%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU249+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 02:56:21 PM UTC 2026
% Result : Theorem 85.61s 37.21s
% Output : CNFRefutation 85.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 210 ( 48 unt; 0 def)
% Number of atoms : 516 ( 77 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 512 ( 206 ~; 231 |; 53 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 345 ( 0 sgn 333 !; 12 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f14,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f19,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f30,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l29_wellord1) ).
fof(f37,axiom,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f38,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_wellord1) ).
fof(f39,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_wellord1) ).
fof(f40,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f45,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f46,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f47,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f48,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f50,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f52,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f53,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f57,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f58,plain,
? [X0,X1,X2] :
( relation(X2)
& in(X0,relation_field(relation_restriction(X2,X1)))
& ( ~ in(X0,X1)
| ~ in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f59,plain,
? [X0,X1,X2] :
( relation(X2)
& in(X0,relation_field(relation_restriction(X2,X1)))
& ( ~ in(X0,X1)
| ~ in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f61,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f62,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f66,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f67,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f68,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f72,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f73,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f53]) ).
fof(f75,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f78,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f81,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f82,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f47]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
( relation(sK2)
& in(sK0,relation_field(relation_restriction(sK2,sK1)))
& ( ~ in(sK0,sK1)
| ~ in(sK0,relation_field(sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f59]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| ( in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0) )
& ( ~ in(sK4(X0,X1,X2),X2)
| ( ~ in(sK4(X0,X1,X2),X1)
& ~ in(sK4(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f94]) ).
fof(f101,plain,
relation(sK2),
inference(cnf_transformation,[],[f87]) ).
fof(f102,plain,
in(sK0,relation_field(relation_restriction(sK2,sK1))),
inference(cnf_transformation,[],[f87]) ).
fof(f103,plain,
( ~ in(sK0,sK1)
| ~ in(sK0,relation_field(sK2)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f104,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f105,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f108,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f113,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f114,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f115,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f120,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f122,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f123,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f129,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f134,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f135,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f136,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f137,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f140,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f143,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f144,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f155,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f156,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f107]) ).
fof(f157,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f115]) ).
fof(f158,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f114]) ).
fof(f159,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f113]) ).
tcf(c_49,negated_conjecture,
( ~ in(sK0,sK1)
| ~ in(sK0,relation_field(sK2)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_50,negated_conjecture,
in(sK0,relation_field(relation_restriction(sK2,sK1))),
inference(cnf_transformation,[],[f102]) ).
tcf(c_51,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f101]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,relation_dom_restriction(X0,X1)) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,X0),X1) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_rng(X0),X1) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X2,powerset(X3))
| ~ relation(X1)
| ( relation_dom(X1) != X3 )
| ( relation_dom(relation_rng_restriction(X0,X1)) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_92]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i] :
( element(relation_dom(relation_rng_restriction(X1,X0)),powerset(relation_dom(X0)))
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_531]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X2,powerset(X3))
| ~ relation(X0)
| ( relation_rng(X0) != X3 )
| ( relation_rng(relation_dom_restriction(X0,X1)) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_92]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i] :
( element(relation_rng(relation_dom_restriction(X0,X1)),powerset(relation_rng(X0)))
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_540]) ).
tcf(c_1693,plain,
set_union2(relation_dom(sK2),relation_rng(sK2)) = relation_field(sK2),
inference(superposition,[status(thm)],[c_51,c_68]) ).
tcf(c_1737,plain,
! [X0: $i] :
( in(X0,relation_field(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_1693,c_64]) ).
tcf(c_1739,plain,
! [X0: $i] :
( in(X0,relation_field(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_1693,c_65]) ).
tcf(c_1761,plain,
( in(sK0,relation_field(sK2))
| ~ in(sK0,relation_rng(sK2)) ),
inference(instantiation,[status(thm)],[c_1739]) ).
tcf(c_1763,plain,
( in(sK0,relation_field(sK2))
| ~ in(sK0,relation_dom(sK2)) ),
inference(instantiation,[status(thm)],[c_1737]) ).
tcf(c_1901,plain,
! [X0: $i] :
( relation(relation_restriction(sK2,X0))
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_1951,plain,
! [X0: $i] :
( relation(relation_dom_restriction(sK2,X0))
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_1957,plain,
! [X0: $i] :
( relation(relation_rng_restriction(X0,sK2))
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1967,plain,
! [X0: $i] : relation_rng_restriction(X0,relation_dom_restriction(sK2,X0)) = relation_restriction(sK2,X0),
inference(superposition,[status(thm)],[c_51,c_69]) ).
tcf(c_1994,plain,
! [X0: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK2),X0) = relation_restriction(sK2,X0),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_2022,plain,
! [X0: $i] : set_intersection2(relation_dom(sK2),X0) = relation_dom(relation_dom_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_51,c_82]) ).
tcf(c_2114,plain,
! [X0: $i] :
( relation(relation_restriction(sK2,X0))
| ~ relation(relation_dom_restriction(sK2,X0)) ),
inference(superposition,[status(thm)],[c_1967,c_91]) ).
tcf(c_2128,plain,
! [X0: $i] : relation(relation_restriction(sK2,X0)),
inference(global_subsumption_just,[status(thm)],[c_2114,c_51,c_1901]) ).
tcf(c_2134,plain,
! [X0: $i] : set_union2(relation_dom(relation_restriction(sK2,X0)),relation_rng(relation_restriction(sK2,X0))) = relation_field(relation_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_2128,c_68]) ).
tcf(c_2228,plain,
! [X0: $i] : set_intersection2(relation_rng(sK2),X0) = relation_rng(relation_rng_restriction(X0,sK2)),
inference(superposition,[status(thm)],[c_51,c_85]) ).
tcf(c_4610,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_restriction(sK2,X1)))
| in(X0,relation_dom(relation_restriction(sK2,X1)))
| ~ in(X0,relation_field(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_2134,c_66]) ).
tcf(c_8812,plain,
! [X0: $i] :
( element(relation_dom(relation_restriction(sK2,X0)),powerset(relation_dom(relation_dom_restriction(sK2,X0))))
| ~ relation(relation_dom_restriction(sK2,X0)) ),
inference(superposition,[status(thm)],[c_1967,c_532]) ).
tcf(c_8838,plain,
! [X0: $i] :
( element(relation_dom(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_dom(sK2),X0)))
| ~ relation(relation_dom_restriction(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_8812,c_2022]) ).
tcf(c_9049,plain,
! [X0: $i] : element(relation_dom(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_dom(sK2),X0))),
inference(global_subsumption_just,[status(thm)],[c_8838,c_51,c_1951,c_8838]) ).
tcf(c_9054,plain,
! [X0: $i] : element(relation_dom(relation_restriction(sK2,X0)),powerset(set_intersection2(X0,relation_dom(sK2)))),
inference(superposition,[status(thm)],[c_77,c_9049]) ).
tcf(c_9187,plain,
! [X0: $i,X1: $i] :
( ~ empty(set_intersection2(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_9054,c_100]) ).
tcf(c_9788,plain,
! [X0: $i] :
( element(relation_rng(relation_restriction(sK2,X0)),powerset(relation_rng(relation_rng_restriction(X0,sK2))))
| ~ relation(relation_rng_restriction(X0,sK2)) ),
inference(superposition,[status(thm)],[c_1994,c_541]) ).
tcf(c_9814,plain,
! [X0: $i] :
( element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_rng(sK2),X0)))
| ~ relation(relation_rng_restriction(X0,sK2)) ),
inference(light_normalisation,[status(thm)],[c_9788,c_2228]) ).
tcf(c_9892,plain,
! [X0: $i] : element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_rng(sK2),X0))),
inference(global_subsumption_just,[status(thm)],[c_9814,c_51,c_1957,c_9814]) ).
tcf(c_9897,plain,
! [X0: $i] : element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(X0,relation_rng(sK2)))),
inference(superposition,[status(thm)],[c_77,c_9892]) ).
tcf(c_9989,plain,
! [X0: $i,X1: $i] :
( element(X0,set_intersection2(X1,relation_rng(sK2)))
| ~ in(X0,relation_rng(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_9897,c_101]) ).
tcf(c_9990,plain,
! [X0: $i,X1: $i] :
( ~ empty(set_intersection2(X1,relation_rng(sK2)))
| ~ in(X0,relation_rng(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_9897,c_100]) ).
tcf(c_18756,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_restriction(X0,X1)),relation_rng(relation_restriction(X0,X1))) = relation_field(relation_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_71,c_68]) ).
tcf(c_18825,plain,
! [X0: $i] : set_union2(relation_dom(relation_restriction(sK2,X0)),relation_rng(relation_restriction(sK2,X0))) = relation_field(relation_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_51,c_18756]) ).
tcf(c_19087,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_restriction(sK2,X1)))
| in(X0,relation_dom(relation_restriction(sK2,X1)))
| ~ in(X0,relation_field(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_18825,c_66]) ).
tcf(c_19246,plain,
( in(sK0,relation_rng(relation_restriction(sK2,sK1)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_50,c_19087]) ).
tcf(c_19339,plain,
! [X0: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK2),X0) = relation_restriction(sK2,X0),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_19373,plain,
! [X0: $i] : set_intersection2(relation_rng(sK2),X0) = relation_rng(relation_rng_restriction(X0,sK2)),
inference(superposition,[status(thm)],[c_51,c_85]) ).
tcf(c_37333,plain,
! [X0: $i] :
( element(relation_rng(relation_restriction(sK2,X0)),powerset(relation_rng(relation_rng_restriction(X0,sK2))))
| ~ relation(relation_rng_restriction(X0,sK2)) ),
inference(superposition,[status(thm)],[c_19339,c_541]) ).
tcf(c_37361,plain,
! [X0: $i] :
( element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_rng(sK2),X0)))
| ~ relation(relation_rng_restriction(X0,sK2)) ),
inference(light_normalisation,[status(thm)],[c_37333,c_19373]) ).
tcf(c_38899,plain,
! [X0: $i] : element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_rng(sK2),X0))),
inference(global_subsumption_just,[status(thm)],[c_37361,c_51,c_1957,c_9814]) ).
tcf(c_38905,plain,
! [X0: $i,X1: $i] :
( element(X0,set_intersection2(relation_rng(sK2),X1))
| ~ in(X0,relation_rng(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_38899,c_101]) ).
tcf(c_43815,plain,
( element(sK0,set_intersection2(relation_rng(sK2),sK1))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_19246,c_38905]) ).
tcf(c_44456,plain,
( element(sK0,set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(demodulation,[status(thm)],[c_43815,c_77]) ).
tcf(c_44463,plain,
( empty(set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1)))
| in(sK0,set_intersection2(sK1,relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_44456,c_53]) ).
tcf(c_50461,plain,
( in(sK0,relation_rng(relation_restriction(sK2,sK1)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_50,c_4610]) ).
tcf(c_51233,plain,
( in(sK0,relation_dom(relation_restriction(sK2,sK1)))
| ~ empty(set_intersection2(sK1,relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_50461,c_9990]) ).
tcf(c_51234,plain,
( element(sK0,set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_50461,c_9989]) ).
tcf(c_51898,plain,
( empty(set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1)))
| in(sK0,set_intersection2(sK1,relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_51234,c_53]) ).
tcf(c_52380,plain,
( in(sK0,set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_51898,c_44463,c_51233]) ).
tcf(c_52381,plain,
( in(sK0,relation_dom(relation_restriction(sK2,sK1)))
| in(sK0,set_intersection2(sK1,relation_rng(sK2))) ),
inference(renaming,[status(thm)],[c_52380]) ).
tcf(c_52389,plain,
( in(sK0,set_intersection2(sK1,relation_rng(sK2)))
| ~ empty(set_intersection2(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_52381,c_9187]) ).
tcf(c_108145,plain,
( in(sK0,relation_rng(sK2))
| ~ empty(set_intersection2(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_52389,c_60]) ).
tcf(c_108146,plain,
( in(sK0,sK1)
| ~ empty(set_intersection2(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_52389,c_59]) ).
tcf(c_108155,plain,
~ empty(set_intersection2(sK1,relation_dom(sK2))),
inference(global_subsumption_just,[status(thm)],[c_108146,c_49,c_1761,c_108146,c_108145]) ).
tcf(c_110797,plain,
! [X0: $i] : relation_rng_restriction(X0,relation_dom_restriction(sK2,X0)) = relation_restriction(sK2,X0),
inference(superposition,[status(thm)],[c_51,c_69]) ).
tcf(c_110813,plain,
! [X0: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK2),X0) = relation_restriction(sK2,X0),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_110888,plain,
! [X0: $i] :
( relation(relation_restriction(sK2,X0))
| ~ relation(relation_dom_restriction(sK2,X0)) ),
inference(superposition,[status(thm)],[c_110797,c_91]) ).
tcf(c_110897,plain,
! [X0: $i] : relation(relation_restriction(sK2,X0)),
inference(global_subsumption_just,[status(thm)],[c_110888,c_51,c_1901]) ).
tcf(c_110901,plain,
! [X0: $i] : set_union2(relation_dom(relation_restriction(sK2,X0)),relation_rng(relation_restriction(sK2,X0))) = relation_field(relation_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_110897,c_68]) ).
tcf(c_110988,plain,
! [X0: $i] : set_intersection2(relation_dom(sK2),X0) = relation_dom(relation_dom_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_51,c_82]) ).
tcf(c_111015,plain,
! [X0: $i] : set_intersection2(relation_rng(sK2),X0) = relation_rng(relation_rng_restriction(X0,sK2)),
inference(superposition,[status(thm)],[c_51,c_85]) ).
tcf(c_112185,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_restriction(sK2,X1)))
| in(X0,relation_dom(relation_restriction(sK2,X1)))
| ~ in(X0,relation_field(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_110901,c_66]) ).
tcf(c_120106,plain,
! [X0: $i] :
( element(relation_dom(relation_restriction(sK2,X0)),powerset(relation_dom(relation_dom_restriction(sK2,X0))))
| ~ relation(relation_dom_restriction(sK2,X0)) ),
inference(superposition,[status(thm)],[c_110797,c_532]) ).
tcf(c_120132,plain,
! [X0: $i] :
( element(relation_dom(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_dom(sK2),X0)))
| ~ relation(relation_dom_restriction(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_120106,c_110988]) ).
tcf(c_120162,plain,
! [X0: $i] :
( element(relation_rng(relation_restriction(sK2,X0)),powerset(relation_rng(relation_rng_restriction(X0,sK2))))
| ~ relation(relation_rng_restriction(X0,sK2)) ),
inference(superposition,[status(thm)],[c_110813,c_541]) ).
tcf(c_120188,plain,
! [X0: $i] :
( element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_rng(sK2),X0)))
| ~ relation(relation_rng_restriction(X0,sK2)) ),
inference(light_normalisation,[status(thm)],[c_120162,c_111015]) ).
tcf(c_120231,plain,
! [X0: $i] : element(relation_dom(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_dom(sK2),X0))),
inference(global_subsumption_just,[status(thm)],[c_120132,c_51,c_1951,c_8838]) ).
tcf(c_120235,plain,
! [X0: $i] : element(relation_dom(relation_restriction(sK2,X0)),powerset(set_intersection2(X0,relation_dom(sK2)))),
inference(superposition,[status(thm)],[c_77,c_120231]) ).
tcf(c_120246,plain,
! [X0: $i] : element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(relation_rng(sK2),X0))),
inference(global_subsumption_just,[status(thm)],[c_120188,c_51,c_1957,c_9814]) ).
tcf(c_120250,plain,
! [X0: $i] : element(relation_rng(relation_restriction(sK2,X0)),powerset(set_intersection2(X0,relation_rng(sK2)))),
inference(superposition,[status(thm)],[c_77,c_120246]) ).
tcf(c_121049,plain,
! [X0: $i,X1: $i] :
( element(X0,set_intersection2(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_120235,c_101]) ).
tcf(c_121050,plain,
! [X0: $i,X1: $i] :
( ~ empty(set_intersection2(X1,relation_dom(sK2)))
| ~ in(X0,relation_dom(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_120235,c_100]) ).
tcf(c_121062,plain,
! [X0: $i,X1: $i] :
( element(X0,set_intersection2(X1,relation_rng(sK2)))
| ~ in(X0,relation_rng(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_120250,c_101]) ).
tcf(c_126560,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_restriction(X0,X1)),relation_rng(relation_restriction(X0,X1))) = relation_field(relation_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_71,c_68]) ).
tcf(c_126621,plain,
! [X0: $i] : set_union2(relation_dom(relation_restriction(sK2,X0)),relation_rng(relation_restriction(sK2,X0))) = relation_field(relation_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_51,c_126560]) ).
tcf(c_126899,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_restriction(sK2,X1)))
| in(X0,relation_dom(relation_restriction(sK2,X1)))
| ~ in(X0,relation_field(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_126621,c_66]) ).
tcf(c_126969,plain,
! [X0: $i] : relation_rng_restriction(X0,relation_dom_restriction(sK2,X0)) = relation_restriction(sK2,X0),
inference(superposition,[status(thm)],[c_51,c_69]) ).
tcf(c_126985,plain,
! [X0: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK2),X0) = relation_restriction(sK2,X0),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_127051,plain,
( in(sK0,relation_rng(relation_restriction(sK2,sK1)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_50,c_126899]) ).
tcf(c_127069,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_rng_restriction(X1,X0)),X2) = relation_dom(relation_dom_restriction(relation_rng_restriction(X1,X0),X2)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_91,c_82]) ).
tcf(c_127085,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_rng(relation_dom_restriction(X0,X1)),X2) = relation_rng(relation_rng_restriction(X2,relation_dom_restriction(X0,X1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_88,c_85]) ).
tcf(c_154304,plain,
( in(sK0,relation_rng(relation_restriction(sK2,sK1)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_50,c_112185]) ).
tcf(c_154856,plain,
( in(sK0,relation_dom(relation_restriction(sK2,sK1)))
| ~ empty(relation_rng(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_154304,c_52]) ).
tcf(c_154858,plain,
( element(sK0,set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_154304,c_121062]) ).
tcf(c_154991,plain,
( ~ empty(relation_rng(relation_restriction(sK2,sK1)))
| ~ empty(set_intersection2(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_154856,c_121050]) ).
tcf(c_155058,plain,
( empty(set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1)))
| in(sK0,set_intersection2(sK1,relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_154858,c_53]) ).
tcf(c_155071,plain,
~ empty(set_intersection2(sK1,relation_dom(sK2))),
inference(global_subsumption_just,[status(thm)],[c_154991,c_108155]) ).
tcf(c_155123,plain,
( in(sK0,set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_155058,c_52381]) ).
tcf(c_155124,plain,
( in(sK0,relation_dom(relation_restriction(sK2,sK1)))
| in(sK0,set_intersection2(sK1,relation_rng(sK2))) ),
inference(renaming,[status(thm)],[c_155123]) ).
tcf(c_155133,plain,
( element(sK0,set_intersection2(sK1,relation_dom(sK2)))
| in(sK0,set_intersection2(sK1,relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_155124,c_121049]) ).
tcf(c_164180,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_dom(relation_rng_restriction(X0,sK2)),X1) = relation_dom(relation_dom_restriction(relation_rng_restriction(X0,sK2),X1)),
inference(superposition,[status(thm)],[c_51,c_127069]) ).
tcf(c_164804,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_rng(relation_dom_restriction(sK2,X0)),X1) = relation_rng(relation_rng_restriction(X1,relation_dom_restriction(sK2,X0))),
inference(superposition,[status(thm)],[c_51,c_127085]) ).
tcf(c_165453,plain,
! [X0: $i] : set_intersection2(relation_dom(relation_rng_restriction(X0,sK2)),X0) = relation_dom(relation_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_126985,c_164180]) ).
tcf(c_165457,plain,
! [X0: $i] : set_intersection2(relation_rng(relation_dom_restriction(sK2,X0)),X0) = relation_rng(relation_restriction(sK2,X0)),
inference(superposition,[status(thm)],[c_126969,c_164804]) ).
tcf(c_165461,plain,
! [X0: $i] : set_intersection2(X0,relation_dom(relation_rng_restriction(X0,sK2))) = relation_dom(relation_restriction(sK2,X0)),
inference(demodulation,[status(thm)],[c_165453,c_77]) ).
tcf(c_165488,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_165461,c_59]) ).
tcf(c_167757,plain,
! [X0: $i] : set_intersection2(X0,relation_rng(relation_dom_restriction(sK2,X0))) = relation_rng(relation_restriction(sK2,X0)),
inference(demodulation,[status(thm)],[c_165457,c_77]) ).
tcf(c_167784,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_restriction(sK2,X1))) ),
inference(superposition,[status(thm)],[c_167757,c_59]) ).
tcf(c_170696,plain,
( in(sK0,sK1)
| in(sK0,relation_dom(relation_restriction(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_127051,c_167784]) ).
tcf(c_174432,plain,
in(sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_170696,c_165488]) ).
tcf(c_174433,plain,
~ in(sK0,relation_field(sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_174432]) ).
tcf(c_191383,plain,
( empty(set_intersection2(sK1,relation_dom(sK2)))
| in(sK0,set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,set_intersection2(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_155133,c_53]) ).
tcf(c_191384,plain,
( in(sK0,set_intersection2(sK1,relation_rng(sK2)))
| in(sK0,set_intersection2(sK1,relation_dom(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_191383,c_155071]) ).
tcf(c_217667,plain,
( in(sK0,relation_rng(sK2))
| in(sK0,set_intersection2(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_191384,c_60]) ).
tcf(c_217668,plain,
( in(sK0,sK1)
| in(sK0,set_intersection2(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_191384,c_59]) ).
tcf(c_217677,plain,
in(sK0,set_intersection2(sK1,relation_dom(sK2))),
inference(global_subsumption_just,[status(thm)],[c_217668,c_1761,c_174433,c_217667]) ).
tcf(c_217682,plain,
in(sK0,relation_dom(sK2)),
inference(superposition,[status(thm)],[c_217677,c_60]) ).
tcf(c_217685,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_217682,c_174433,c_1763]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU249+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/15.38 % Computer : n006.cluster.edu
% 0.09/15.38 % Model : x86_64 x86_64
% 0.09/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.38 % Memory : 8046.5625MB
% 0.09/15.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.38 % CPULimit : 300
% 0.09/15.38 % WCLimit : 300
% 0.09/15.38 % DateTime : Thu Sep 24 13:23:57 UTC 2026
% 0.09/15.39 % CPUTime :
% 0.09/15.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/15.44 Running first-order theorem proving
% 0.15/15.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/15.46
% 0.15/15.46 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.46
% 0.15/15.46 % Detected problem language: tptp
% 0.15/15.47 % Proving...
% 85.61/37.21 % SZS status Started for theBenchmark.p
% 85.61/37.21 % SZS status Theorem for theBenchmark.p
% 85.61/37.21
% 85.61/37.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 85.61/37.21
% 85.61/37.21 % ------ iProver source info
% 85.61/37.21
% 85.61/37.21 % git: date: 2026-07-19 20:42:38 +0200
% 85.61/37.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 85.61/37.21 % git: non_committed_changes: false
% 85.61/37.21
% 85.61/37.21 % ------ Parsing...
% 85.61/37.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 85.61/37.21
% 85.61/37.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 85.61/37.21
% 85.61/37.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 85.61/37.21
% 85.61/37.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 85.61/37.21 % ------ Proving...
% 85.61/37.21 % ------ Problem Properties
% 85.61/37.21
% 85.61/37.21 %
% 85.61/37.21 % clauses 45
% 85.61/37.21 % conjectures 3
% 85.61/37.21 % EPR 11
% 85.61/37.21 % Horn 40
% 85.61/37.21 % unary 13
% 85.61/37.21 % binary 20
% 85.61/37.21 % lits 91
% 85.61/37.21 % lits eq 16
% 85.61/37.21 % fd_pure 0
% 85.61/37.21 % fd_pseudo 0
% 85.61/37.21 % fd_cond 0
% 85.61/37.21 % fd_pseudo_cond 7
% 85.61/37.21 % AC symbols 0
% 85.61/37.21
% 85.61/37.21 % ------ Schedule dynamic 5 is on
% 85.61/37.21
% 85.61/37.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 85.61/37.21
% 85.61/37.21
% 85.61/37.21 % ------
% 85.61/37.21 % Current options:
% 85.61/37.21 % ------
% 85.61/37.21
% 85.61/37.21
% 85.61/37.21 %
% 85.61/37.21
% 85.61/37.21 % ------ Proving...
% 85.61/37.21 % Proof_search_loop: time out after: 2640 full_loop iterations
% 85.61/37.21
% 85.61/37.21 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 85.61/37.21
% 85.61/37.21
% 85.61/37.21 % ------
% 85.61/37.21 % Current options:
% 85.61/37.21 % ------
% 85.61/37.21
% 85.61/37.21
% 85.61/37.21 %
% 85.61/37.21
% 85.61/37.21 % ------ Proving...
% 85.61/37.21 %
% 85.61/37.21
% 85.61/37.21 % SZS status Theorem for theBenchmark.p
% 85.61/37.21
% 85.61/37.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 85.61/37.22
% 85.61/37.22
%------------------------------------------------------------------------------