TSTP Solution File: SEU228+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU228+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 17:04:57 EDT 2023
% Result : Theorem 45.33s 6.74s
% Output : CNFRefutation 45.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of formulae : 154 ( 19 unt; 0 def)
% Number of atoms : 707 ( 170 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 916 ( 363 ~; 378 |; 132 &)
% ( 22 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 339 ( 3 sgn; 216 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f6,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(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f22,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f37,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f39,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f40,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
inference(negated_conjecture,[],[f39]) ).
fof(f41,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f43,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f45,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f46,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f49,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f37]) ).
fof(f59,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,[],[f6]) ).
fof(f60,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,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f62,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f64]) ).
fof(f73,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f74,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != X0
& subset(X0,relation_rng(X1))
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f76,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != X0
& subset(X0,relation_rng(X1))
& function(X1)
& relation(X1) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f78,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f79,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f78]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f83,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f86,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f87,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f86]) ).
fof(f88,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,[],[f60]) ).
fof(f89,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,[],[f88]) ).
fof(f90,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) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X5] :
( apply(X0,X5) = sK0(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ? [X5] :
( apply(X0,X5) = sK0(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
=> ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
& in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1,X6] :
( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
=> ( apply(X0,sK2(X0,X1,X6)) = X6
& in(sK2(X0,X1,X6),X1)
& in(sK2(X0,X1,X6),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ! [X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
& in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),relation_dom(X0)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ( apply(X0,sK2(X0,X1,X6)) = X6
& in(sK2(X0,X1,X6),X1)
& in(sK2(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,[sK0,sK1,sK2])],[f89,f92,f91,f90]) ).
fof(f94,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f95,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ~ in(apply(X0,sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),relation_dom(X0))
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK3(X0,X1,X2)),X1)
& in(sK3(X0,X1,X2),relation_dom(X0)) )
| in(sK3(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ( ( ~ in(apply(X0,sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),relation_dom(X0))
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK3(X0,X1,X2)),X1)
& in(sK3(X0,X1,X2),relation_dom(X0)) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f96,f97]) ).
fof(f99,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,[],[f63]) ).
fof(f100,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,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f100,f101]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK5(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK5(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK5(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK5(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK5(X0,X1) = apply(X0,sK6(X0,X1))
& in(sK6(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK7(X0,X5)) = X5
& in(sK7(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] :
( apply(X0,X3) != sK5(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK5(X0,X1),X1) )
& ( ( sK5(X0,X1) = apply(X0,sK6(X0,X1))
& in(sK6(X0,X1),relation_dom(X0)) )
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK7(X0,X5)) = X5
& in(sK7(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f104,f107,f106,f105]) ).
fof(f131,plain,
( ? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != X0
& subset(X0,relation_rng(X1))
& function(X1)
& relation(X1) )
=> ( sK19 != relation_image(sK20,relation_inverse_image(sK20,sK19))
& subset(sK19,relation_rng(sK20))
& function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( sK19 != relation_image(sK20,relation_inverse_image(sK20,sK19))
& subset(sK19,relation_rng(sK20))
& function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f76,f131]) ).
fof(f133,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f141,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f147,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
| in(sK0(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f149,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ in(sK0(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f151,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f152,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f156,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f157,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f159,plain,
! [X0,X1,X5] :
( in(sK7(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f160,plain,
! [X0,X1,X5] :
( apply(X0,sK7(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
empty(empty_set),
inference(cnf_transformation,[],[f22]) ).
fof(f196,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f49]) ).
fof(f197,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f198,plain,
relation(sK20),
inference(cnf_transformation,[],[f132]) ).
fof(f199,plain,
function(sK20),
inference(cnf_transformation,[],[f132]) ).
fof(f200,plain,
subset(sK19,relation_rng(sK20)),
inference(cnf_transformation,[],[f132]) ).
fof(f201,plain,
sK19 != relation_image(sK20,relation_inverse_image(sK20,sK19)),
inference(cnf_transformation,[],[f132]) ).
fof(f202,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f203,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f205,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f208,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f218,plain,
! [X0,X1,X4] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f152]) ).
fof(f219,plain,
! [X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f151]) ).
fof(f223,plain,
! [X0,X5] :
( apply(X0,sK7(X0,X5)) = X5
| ~ in(X5,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f160]) ).
fof(f224,plain,
! [X0,X5] :
( in(sK7(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f159]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_55,plain,
( sK0(X0,X1,X2) != apply(X0,X3)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X1)
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_56,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK1(X0,X1,X2)) = sK0(X0,X1,X2)
| relation_image(X0,X1) = X2
| in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_57,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_66,plain,
( ~ in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| in(X1,relation_inverse_image(X0,X2)) ),
inference(cnf_transformation,[],[f218]) ).
cnf(c_67,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),X2) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_70,plain,
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_71,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_76,plain,
( ~ in(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,sK7(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_77,plain,
( ~ in(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| in(sK7(X1,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f224]) ).
cnf(c_84,plain,
empty(empty_set),
inference(cnf_transformation,[],[f170]) ).
cnf(c_109,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f196]) ).
cnf(c_110,plain,
( ~ function(X0)
| ~ relation(X0)
| subset(relation_image(X0,relation_inverse_image(X0,X1)),X1) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_111,negated_conjecture,
relation_image(sK20,relation_inverse_image(sK20,sK19)) != sK19,
inference(cnf_transformation,[],[f201]) ).
cnf(c_112,negated_conjecture,
subset(sK19,relation_rng(sK20)),
inference(cnf_transformation,[],[f200]) ).
cnf(c_113,negated_conjecture,
function(sK20),
inference(cnf_transformation,[],[f199]) ).
cnf(c_114,negated_conjecture,
relation(sK20),
inference(cnf_transformation,[],[f198]) ).
cnf(c_115,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_116,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f203]) ).
cnf(c_117,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_120,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_121,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_124,plain,
subset(empty_set,empty_set),
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_135,plain,
( ~ empty(empty_set)
| empty_set = empty_set ),
inference(instantiation,[status(thm)],[c_121]) ).
cnf(c_161,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_117]) ).
cnf(c_324,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| ~ empty(X2) ),
inference(bin_hyper_res,[status(thm)],[c_120,c_161]) ).
cnf(c_13753,plain,
X0 = X0,
theory(equality) ).
cnf(c_13755,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_13756,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_13760,plain,
( X0 != X1
| X2 != X3
| ~ subset(X1,X3)
| subset(X0,X2) ),
theory(equality) ).
cnf(c_13765,plain,
( X0 != X1
| X2 != X3
| ~ element(X1,X3)
| element(X0,X2) ),
theory(equality) ).
cnf(c_15662,plain,
( ~ subset(relation_image(sK20,relation_inverse_image(sK20,sK19)),sK19)
| ~ subset(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19)))
| relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19 ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_15722,plain,
( ~ function(sK20)
| ~ relation(sK20)
| relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19
| in(sK1(sK20,relation_inverse_image(sK20,sK19),sK19),relation_inverse_image(sK20,sK19))
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_15779,plain,
( ~ function(sK20)
| ~ relation(sK20)
| apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) = sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_15780,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,X0)
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| ~ in(X0,relation_inverse_image(sK20,sK19))
| ~ in(X0,relation_dom(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19 ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_16027,plain,
( ~ element(X0,sK19)
| in(X0,sK19)
| empty(sK19) ),
inference(instantiation,[status(thm)],[c_116]) ).
cnf(c_16093,plain,
( ~ function(sK20)
| ~ relation(sK20)
| subset(relation_image(sK20,relation_inverse_image(sK20,sK19)),sK19) ),
inference(instantiation,[status(thm)],[c_110]) ).
cnf(c_16129,plain,
( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| ~ subset(sK19,X0)
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_16136,plain,
( X0 != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| X1 != sK19
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| in(X0,X1) ),
inference(instantiation,[status(thm)],[c_13756]) ).
cnf(c_16237,plain,
( ~ subset(X0,sK19)
| ~ subset(sK19,X0)
| sK19 = X0 ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_16242,plain,
( ~ empty(sK19)
| sK19 = empty_set ),
inference(instantiation,[status(thm)],[c_121]) ).
cnf(c_17797,plain,
( in(sK4(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))),sK19)
| subset(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_17904,plain,
( ~ in(sK1(sK20,relation_inverse_image(sK20,sK19),sK19),relation_inverse_image(sK20,sK19))
| ~ function(sK20)
| ~ relation(sK20)
| in(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_20986,plain,
( ~ subset(sK19,sK19)
| sK19 = sK19 ),
inference(instantiation,[status(thm)],[c_16237]) ).
cnf(c_20987,plain,
subset(sK19,sK19),
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_21448,plain,
( ~ element(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| empty(sK19) ),
inference(instantiation,[status(thm)],[c_16027]) ).
cnf(c_21573,plain,
( X0 != X1
| sK19 != X2
| ~ subset(X2,X1)
| subset(sK19,X0) ),
inference(instantiation,[status(thm)],[c_13760]) ).
cnf(c_21574,plain,
( empty_set != empty_set
| sK19 != empty_set
| ~ subset(empty_set,empty_set)
| subset(sK19,empty_set) ),
inference(instantiation,[status(thm)],[c_21573]) ).
cnf(c_21579,plain,
( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| ~ subset(sK19,relation_rng(sK20))
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),relation_rng(sK20)) ),
inference(instantiation,[status(thm)],[c_16129]) ).
cnf(c_22528,plain,
( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),relation_rng(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) = sK0(sK20,relation_inverse_image(sK20,sK19),sK19) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_22529,plain,
( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),relation_rng(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20)) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_22862,plain,
( ~ in(sK4(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))),sK19)
| ~ subset(sK19,X0)
| ~ empty(X0) ),
inference(instantiation,[status(thm)],[c_324]) ).
cnf(c_22863,plain,
( ~ in(sK4(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))),sK19)
| ~ subset(sK19,empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_22862]) ).
cnf(c_24007,plain,
( X0 != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK19 != sK19
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| in(X0,sK19) ),
inference(instantiation,[status(thm)],[c_16136]) ).
cnf(c_26172,plain,
sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = sK0(sK20,relation_inverse_image(sK20,sK19),sK19),
inference(instantiation,[status(thm)],[c_13753]) ).
cnf(c_37422,plain,
( ~ in(apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))),X0)
| ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_inverse_image(sK20,X0)) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_37428,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)))
| ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_inverse_image(sK20,sK19))
| ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20))
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| ~ function(sK20)
| ~ relation(sK20)
| relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19 ),
inference(instantiation,[status(thm)],[c_15780]) ).
cnf(c_64647,plain,
( ~ in(apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))),sK19)
| ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_inverse_image(sK20,sK19)) ),
inference(instantiation,[status(thm)],[c_37422]) ).
cnf(c_64649,plain,
( apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK19 != sK19
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| in(apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))),sK19) ),
inference(instantiation,[status(thm)],[c_24007]) ).
cnf(c_90485,plain,
( apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) != X0
| sK0(sK20,relation_inverse_image(sK20,sK19),X1) != X0
| sK0(sK20,relation_inverse_image(sK20,sK19),X1) = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
inference(instantiation,[status(thm)],[c_13755]) ).
cnf(c_103120,plain,
( apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),X0) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),X0) = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
inference(instantiation,[status(thm)],[c_90485]) ).
cnf(c_112579,plain,
( apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
inference(instantiation,[status(thm)],[c_103120]) ).
cnf(c_121654,plain,
( ~ in(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
| element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19) ),
inference(instantiation,[status(thm)],[c_115]) ).
cnf(c_122323,plain,
( X0 != apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19))
| X1 != sK19
| ~ element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
| element(X0,X1) ),
inference(instantiation,[status(thm)],[c_13765]) ).
cnf(c_131217,plain,
( X0 != apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19))
| sK19 != sK19
| ~ element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
| element(X0,sK19) ),
inference(instantiation,[status(thm)],[c_122323]) ).
cnf(c_138002,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != X0
| apply(sK20,X1) != X0
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,X1) ),
inference(instantiation,[status(thm)],[c_13755]) ).
cnf(c_143658,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| apply(sK20,X0) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,X0) ),
inference(instantiation,[status(thm)],[c_138002]) ).
cnf(c_166865,plain,
( apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) ),
inference(instantiation,[status(thm)],[c_143658]) ).
cnf(c_187465,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19))
| sK19 != sK19
| ~ element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
| element(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(instantiation,[status(thm)],[c_131217]) ).
cnf(c_187469,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_187465,c_166865,c_121654,c_112579,c_64649,c_64647,c_37428,c_26172,c_22863,c_22528,c_22529,c_21579,c_21574,c_21448,c_20987,c_20986,c_17904,c_17797,c_16242,c_16093,c_15779,c_15722,c_15662,c_111,c_135,c_112,c_124,c_84,c_113,c_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU228+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 22:31:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 45.33/6.74 % SZS status Started for theBenchmark.p
% 45.33/6.74 % SZS status Theorem for theBenchmark.p
% 45.33/6.74
% 45.33/6.74 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 45.33/6.74
% 45.33/6.74 ------ iProver source info
% 45.33/6.74
% 45.33/6.74 git: date: 2023-05-31 18:12:56 +0000
% 45.33/6.74 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 45.33/6.74 git: non_committed_changes: false
% 45.33/6.74 git: last_make_outside_of_git: false
% 45.33/6.74
% 45.33/6.74 ------ Parsing...
% 45.33/6.74 ------ Clausification by vclausify_rel & Parsing by iProver...
% 45.33/6.74
% 45.33/6.74 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 45.33/6.74
% 45.33/6.74 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 45.33/6.74
% 45.33/6.74 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 45.33/6.74 ------ Proving...
% 45.33/6.74 ------ Problem Properties
% 45.33/6.74
% 45.33/6.74
% 45.33/6.74 clauses 70
% 45.33/6.74 conjectures 4
% 45.33/6.74 EPR 31
% 45.33/6.74 Horn 60
% 45.33/6.74 unary 25
% 45.33/6.74 binary 16
% 45.33/6.74 lits 180
% 45.33/6.74 lits eq 20
% 45.33/6.74 fd_pure 0
% 45.33/6.74 fd_pseudo 0
% 45.33/6.74 fd_cond 1
% 45.33/6.74 fd_pseudo_cond 12
% 45.33/6.74 AC symbols 0
% 45.33/6.74
% 45.33/6.74 ------ Schedule dynamic 5 is on
% 45.33/6.74
% 45.33/6.74 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 45.33/6.74
% 45.33/6.74
% 45.33/6.74 ------
% 45.33/6.74 Current options:
% 45.33/6.74 ------
% 45.33/6.74
% 45.33/6.74
% 45.33/6.74
% 45.33/6.74
% 45.33/6.74 ------ Proving...
% 45.33/6.74
% 45.33/6.74
% 45.33/6.74 % SZS status Theorem for theBenchmark.p
% 45.33/6.74
% 45.33/6.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 45.33/6.74
% 45.33/6.75
%------------------------------------------------------------------------------