plain,
iPr_def_12 = iPr_def_12,
inference(instantiation,[status(thm)],[c_3642]) ).
tcf(c_56987,plain,
! [X0: $i] :
( in(sK0(X0,sK12),iPr_def_11)
| in(sK0(X0,sK12),X0)
| ( identity_relation(X0) = sK12 )
| ~ relation(sK12)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_3634,c_32481]) ).
tcf(c_57074,plain,
! [X0: $i] :
( in(sK0(X0,sK12),iPr_def_11)
| in(sK0(X0,sK12),X0)
| ( identity_relation(X0) = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56987,c_3637,c_3636]) ).
tcf(c_59315,plain,
( in(sK0(iPr_def_11,sK12),iPr_def_11)
| ( identity_relation(iPr_def_11) = sK12 ) ),
inference(equality_factoring,[status(thm)],[c_57074]) ).
tcf(c_60087,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ( apply(sK12,sK0(iPr_def_11,sK12)) = sK0(iPr_def_11,sK12) ) ),
inference(superposition,[status(thm)],[c_59315,c_31475]) ).
tcf(c_74413,plain,
( ( iPr_def_11 = sK11 )
| ( iPr_def_11 != iPr_def_11 )
| ( sK11 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_5052]) ).
tcf(c_74414,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_3642]) ).
tcf(c_78474,plain,
( in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK0(iPr_def_11,sK12))),sK12)
| ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(sK0(iPr_def_11,sK12),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_60087,c_554]) ).
tcf(c_78486,plain,
( in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK0(iPr_def_11,sK12))),sK12)
| ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(sK0(iPr_def_11,sK12),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_78474,c_3634]) ).
tcf(c_78487,plain,
( in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK0(iPr_def_11,sK12))),sK12)
| ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ in(sK0(iPr_def_11,sK12),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_78486,c_3637,c_3636]) ).
tcf(c_80202,plain,
( in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK0(iPr_def_11,sK12))),sK12)
| ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 ) ),
inference(global_subsumption_just,[status(thm)],[c_78487,c_59315,c_78487]) ).
tcf(c_80215,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ in(sK12,unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK0(iPr_def_11,sK12)))) ),
inference(superposition,[status(thm)],[c_80202,c_49]) ).
tcf(c_121787,plain,
! [X0: $i] :
( ( identity_relation(X0) = sK12 )
| ( sK0(X0,sK12) = sK1(X0,sK12) )
| ( apply(sK12,sK0(X0,sK12)) = sK1(X0,sK12) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_3636,c_32576]) ).
tcf(c_121792,plain,
! [X0: $i] :
( ( identity_relation(X0) = sK12 )
| ( sK0(X0,sK12) = sK1(X0,sK12) )
| ( apply(sK12,sK0(X0,sK12)) = sK1(X0,sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121787,c_3637]) ).
tcf(c_121989,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ( sK0(iPr_def_11,sK12) = sK1(iPr_def_11,sK12) ) ),
inference(superposition,[status(thm)],[c_121792,c_60087]) ).
tcf(c_122816,plain,
! [X0: $i] :
( in(sK2(sK5(sK2(powerset(X0)))),X0)
| empty(sK2(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_24960,c_6276,c_24960]) ).
tcf(c_122817,plain,
! [X0: $i] :
( empty(sK2(powerset(X0)))
| in(sK2(sK5(sK2(powerset(X0)))),X0) ),
inference(renaming,[status(thm)],[c_122816]) ).
tcf(c_122843,plain,
( empty(sK2(powerset(sK11)))
| ( sK12 = iPr_def_10 )
| ( apply(sK12,sK2(sK5(sK2(powerset(sK11))))) = sK2(sK5(sK2(powerset(sK11)))) ) ),
inference(superposition,[status(thm)],[c_122817,c_3638]) ).
tcf(c_123030,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ relation(sK12)
| ~ in(sK0(iPr_def_11,sK12),iPr_def_11)
| ~ in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK1(iPr_def_11,sK12))),sK12) ),
inference(superposition,[status(thm)],[c_121989,c_593]) ).
tcf(c_123032,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ in(sK0(iPr_def_11,sK12),iPr_def_11)
| ~ in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK1(iPr_def_11,sK12))),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_123030,c_3637]) ).
tcf(c_123043,plain,
( empty(sK2(powerset(iPr_def_11)))
| ( sK12 = iPr_def_10 )
| ( apply(sK12,sK2(sK5(sK2(powerset(sK11))))) = sK2(sK5(sK2(powerset(sK11)))) ) ),
inference(superposition,[status(thm)],[c_4395,c_122843]) ).
tcf(c_124527,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK1(iPr_def_11,sK12))),sK12) ),
inference(global_subsumption_just,[status(thm)],[c_123032,c_59315,c_123032]) ).
tcf(c_124540,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 )
| ~ in(unordered_pair(singleton(sK0(iPr_def_11,sK12)),unordered_pair(sK0(iPr_def_11,sK12),sK0(iPr_def_11,sK12))),sK12) ),
inference(superposition,[status(thm)],[c_121989,c_124527]) ).
tcf(c_127470,plain,
( ( sK12 = iPr_def_10 )
| ( identity_relation(iPr_def_11) = sK12 ) ),
inference(global_subsumption_just,[status(thm)],[c_80215,c_59315,c_78487,c_124540]) ).
tcf(c_127514,plain,
sK12 = iPr_def_10,
inference(superposition,[status(thm)],[c_127470,c_31507]) ).
tcf(c_127594,plain,
relation_dom(iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3634,c_127514]) ).
tcf(c_127607,plain,
sK11 = iPr_def_11,
inference(demodulation,[status(thm)],[c_31556,c_127594]) ).
tcf(c_129698,plain,
sK12 = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_123043,c_127514]) ).
tcf(c_130177,plain,
apply(iPr_def_10,sK13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3635,c_129698]) ).
tcf(c_130178,plain,
relation_dom(iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3634,c_129698]) ).
tcf(c_130183,plain,
( in(sK13,sK11)
| ( iPr_def_10 != iPr_def_10 )
| ( sK11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_3640,c_129698]) ).
tcf(c_130203,plain,
( in(sK13,sK11)
| ( sK11 != iPr_def_11 ) ),
inference(equality_resolution_simp,[status(thm)],[c_130183]) ).
tcf(c_130227,plain,
sK11 = iPr_def_11,
inference(demodulation,[status(thm)],[c_4374,c_130178]) ).
tcf(c_130229,plain,
in(sK13,sK11),
inference(backward_subsumption_resolution,[status(thm)],[c_130203,c_130227]) ).
tcf(c_130252,plain,
identity_relation(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_3633,c_130227]) ).
tcf(c_131584,plain,
in(sK13,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_130229,c_130227]) ).
tcf(c_131586,plain,
apply(identity_relation(iPr_def_11),sK13) = sK13,
inference(superposition,[status(thm)],[c_131584,c_5189]) ).
tcf(c_131592,plain,
sK13 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_131586,c_130177,c_130252]) ).
tcf(c_131594,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_131592,c_127514,c_127607,c_74414,c_74413,c_46658,c_46657,c_43297,c_43296,c_3641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU216+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:13:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 31.54/5.36 % SZS status Started for theBenchmark.p
% 31.54/5.36 % SZS status Theorem for theBenchmark.p
% 31.54/5.36
% 31.54/5.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.54/5.36
% 31.54/5.36 % ------ iProver source info
% 31.54/5.36
% 31.54/5.36 % git: date: 2026-07-19 20:42:38 +0200
% 31.54/5.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.54/5.36 % git: non_committed_changes: false
% 31.54/5.36
% 31.54/5.36 % ------ Parsing...
% 31.54/5.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.54/5.36
% 31.54/5.36 % ------ Preprocessing... sup_sim: 9 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 31.54/5.36
% 31.54/5.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.54/5.36
% 31.54/5.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.54/5.36 % ------ Proving...
% 31.54/5.36 % ------ Problem Properties
% 31.54/5.36
% 31.54/5.36 %
% 31.54/5.36 % clauses 60
% 31.54/5.36 % conjectures 6
% 31.54/5.36 % EPR 24
% 31.54/5.36 % Horn 53
% 31.54/5.36 % unary 28
% 31.54/5.36 % binary 16
% 31.54/5.36 % lits 116
% 31.54/5.36 % lits eq 25
% 31.54/5.36 % fd_pure 0
% 31.54/5.36 % fd_pseudo 0
% 31.54/5.36 % fd_cond 1
% 31.54/5.36 % fd_pseudo_cond 6
% 31.54/5.36 % AC symbols 0
% 31.54/5.36
% 31.54/5.36 % ------ Schedule dynamic 5 is on
% 31.54/5.36
% 31.54/5.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 31.54/5.36
% 31.54/5.36
% 31.54/5.36 % ------
% 31.54/5.36 % Current options:
% 31.54/5.36 % ------
% 31.54/5.36
% 31.54/5.36
% 31.54/5.36 %
% 31.54/5.36
% 31.54/5.36 % ------ Proving...
% 31.54/5.36 %
% 31.54/5.36
% 31.54/5.36 % SZS status Theorem for theBenchmark.p
% 31.54/5.36
% 31.54/5.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.54/5.36
% 31.54/5.36
%------------------------------------------------------------------------------