%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU051+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 : n001.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 02:55:10 PM UTC 2026
% Result : Theorem 159.34s 22.41s
% Output : CNFRefutation 159.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 132 ( 10 unt; 2 def)
% Number of atoms : 574 ( 115 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 755 ( 313 ~; 318 |; 91 &)
% ( 19 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 310 ( 0 sgn 287 !; 23 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f30,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f36,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f39,plain,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X4] :
( in(X4,relation_dom(X1))
=> apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
inference(rectify,[],[f36]) ).
fof(f49,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f54,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(flattening,[],[f53]) ).
fof(f59,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ~ subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f60,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ~ subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f62,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f63,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f62]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f69,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f70,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
inference(flattening,[],[f69]) ).
fof(f75,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f76,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK4(X0,X1,X6)) = X6
& in(sK4(X0,X1,X6),X1)
& in(sK4(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| ( sK2(X0,X1,X2) = apply(X0,sK3(X0,X1,X2))
& in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK2(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X5,sK3(X0,X1,X2)),skolemize(X8,sK4(X0,X1,X6))],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f79,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK5(X0,X1),X0)
& ~ in(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f79]) ).
fof(f92,plain,
( function(sK19)
& relation(sK19)
& ~ subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f60]) ).
fof(f94,plain,
! [X1,X0,X2] :
( ~ sP1(X1,X0,X2)
| ( ( relation_rng_restriction(X0,X2) != X1
| sP0(X2,X0,X1) )
& ( ~ sP0(X2,X0,X1)
| X1 = relation_rng_restriction(X0,X2) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ( ( relation_rng_restriction(X1,X2) != X0
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) = X0 ) ) ),
inference(rectify,[],[f94]) ).
fof(f105,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK4(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f77]) ).
fof(f106,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK4(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f107,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK4(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f108,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f114,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f124,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| function(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f148,plain,
function(sK19),
inference(cnf_transformation,[],[f92]) ).
fof(f149,plain,
relation(sK19),
inference(cnf_transformation,[],[f92]) ).
fof(f150,plain,
~ subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f92]) ).
fof(f151,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f152,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f158,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| relation_rng_restriction(X1,X2) != X0
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f173,plain,
! [X2,X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),X2) ),
inference(equality_resolution,[],[f108]) ).
fof(f174,plain,
! [X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),relation_image(X0,X1)) ),
inference(equality_resolution,[],[f173]) ).
fof(f175,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK4(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f107]) ).
fof(f176,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK4(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f106]) ).
fof(f177,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK4(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f105]) ).
fof(f178,plain,
! [X2,X1] :
( ~ sP1(relation_rng_restriction(X1,X2),X1,X2)
| sP0(X2,X1,relation_rng_restriction(X1,X2)) ),
inference(equality_resolution,[],[f159]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK4(X1,X2,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_95,negated_conjecture,
~ subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f150]) ).
tcf(c_96,negated_conjecture,
relation(sK19),
inference(cnf_transformation,[],[f149]) ).
tcf(c_97,negated_conjecture,
function(sK19),
inference(cnf_transformation,[],[f148]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0,relation_rng_restriction(X0,X1))
| ~ sP1(relation_rng_restriction(X0,X1),X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X0,X2,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_182,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,X2)
| ~ element(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_234,plain,
( subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))
| in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] :
( sP1(relation_rng_restriction(X0,X1),X0,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(relation_rng_restriction(X0,X1)) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_383,plain,
( ( apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) = sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) )
| ~ relation(relation_rng_restriction(sK17,sK19))
| ~ function(relation_rng_restriction(sK17,sK19))
| ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_384,plain,
( in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),sK18)
| ~ relation(relation_rng_restriction(sK17,sK19))
| ~ function(relation_rng_restriction(sK17,sK19))
| ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_385,plain,
( in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(relation_rng_restriction(sK17,sK19)))
| ~ relation(relation_rng_restriction(sK17,sK19))
| ~ function(relation_rng_restriction(sK17,sK19))
| ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_407,plain,
relation_image(sK19,sK18) = relation_image(sK19,sK18),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_701,plain,
( relation(relation_rng_restriction(sK17,sK19))
| ~ relation(sK19) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_814,plain,
sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) = sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_1029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(X0,X2)
| ~ element(X1,relation_image(X3,X4))
| ( X2 != relation_image(X3,X4) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_193]) ).
tcf(c_1451,plain,
( function(relation_rng_restriction(sK17,sK19))
| ~ relation(sK19)
| ~ function(sK19) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_2060,plain,
! [X0: $i,X1: $i] :
( ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) = X1 )
| ( X1 != X0 )
| ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) != X0 ) ),
inference(instantiation,[status(thm)],[c_184]) ).
tcf(c_2192,plain,
! [X0: $i] :
( element(X0,relation_image(sK19,sK18))
| ~ in(X0,relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_2193,plain,
! [X0: $i] :
( ~ empty(relation_image(sK19,sK18))
| ~ in(X0,relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_2908,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ element(X1,relation_image(sK19,sK18))
| ( X2 != relation_image(sK19,sK18) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1029]) ).
tcf(c_4467,plain,
! [X0: $i] :
( in(apply(X0,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(X0,sK18))
| ~ relation(X0)
| ~ function(X0)
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),sK18)
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(X0)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_6134,plain,
! [X0: $i] :
( ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) = X0 )
| ( X0 != sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) )
| ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) != sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) ) ),
inference(instantiation,[status(thm)],[c_2060]) ).
tcf(c_6536,plain,
! [X0: $i,X1: $i] :
( element(X0,relation_image(sK19,sK18))
| ~ element(X1,relation_image(sK19,sK18))
| ( X0 != X1 )
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) ) ),
inference(instantiation,[status(thm)],[c_2908]) ).
tcf(c_12032,plain,
( sP0(sK19,sK17,relation_rng_restriction(sK17,sK19))
| ~ sP1(relation_rng_restriction(sK17,sK19),sK17,sK19) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_13395,plain,
( in(apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ~ relation(sK19)
| ~ function(sK19)
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),sK18)
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(sK19)) ),
inference(instantiation,[status(thm)],[c_4467]) ).
tcf(c_13396,plain,
( element(apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ~ in(apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_2192]) ).
tcf(c_13400,plain,
( ~ empty(relation_image(sK19,sK18))
| ~ in(apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_2193]) ).
tcf(c_14493,plain,
( ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) = apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) != sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) )
| ( apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) != sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) ) ),
inference(instantiation,[status(thm)],[c_6134]) ).
tcf(c_14586,plain,
( sP1(relation_rng_restriction(sK17,sK19),sK17,sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ relation(relation_rng_restriction(sK17,sK19))
| ~ function(relation_rng_restriction(sK17,sK19)) ),
inference(instantiation,[status(thm)],[c_235]) ).
tcf(c_23187,plain,
! [X0: $i] :
( element(X0,relation_image(sK19,sK18))
| ~ element(apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ( X0 != apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) ) ),
inference(instantiation,[status(thm)],[c_6536]) ).
tcf(c_35746,plain,
( element(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18))
| ~ element(apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) )
| ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) != apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) ) ),
inference(instantiation,[status(thm)],[c_23187]) ).
tcf(c_41364,plain,
! [X0: $i] :
( empty(relation_image(sK19,sK18))
| in(X0,relation_image(sK19,sK18))
| ~ element(X0,relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_42012,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,relation_image(sK19,sK18))
| ~ element(X2,X0)
| ( X1 != X2 )
| ( relation_image(sK19,sK18) != X0 ) ),
inference(instantiation,[status(thm)],[c_193]) ).
tcf(c_45351,plain,
! [X0: $i,X1: $i] :
( element(X0,relation_image(sK19,sK18))
| ~ element(X1,relation_image(sK19,sK18))
| ( X0 != X1 )
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) ) ),
inference(instantiation,[status(thm)],[c_42012]) ).
tcf(c_63941,plain,
( empty(relation_image(sK19,sK18))
| in(apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ~ element(apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_41364]) ).
tcf(c_65944,plain,
! [X0: $i] :
( element(apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ~ element(X0,relation_image(sK19,sK18))
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) )
| ( apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) != X0 ) ),
inference(instantiation,[status(thm)],[c_45351]) ).
tcf(c_72393,plain,
( element(apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ~ element(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18))
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) )
| ( apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) != sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) ) ),
inference(instantiation,[status(thm)],[c_65944]) ).
tcf(c_128729,plain,
! [X0: $i,X1: $i] :
( ( X1 = apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ( X1 != X0 )
| ( apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) != X0 ) ),
inference(instantiation,[status(thm)],[c_184]) ).
tcf(c_136636,plain,
! [X0: $i] :
( ( X0 = apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ( X0 != apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ( apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) != apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) ) ),
inference(instantiation,[status(thm)],[c_128729]) ).
tcf(c_164364,plain,
! [X0: $i] :
( subset(X0,relation_image(sK19,sK18))
| ~ in(sK5(X0,relation_image(sK19,sK18)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_164367,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X1,relation_image(sK19,sK18))
| ( X2 != relation_image(sK19,sK18) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_185]) ).
tcf(c_167667,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_image(sK19,sK18))
| ~ in(X1,relation_image(sK19,sK18))
| ( X0 != X1 )
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) ) ),
inference(instantiation,[status(thm)],[c_164367]) ).
tcf(c_171445,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,relation_image(sK19,sK18)),relation_image(sK19,sK18))
| ~ in(X1,relation_image(sK19,sK18))
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) )
| ( sK5(X0,relation_image(sK19,sK18)) != X1 ) ),
inference(instantiation,[status(thm)],[c_167667]) ).
tcf(c_178871,plain,
( in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18))
| ~ in(apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))),relation_image(sK19,sK18))
| ( relation_image(sK19,sK18) != relation_image(sK19,sK18) )
| ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) != apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) ) ),
inference(instantiation,[status(thm)],[c_171445]) ).
tcf(c_195000,plain,
( ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) = apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) != apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ( apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) != apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) ) ),
inference(instantiation,[status(thm)],[c_136636]) ).
tcf(c_197831,plain,
( subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))
| ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_164364]) ).
fof(f72,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f73,definition,
! [X1,X0,X2] :
( ~ sP1(X1,X0,X2)
| ( X1 = relation_rng_restriction(X0,X2)
<=> sP0(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f74,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| sP1(X1,X0,X2) ) ),
inference(definition_folding,[],[f70,f73,f72]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( ( ~ in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(X1)) ) ) ) )
& ( ? [X4] :
( in(X4,relation_dom(X1))
& apply(X2,X4) != apply(X1,X4) )
| ? [X3] :
( ( in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(X3,relation_dom(X1))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2)) ) )
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( ( ~ in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(X1)) ) ) ) )
& ( ? [X4] :
( in(X4,relation_dom(X1))
& apply(X2,X4) != apply(X1,X4) )
| ? [X3] :
( ( in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(X3,relation_dom(X1))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2)) ) )
| sP0(X2,X0,X1) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) )
& ! [X5] :
( ( ~ in(X5,relation_dom(X2))
| ( in(apply(X0,X5),X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X5),X1)
| ~ in(X5,relation_dom(X0))
| in(X5,relation_dom(X2)) ) ) ) )
& ( ? [X4] :
( in(X4,relation_dom(X2))
& apply(X0,X4) != apply(X2,X4) )
| ? [X3] :
( ( in(X3,relation_dom(X2))
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) )
& ! [X5] :
( ( ~ in(X5,relation_dom(X2))
| ( in(apply(X0,X5),X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X5),X1)
| ~ in(X5,relation_dom(X0))
| in(X5,relation_dom(X2)) ) ) ) )
& ( ( in(sK21(X0,X2),relation_dom(X2))
& apply(X0,sK21(X0,X2)) != apply(X2,sK21(X0,X2)) )
| ( ( in(sK20(X0,X1,X2),relation_dom(X2))
| ( in(apply(X0,sK20(X0,X1,X2)),X1)
& in(sK20(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK20(X0,X1,X2),relation_dom(X2))
| ~ in(apply(X0,sK20(X0,X1,X2)),X1)
| ~ in(sK20(X0,X1,X2),relation_dom(X0)) ) )
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X3,sK20(X0,X1,X2)),skolemize(X4,sK21(X0,X2))],[f98]) ).
fof(f161,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) ),
inference(cnf_transformation,[],[f99]) ).
fof(f163,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0,X1,X2)
| ~ in(X5,relation_dom(X2))
| in(X5,relation_dom(X0)) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,relation_dom(X0))
| ~ in(X3,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X0,X3) = apply(X2,X3) )
| ~ in(X3,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_4499,plain,
! [X0: $i,X1: $i] :
( in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(X0))
| ~ sP0(X0,X1,relation_rng_restriction(sK17,sK19))
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(relation_rng_restriction(sK17,sK19))) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_12031,plain,
( in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(sK19))
| ~ sP0(sK19,sK17,relation_rng_restriction(sK17,sK19))
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(relation_rng_restriction(sK17,sK19))) ),
inference(instantiation,[status(thm)],[c_4499]) ).
tcf(c_124852,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) = apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ~ sP0(X0,X1,relation_rng_restriction(sK17,sK19))
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(relation_rng_restriction(sK17,sK19))) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_132159,plain,
( ( apply(sK19,sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) = apply(relation_rng_restriction(sK17,sK19),sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)))) )
| ~ sP0(sK19,sK17,relation_rng_restriction(sK17,sK19))
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(relation_rng_restriction(sK17,sK19))) ),
inference(instantiation,[status(thm)],[c_124852]) ).
tcf(c_197832,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_197831,c_195000,c_178871,c_132159,c_72393,c_63941,c_35746,c_14586,c_14493,c_13396,c_13400,c_13395,c_12032,c_12031,c_1451,c_814,c_701,c_407,c_383,c_384,c_385,c_234,c_95,c_96,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU051+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:44:22 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 159.34/22.41 % SZS status Started for theBenchmark.p
% 159.34/22.41 % SZS status Theorem for theBenchmark.p
% 159.34/22.41
% 159.34/22.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 159.34/22.41
% 159.34/22.41 % ------ iProver source info
% 159.34/22.41
% 159.34/22.41 % git: date: 2026-07-19 20:42:38 +0200
% 159.34/22.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 159.34/22.41 % git: non_committed_changes: false
% 159.34/22.41
% 159.34/22.41 % ------ Parsing...
% 159.34/22.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 159.34/22.41
% 159.34/22.41 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 159.34/22.41
% 159.34/22.41 % ------ Preprocessing...%
% 159.34/22.41
% 159.34/22.41 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 159.34/22.41 % ------ Proving...
% 159.34/22.41 % ------ Problem Properties
% 159.34/22.41
% 159.34/22.41 %
% 159.34/22.41 % clauses 67
% 159.34/22.41 % conjectures 3
% 159.34/22.41 % EPR 29
% 159.34/22.41 % Horn 56
% 159.34/22.41 % unary 24
% 159.34/22.41 % binary 16
% 159.34/22.41 % lits 163
% 159.34/22.41 % lits eq 14
% 159.34/22.41 % fd_pure 0
% 159.34/22.41 % fd_pseudo 0
% 159.34/22.41 % fd_cond 1
% 159.34/22.41 % fd_pseudo_cond 6
% 159.34/22.41 % AC symbols 0
% 159.34/22.41
% 159.34/22.41 % ------ Input Options Time Limit: Unbounded
% 159.34/22.41
% 159.34/22.41
% 159.34/22.41 % ------
% 159.34/22.41 % Current options:
% 159.34/22.41 % ------
% 159.34/22.41
% 159.34/22.41
% 159.34/22.41 %
% 159.34/22.41
% 159.34/22.41 % ------ Proving...
% 159.34/22.41 %
% 159.34/22.41
% 159.34/22.41 % SZS status Theorem for theBenchmark.p
% 159.34/22.41
% 159.34/22.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 159.34/22.41
% 159.34/22.41
%------------------------------------------------------------------------------