TSTP Solution File: SEU051+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU051+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:03:32 EDT 2023
% Result : Theorem 76.78s 11.31s
% Output : CNFRefutation 76.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of formulae : 191 ( 19 unt; 0 def)
% Number of atoms : 778 ( 138 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 1005 ( 418 ~; 422 |; 123 &)
% ( 20 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 418 ( 17 sgn; 247 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& 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(f12,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_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(f26,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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,[],[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(f31,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f33,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f34,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
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) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,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(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f26]) ).
fof(f39,plain,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) ) ) ),
inference(rectify,[],[f36]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f54,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f53]) ).
fof(f59,plain,
? [X0,X1,X2] :
( ~ subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f60,plain,
? [X0,X1,X2] :
( ~ subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f62,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f63,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f62]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f67,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f72,plain,
! [X1,X2,X0] :
( sP0(X1,X2,X0)
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f73,plain,
! [X0,X2,X1] :
( ( relation_rng_restriction(X0,X2) = X1
<=> sP0(X1,X2,X0) )
| ~ sP1(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_folding,[],[f70,f73,f72]) ).
fof(f75,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f76,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( apply(X0,X4) != sK2(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ? [X5] :
( apply(X0,X5) = sK2(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(sK2(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ? [X5] :
( apply(X0,X5) = sK2(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
=> ( sK2(X0,X1,X2) = apply(X0,sK3(X0,X1,X2))
& in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1,X6] :
( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
=> ( apply(X0,sK4(X0,X1,X6)) = X6
& in(sK4(X0,X1,X6),X1)
& in(sK4(X0,X1,X6),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ! [X4] :
( apply(X0,X4) != sK2(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ 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) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ( apply(X0,sK4(X0,X1,X6)) = X6
& in(sK4(X0,X1,X6),X1)
& in(sK4(X0,X1,X6),relation_dom(X0)) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f76,f79,f78,f77]) ).
fof(f81,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f82,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f82,f83]) ).
fof(f107,plain,
( ? [X0,X1,X2] :
( ~ subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1))
& function(X2)
& relation(X2) )
=> ( ~ subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))
& function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
( ~ subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))
& function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f60,f107]) ).
fof(f109,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f110,plain,
! [X0,X2,X1] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ~ sP0(X1,X2,X0) )
& ( sP0(X1,X2,X0)
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ sP1(X0,X2,X1) ),
inference(nnf_transformation,[],[f73]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ sP0(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f113,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ sP0(X1,X2,X0) ) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( apply(X1,X3) != apply(X0,X3)
& in(X3,relation_dom(X0)) )
| ? [X4] :
( ( ~ in(apply(X1,X4),X2)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X1,X4),X2)
& in(X4,relation_dom(X1)) )
| in(X4,relation_dom(X0)) ) ) )
& ( ( ! [X5] :
( apply(X0,X5) = apply(X1,X5)
| ~ in(X5,relation_dom(X0)) )
& ! [X6] :
( ( in(X6,relation_dom(X0))
| ~ in(apply(X1,X6),X2)
| ~ in(X6,relation_dom(X1)) )
& ( ( in(apply(X1,X6),X2)
& in(X6,relation_dom(X1)) )
| ~ in(X6,relation_dom(X0)) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( ? [X3] :
( apply(X1,X3) != apply(X0,X3)
& in(X3,relation_dom(X0)) )
=> ( apply(X1,sK20(X0,X1)) != apply(X0,sK20(X0,X1))
& in(sK20(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(apply(X1,X4),X2)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X1,X4),X2)
& in(X4,relation_dom(X1)) )
| in(X4,relation_dom(X0)) ) )
=> ( ( ~ in(apply(X1,sK21(X0,X1,X2)),X2)
| ~ in(sK21(X0,X1,X2),relation_dom(X1))
| ~ in(sK21(X0,X1,X2),relation_dom(X0)) )
& ( ( in(apply(X1,sK21(X0,X1,X2)),X2)
& in(sK21(X0,X1,X2),relation_dom(X1)) )
| in(sK21(X0,X1,X2),relation_dom(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( apply(X1,sK20(X0,X1)) != apply(X0,sK20(X0,X1))
& in(sK20(X0,X1),relation_dom(X0)) )
| ( ( ~ in(apply(X1,sK21(X0,X1,X2)),X2)
| ~ in(sK21(X0,X1,X2),relation_dom(X1))
| ~ in(sK21(X0,X1,X2),relation_dom(X0)) )
& ( ( in(apply(X1,sK21(X0,X1,X2)),X2)
& in(sK21(X0,X1,X2),relation_dom(X1)) )
| in(sK21(X0,X1,X2),relation_dom(X0)) ) ) )
& ( ( ! [X5] :
( apply(X0,X5) = apply(X1,X5)
| ~ in(X5,relation_dom(X0)) )
& ! [X6] :
( ( in(X6,relation_dom(X0))
| ~ in(apply(X1,X6),X2)
| ~ in(X6,relation_dom(X1)) )
& ( ( in(apply(X1,X6),X2)
& in(X6,relation_dom(X1)) )
| ~ in(X6,relation_dom(X0)) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f114,f116,f115]) ).
fof(f123,plain,
! [X2,X0,X1,X6] :
( in(sK4(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
! [X2,X0,X1,X6] :
( in(sK4(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f125,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK4(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f127,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK3(X0,X1,X2),relation_dom(X0))
| in(sK2(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f128,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK3(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f132,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f133,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f134,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f140,plain,
empty(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f143,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f165,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f166,plain,
relation(sK19),
inference(cnf_transformation,[],[f108]) ).
fof(f167,plain,
function(sK19),
inference(cnf_transformation,[],[f108]) ).
fof(f168,plain,
~ subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f170,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f172,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f175,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f176,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_rng_restriction(X0,X1) != X2
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f179,plain,
! [X2,X0,X1,X6] :
( in(X6,relation_dom(X1))
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f182,plain,
! [X2,X0,X1,X5] :
( apply(X0,X5) = apply(X1,X5)
| ~ in(X5,relation_dom(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f189,plain,
! [X2,X0,X1] :
( sP1(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f190,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f191,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f126]) ).
fof(f192,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),relation_image(X0,X1))
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f191]) ).
fof(f193,plain,
! [X0,X1,X6] :
( apply(X0,sK4(X0,X1,X6)) = X6
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f194,plain,
! [X0,X1,X6] :
( in(sK4(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f124]) ).
fof(f195,plain,
! [X0,X1,X6] :
( in(sK4(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f123]) ).
fof(f196,plain,
! [X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X1,X0)
| ~ sP1(X0,X1,relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f177]) ).
cnf(c_54,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK2(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_55,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK3(X0,X1,X2),relation_dom(X0))
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_56,plain,
( ~ in(X0,relation_dom(X1))
| ~ in(X0,X2)
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_57,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,sK4(X1,X2,X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_58,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(sK4(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_59,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(sK4(X1,X2,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_60,plain,
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_61,plain,
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_63,plain,
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_70,plain,
empty(empty_set),
inference(cnf_transformation,[],[f140]) ).
cnf(c_71,plain,
( ~ function(X0)
| ~ relation(X0)
| function(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_94,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f165]) ).
cnf(c_95,negated_conjecture,
~ subset(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),
inference(cnf_transformation,[],[f168]) ).
cnf(c_96,negated_conjecture,
function(sK19),
inference(cnf_transformation,[],[f167]) ).
cnf(c_97,negated_conjecture,
relation(sK19),
inference(cnf_transformation,[],[f166]) ).
cnf(c_98,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_99,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_100,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_103,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_104,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_105,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_107,plain,
( ~ sP1(X0,X1,relation_rng_restriction(X0,X1))
| sP0(relation_rng_restriction(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_114,plain,
( ~ sP0(X0,X1,X2)
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) = apply(X1,X3) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_117,plain,
( ~ sP0(X0,X1,X2)
| ~ in(X3,relation_dom(X0))
| in(X3,relation_dom(X1)) ),
inference(cnf_transformation,[],[f179]) ).
cnf(c_118,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_119,plain,
( ~ empty(X0)
| ~ empty(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_120,plain,
subset(empty_set,empty_set),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_129,plain,
( ~ empty(empty_set)
| empty_set = empty_set ),
inference(instantiation,[status(thm)],[c_104]) ).
cnf(c_156,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_100]) ).
cnf(c_182,plain,
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
cnf(c_188,plain,
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
cnf(c_198,plain,
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
cnf(c_199,plain,
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_198]) ).
cnf(c_200,plain,
( ~ sP1(X0,X1,relation_rng_restriction(X0,X1))
| sP0(relation_rng_restriction(X0,X1),X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_107]) ).
cnf(c_320,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| ~ empty(X2) ),
inference(bin_hyper_res,[status(thm)],[c_103,c_156]) ).
cnf(c_958,plain,
( relation_rng_restriction(X0,X1) != X2
| X0 != X4
| X1 != X3
| ~ function(X2)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| sP0(relation_rng_restriction(X0,X1),X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_118,c_200]) ).
cnf(c_959,plain,
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| sP0(relation_rng_restriction(X0,X1),X1,X0) ),
inference(unflattening,[status(thm)],[c_958]) ).
cnf(c_971,plain,
( ~ function(X0)
| ~ relation(X0)
| sP0(relation_rng_restriction(X1,X0),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_959,c_182,c_71]) ).
cnf(c_1227,plain,
( relation_image(relation_rng_restriction(sK17,sK19),sK18) != X0
| relation_image(sK19,sK18) != X1
| in(sK5(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_199,c_95]) ).
cnf(c_1228,plain,
in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18)),
inference(unflattening,[status(thm)],[c_1227]) ).
cnf(c_1232,plain,
( relation_image(relation_rng_restriction(sK17,sK19),sK18) != X0
| relation_image(sK19,sK18) != X1
| ~ in(sK5(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_188,c_95]) ).
cnf(c_1233,plain,
~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18)),
inference(unflattening,[status(thm)],[c_1232]) ).
cnf(c_4103,plain,
X0 = X0,
theory(equality) ).
cnf(c_4105,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_4108,plain,
( X0 != X1
| ~ empty(X1)
| empty(X0) ),
theory(equality) ).
cnf(c_4112,plain,
( X0 != X1
| X2 != X3
| ~ subset(X1,X3)
| subset(X0,X2) ),
theory(equality) ).
cnf(c_4114,plain,
( X0 != X1
| X2 != X3
| ~ element(X1,X3)
| element(X0,X2) ),
theory(equality) ).
cnf(c_5310,plain,
( ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18))
| ~ empty(relation_image(relation_rng_restriction(sK17,sK19),sK18)) ),
inference(instantiation,[status(thm)],[c_105]) ).
cnf(c_5320,plain,
( ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18))
| ~ function(relation_rng_restriction(sK17,sK19))
| ~ relation(relation_rng_restriction(sK17,sK19))
| 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_57]) ).
cnf(c_5321,plain,
( ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18))
| ~ function(relation_rng_restriction(sK17,sK19))
| ~ relation(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_59]) ).
cnf(c_5322,plain,
( ~ in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(relation_rng_restriction(sK17,sK19),sK18))
| ~ function(relation_rng_restriction(sK17,sK19))
| ~ relation(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))),sK18) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_5331,plain,
( ~ empty(relation_image(sK19,sK18))
| ~ empty(X0)
| relation_image(sK19,sK18) = X0 ),
inference(instantiation,[status(thm)],[c_119]) ).
cnf(c_5332,plain,
( ~ empty(relation_image(sK19,sK18))
| ~ empty(empty_set)
| relation_image(sK19,sK18) = empty_set ),
inference(instantiation,[status(thm)],[c_5331]) ).
cnf(c_5344,plain,
relation_image(sK19,sK18) = relation_image(sK19,sK18),
inference(instantiation,[status(thm)],[c_4103]) ).
cnf(c_5682,plain,
( relation_image(relation_rng_restriction(sK17,sK19),sK18) != X0
| ~ empty(X0)
| empty(relation_image(relation_rng_restriction(sK17,sK19),sK18)) ),
inference(instantiation,[status(thm)],[c_4108]) ).
cnf(c_5685,plain,
( relation_image(relation_rng_restriction(sK17,sK19),sK18) != empty_set
| ~ empty(empty_set)
| empty(relation_image(relation_rng_restriction(sK17,sK19),sK18)) ),
inference(instantiation,[status(thm)],[c_5682]) ).
cnf(c_5689,plain,
( ~ relation(sK19)
| relation(relation_rng_restriction(sK17,sK19)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_5757,plain,
( ~ function(relation_rng_restriction(sK17,sK19))
| ~ relation(relation_rng_restriction(sK17,sK19))
| relation_image(relation_rng_restriction(sK17,sK19),sK18) = X0
| in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),relation_dom(relation_rng_restriction(sK17,sK19)))
| in(sK2(relation_rng_restriction(sK17,sK19),sK18,X0),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_5758,plain,
( ~ function(relation_rng_restriction(sK17,sK19))
| ~ relation(relation_rng_restriction(sK17,sK19))
| relation_image(relation_rng_restriction(sK17,sK19),sK18) = X0
| in(sK2(relation_rng_restriction(sK17,sK19),sK18,X0),X0)
| in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),sK18) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_5759,plain,
( ~ function(relation_rng_restriction(sK17,sK19))
| ~ relation(relation_rng_restriction(sK17,sK19))
| relation_image(relation_rng_restriction(sK17,sK19),sK18) = empty_set
| in(sK2(relation_rng_restriction(sK17,sK19),sK18,empty_set),empty_set)
| in(sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set),sK18) ),
inference(instantiation,[status(thm)],[c_5758]) ).
cnf(c_5760,plain,
( ~ function(relation_rng_restriction(sK17,sK19))
| ~ relation(relation_rng_restriction(sK17,sK19))
| relation_image(relation_rng_restriction(sK17,sK19),sK18) = empty_set
| in(sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set),relation_dom(relation_rng_restriction(sK17,sK19)))
| in(sK2(relation_rng_restriction(sK17,sK19),sK18,empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_5757]) ).
cnf(c_6127,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_4103]) ).
cnf(c_6936,plain,
( ~ function(sK19)
| ~ relation(sK19)
| function(relation_rng_restriction(sK17,sK19)) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_8268,plain,
( sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) != X0
| X1 != X0
| sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)) = X1 ),
inference(instantiation,[status(thm)],[c_4105]) ).
cnf(c_8450,plain,
( ~ in(X0,relation_image(sK19,sK18))
| element(X0,relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_8454,plain,
( ~ in(X0,relation_image(sK19,sK18))
| ~ subset(relation_image(sK19,sK18),X1)
| ~ empty(X1) ),
inference(instantiation,[status(thm)],[c_320]) ).
cnf(c_12140,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)))
| ~ sP0(relation_rng_restriction(sK17,sK19),X0,X1)
| 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_117]) ).
cnf(c_12194,plain,
( ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),relation_dom(X0))
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),sK18)
| ~ function(X0)
| ~ relation(X0)
| 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)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_12250,plain,
( ~ in(sK2(relation_rng_restriction(sK17,sK19),sK18,X0),X0)
| ~ subset(X0,X1)
| ~ empty(X1) ),
inference(instantiation,[status(thm)],[c_320]) ).
cnf(c_12251,plain,
( ~ in(sK2(relation_rng_restriction(sK17,sK19),sK18,empty_set),empty_set)
| ~ subset(empty_set,empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_12250]) ).
cnf(c_15191,plain,
( ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),relation_dom(relation_rng_restriction(sK17,sK19)))
| ~ sP0(relation_rng_restriction(sK17,sK19),X1,X2)
| in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),relation_dom(X1)) ),
inference(instantiation,[status(thm)],[c_117]) ).
cnf(c_15259,plain,
( ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),relation_dom(X1))
| ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),sK18)
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,sK3(relation_rng_restriction(sK17,sK19),sK18,X0)),relation_image(X1,sK18)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_15417,plain,
( relation_image(sK19,sK18) != X0
| X1 != X2
| ~ subset(X0,X2)
| subset(relation_image(sK19,sK18),X1) ),
inference(instantiation,[status(thm)],[c_4112]) ).
cnf(c_15418,plain,
( relation_image(sK19,sK18) != empty_set
| empty_set != empty_set
| ~ subset(empty_set,empty_set)
| subset(relation_image(sK19,sK18),empty_set) ),
inference(instantiation,[status(thm)],[c_15417]) ).
cnf(c_16224,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))
| 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)) = X0 ),
inference(instantiation,[status(thm)],[c_8268]) ).
cnf(c_23254,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)))
| ~ sP0(relation_rng_restriction(sK17,sK19),sK19,sK17)
| 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_12140]) ).
cnf(c_23255,plain,
( ~ function(sK19)
| ~ relation(sK19)
| sP0(relation_rng_restriction(sK17,sK19),sK19,sK17) ),
inference(instantiation,[status(thm)],[c_971]) ).
cnf(c_28023,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))
| 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)))) ),
inference(instantiation,[status(thm)],[c_16224]) ).
cnf(c_28903,plain,
( ~ in(apply(sK19,sK3(relation_rng_restriction(sK17,sK19),sK18,X0)),relation_image(sK19,sK18))
| ~ subset(relation_image(sK19,sK18),X1)
| ~ empty(X1) ),
inference(instantiation,[status(thm)],[c_8454]) ).
cnf(c_28904,plain,
( ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),relation_dom(sK19))
| ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),sK18)
| ~ function(sK19)
| ~ relation(sK19)
| in(apply(sK19,sK3(relation_rng_restriction(sK17,sK19),sK18,X0)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_15259]) ).
cnf(c_28905,plain,
( ~ in(apply(sK19,sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set)),relation_image(sK19,sK18))
| ~ subset(relation_image(sK19,sK18),empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_28903]) ).
cnf(c_28906,plain,
( ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set),relation_dom(sK19))
| ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set),sK18)
| ~ function(sK19)
| ~ relation(sK19)
| in(apply(sK19,sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_28904]) ).
cnf(c_32476,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))
| ~ in(sK4(relation_rng_restriction(sK17,sK19),sK18,sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18))),sK18)
| ~ function(sK19)
| ~ relation(sK19)
| 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_12194]) ).
cnf(c_32507,plain,
( ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),relation_dom(relation_rng_restriction(sK17,sK19)))
| ~ sP0(relation_rng_restriction(sK17,sK19),sK19,sK17)
| in(sK3(relation_rng_restriction(sK17,sK19),sK18,X0),relation_dom(sK19)) ),
inference(instantiation,[status(thm)],[c_15191]) ).
cnf(c_32510,plain,
( ~ in(sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set),relation_dom(relation_rng_restriction(sK17,sK19)))
| ~ sP0(relation_rng_restriction(sK17,sK19),sK19,sK17)
| in(sK3(relation_rng_restriction(sK17,sK19),sK18,empty_set),relation_dom(sK19)) ),
inference(instantiation,[status(thm)],[c_32507]) ).
cnf(c_44000,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))
| 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)) ),
inference(instantiation,[status(thm)],[c_8450]) ).
cnf(c_59316,plain,
( ~ element(X0,relation_image(sK19,sK18))
| in(X0,relation_image(sK19,sK18))
| empty(relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_99]) ).
cnf(c_59875,plain,
( relation_image(sK19,sK18) != X0
| X1 != X2
| ~ element(X2,X0)
| element(X1,relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_4114]) ).
cnf(c_62491,plain,
( relation_image(sK19,sK18) != relation_image(sK19,sK18)
| X0 != X1
| ~ element(X1,relation_image(sK19,sK18))
| element(X0,relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_59875]) ).
cnf(c_69566,plain,
( 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))))
| ~ 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))
| element(X0,relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_62491]) ).
cnf(c_71494,plain,
( ~ element(sK5(X0,relation_image(sK19,sK18)),relation_image(sK19,sK18))
| in(sK5(X0,relation_image(sK19,sK18)),relation_image(sK19,sK18))
| empty(relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_59316]) ).
cnf(c_95753,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)))) != 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)
| ~ 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))
| 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_69566]) ).
cnf(c_104674,plain,
( ~ element(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18))
| in(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18))
| empty(relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_71494]) ).
cnf(c_138375,plain,
( 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))))
| X1 != 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))
| element(X0,X1) ),
inference(instantiation,[status(thm)],[c_4114]) ).
cnf(c_141110,plain,
( ~ 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,sK19,X1)
| apply(X0,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)))) ),
inference(instantiation,[status(thm)],[c_114]) ).
cnf(c_146160,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)))
| ~ sP0(relation_rng_restriction(sK17,sK19),sK19,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)))) ),
inference(instantiation,[status(thm)],[c_141110]) ).
cnf(c_151013,plain,
( relation_image(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))))
| ~ 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)) ),
inference(instantiation,[status(thm)],[c_138375]) ).
cnf(c_151187,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)))
| ~ sP0(relation_rng_restriction(sK17,sK19),sK19,sK17)
| 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)))) ),
inference(instantiation,[status(thm)],[c_146160]) ).
cnf(c_155470,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))))
| 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))
| element(sK5(relation_image(relation_rng_restriction(sK17,sK19),sK18),relation_image(sK19,sK18)),relation_image(sK19,sK18)) ),
inference(instantiation,[status(thm)],[c_151013]) ).
cnf(c_155472,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_155470,c_151187,c_104674,c_95753,c_44000,c_32510,c_32476,c_28906,c_28905,c_28023,c_23255,c_23254,c_15418,c_12251,c_6936,c_6127,c_5760,c_5759,c_5689,c_5685,c_5344,c_5332,c_5320,c_5321,c_5322,c_5310,c_1233,c_1228,c_129,c_120,c_70,c_96,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU051+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 12:55:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 76.78/11.31 % SZS status Started for theBenchmark.p
% 76.78/11.31 % SZS status Theorem for theBenchmark.p
% 76.78/11.31
% 76.78/11.31 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 76.78/11.31
% 76.78/11.31 ------ iProver source info
% 76.78/11.31
% 76.78/11.31 git: date: 2023-05-31 18:12:56 +0000
% 76.78/11.31 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 76.78/11.31 git: non_committed_changes: false
% 76.78/11.31 git: last_make_outside_of_git: false
% 76.78/11.31
% 76.78/11.31 ------ Parsing...
% 76.78/11.31 ------ Clausification by vclausify_rel & Parsing by iProver...
% 76.78/11.31
% 76.78/11.31 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 76.78/11.31
% 76.78/11.31 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 76.78/11.31
% 76.78/11.31 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 76.78/11.31 ------ Proving...
% 76.78/11.31 ------ Problem Properties
% 76.78/11.31
% 76.78/11.31
% 76.78/11.31 clauses 66
% 76.78/11.31 conjectures 3
% 76.78/11.31 EPR 30
% 76.78/11.31 Horn 55
% 76.78/11.31 unary 24
% 76.78/11.31 binary 15
% 76.78/11.31 lits 162
% 76.78/11.31 lits eq 14
% 76.78/11.31 fd_pure 0
% 76.78/11.31 fd_pseudo 0
% 76.78/11.31 fd_cond 1
% 76.78/11.31 fd_pseudo_cond 6
% 76.78/11.31 AC symbols 0
% 76.78/11.31
% 76.78/11.31 ------ Input Options Time Limit: Unbounded
% 76.78/11.31
% 76.78/11.31
% 76.78/11.31 ------
% 76.78/11.31 Current options:
% 76.78/11.31 ------
% 76.78/11.31
% 76.78/11.31
% 76.78/11.31
% 76.78/11.31
% 76.78/11.31 ------ Proving...
% 76.78/11.31
% 76.78/11.31
% 76.78/11.31 % SZS status Theorem for theBenchmark.p
% 76.78/11.31
% 76.78/11.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 76.78/11.31
% 76.78/11.32
%------------------------------------------------------------------------------