TSTP Solution File: SEU228+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU228+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.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 : Fri May 3 03:05:06 EDT 2024
% Result : Theorem 135.35s 18.27s
% Output : CNFRefutation 135.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 110 ( 10 unt; 0 def)
% Number of atoms : 604 ( 151 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 819 ( 325 ~; 334 |; 123 &)
% ( 20 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 2 con; 0-3 aty)
% Number of variables : 272 ( 1 sgn 168 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f47,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
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(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(f84,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
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(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(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(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(f209,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
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_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_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_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_122,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_13139,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_13140,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_14392,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_14461,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != X0
| sK19 != X1
| ~ in(X0,X1)
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(instantiation,[status(thm)],[c_13140]) ).
cnf(c_15226,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != X0
| sK19 != sK19
| ~ in(X0,sK19)
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(instantiation,[status(thm)],[c_14461]) ).
cnf(c_15227,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != X0
| ~ in(X0,sK19)
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(equality_resolution_simp,[status(thm)],[c_15226]) ).
cnf(c_15719,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_15870,plain,
( apply(X0,X1) != X2
| X3 != X2
| X3 = apply(X0,X1) ),
inference(instantiation,[status(thm)],[c_13139]) ).
cnf(c_17212,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_15719]) ).
cnf(c_22185,plain,
( apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| X0 != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| X0 = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
inference(instantiation,[status(thm)],[c_15870]) ).
cnf(c_25050,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19))
| ~ in(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(instantiation,[status(thm)],[c_15227]) ).
cnf(c_31063,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_22185]) ).
cnf(c_31064,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) = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
inference(equality_resolution_simp,[status(thm)],[c_31063]) ).
cnf(c_33878,plain,
( ~ function(X0)
| ~ empty(X1)
| ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK0(X0,X1,X2),X2) ),
inference(resolution,[status(thm)],[c_57,c_122]) ).
cnf(c_33888,plain,
( ~ function(sK20)
| ~ relation(sK20)
| 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(resolution,[status(thm)],[c_57,c_111]) ).
cnf(c_36305,plain,
( 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(global_subsumption_just,[status(thm)],[c_33888,c_114,c_113,c_33888]) ).
cnf(c_44982,plain,
( ~ in(X0,relation_inverse_image(sK20,X1))
| ~ function(sK20)
| ~ relation(sK20)
| in(apply(sK20,X0),X1) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_54244,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_44982]) ).
cnf(c_58835,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_138189,plain,
( ~ empty(relation_inverse_image(sK20,sK19))
| ~ function(sK20)
| ~ relation(sK20)
| in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
inference(resolution,[status(thm)],[c_33878,c_111]) ).
cnf(c_150363,plain,
in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19),
inference(global_subsumption_just,[status(thm)],[c_138189,c_114,c_113,c_111,c_14392,c_25050,c_31064,c_36305,c_54244]) ).
cnf(c_154783,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_154833,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,sK7(sK20,X0))
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| ~ in(sK7(sK20,X0),relation_inverse_image(sK20,sK19))
| ~ in(sK7(sK20,X0),relation_dom(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19 ),
inference(instantiation,[status(thm)],[c_154783]) ).
cnf(c_154928,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != X0
| apply(sK20,sK7(sK20,X1)) != X0
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,sK7(sK20,X1)) ),
inference(instantiation,[status(thm)],[c_13139]) ).
cnf(c_154934,plain,
( ~ in(apply(sK20,X0),X1)
| ~ in(X0,relation_dom(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| in(X0,relation_inverse_image(sK20,X1)) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_155355,plain,
( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| apply(sK20,sK7(sK20,X0)) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,sK7(sK20,X0)) ),
inference(instantiation,[status(thm)],[c_154928]) ).
cnf(c_155356,plain,
( apply(sK20,sK7(sK20,X0)) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,sK7(sK20,X0)) ),
inference(equality_resolution_simp,[status(thm)],[c_155355]) ).
cnf(c_155514,plain,
( ~ in(apply(sK20,X0),sK19)
| ~ in(X0,relation_dom(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| in(X0,relation_inverse_image(sK20,sK19)) ),
inference(instantiation,[status(thm)],[c_154934]) ).
cnf(c_155525,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_13140]) ).
cnf(c_156057,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) = apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) ),
inference(instantiation,[status(thm)],[c_155356]) ).
cnf(c_156218,plain,
( ~ in(apply(sK20,sK7(sK20,X0)),sK19)
| ~ in(sK7(sK20,X0),relation_dom(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| in(sK7(sK20,X0),relation_inverse_image(sK20,sK19)) ),
inference(instantiation,[status(thm)],[c_155514]) ).
cnf(c_156355,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_155525]) ).
cnf(c_156356,plain,
( X0 != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| in(X0,sK19) ),
inference(equality_resolution_simp,[status(thm)],[c_156355]) ).
cnf(c_156727,plain,
( ~ in(X0,relation_rng(sK20))
| ~ function(sK20)
| ~ relation(sK20)
| apply(sK20,sK7(sK20,X0)) = X0 ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_160189,plain,
( apply(X0,sK7(X0,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
| ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
| in(apply(X0,sK7(X0,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))),sK19) ),
inference(instantiation,[status(thm)],[c_156356]) ).
cnf(c_161848,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_156727]) ).
cnf(c_163367,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_154833]) ).
cnf(c_180993,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_156218]) ).
cnf(c_225307,plain,
( apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) != sK0(sK20,relation_inverse_image(sK20,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_160189]) ).
cnf(c_225308,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_225307,c_180993,c_163367,c_161848,c_156057,c_150363,c_58835,c_17212,c_111,c_112,c_113,c_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU228+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n012.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 17:43:55 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 135.35/18.27 % SZS status Started for theBenchmark.p
% 135.35/18.27 % SZS status Theorem for theBenchmark.p
% 135.35/18.27
% 135.35/18.27 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 135.35/18.27
% 135.35/18.27 ------ iProver source info
% 135.35/18.27
% 135.35/18.27 git: date: 2024-05-02 19:28:25 +0000
% 135.35/18.27 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 135.35/18.27 git: non_committed_changes: false
% 135.35/18.27
% 135.35/18.27 ------ Parsing...
% 135.35/18.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 135.35/18.27
% 135.35/18.27 ------ 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
% 135.35/18.27
% 135.35/18.27 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 135.35/18.27
% 135.35/18.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 135.35/18.27 ------ Proving...
% 135.35/18.27 ------ Problem Properties
% 135.35/18.27
% 135.35/18.27
% 135.35/18.27 clauses 70
% 135.35/18.27 conjectures 4
% 135.35/18.27 EPR 31
% 135.35/18.27 Horn 60
% 135.35/18.27 unary 25
% 135.35/18.27 binary 16
% 135.35/18.27 lits 180
% 135.35/18.27 lits eq 20
% 135.35/18.27 fd_pure 0
% 135.35/18.27 fd_pseudo 0
% 135.35/18.27 fd_cond 1
% 135.35/18.27 fd_pseudo_cond 12
% 135.35/18.27 AC symbols 0
% 135.35/18.27
% 135.35/18.27 ------ Input Options Time Limit: Unbounded
% 135.35/18.27
% 135.35/18.27
% 135.35/18.27 ------
% 135.35/18.27 Current options:
% 135.35/18.27 ------
% 135.35/18.27
% 135.35/18.27
% 135.35/18.27
% 135.35/18.27
% 135.35/18.27 ------ Proving...
% 135.35/18.27
% 135.35/18.27
% 135.35/18.27 % SZS status Theorem for theBenchmark.p
% 135.35/18.27
% 135.35/18.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 135.35/18.27
% 135.35/18.28
%------------------------------------------------------------------------------