TSTP Solution File: SEU027+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU027+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 17:03:27 EDT 2023
% Result : Theorem 84.58s 12.24s
% Output : CNFRefutation 84.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 96 ( 23 unt; 0 def)
% Number of atoms : 621 ( 224 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 850 ( 325 ~; 319 |; 165 &)
% ( 15 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 198 ( 0 sgn; 138 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f31,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f33,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> function_inverse(X0) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> function_inverse(X0) = X1 ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f38,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X1,X2) = apply(X0,X2) )
& relation_dom(X0) = relation_dom(X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f48,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,[],[f5]) ).
fof(f49,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,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f50]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f65]) ).
fof(f68,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f69,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(flattening,[],[f68]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( sP0(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f66,f75]) ).
fof(f77,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,[],[f49]) ).
fof(f78,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,[],[f77]) ).
fof(f79,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) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK1(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK1(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK1(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] :
( apply(X0,X3) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK1(X0,X1),X1) )
& ( ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f78,f81,f80,f79]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
=> ( ( ( sK16(X0,X1) != apply(X1,sK15(X0,X1))
| ~ in(sK15(X0,X1),relation_rng(X0)) )
& sK15(X0,X1) = apply(X0,sK16(X0,X1))
& in(sK16(X0,X1),relation_dom(X0)) )
| ~ sP0(sK15(X0,X1),sK16(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ( ( sK16(X0,X1) != apply(X1,sK15(X0,X1))
| ~ in(sK15(X0,X1),relation_rng(X0)) )
& sK15(X0,X1) = apply(X0,sK16(X0,X1))
& in(sK16(X0,X1),relation_dom(X0)) )
| ~ sP0(sK15(X0,X1),sK16(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f110,f111]) ).
fof(f113,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( ( apply(X0,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(X0,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f114,plain,
( ? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( ( apply(X0,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(X0,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) )
=> ( ? [X1] :
( function_inverse(sK17) != X1
& ! [X3,X2] :
( ( ( apply(sK17,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(sK17,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(sK17)) )
& relation_dom(X1) = relation_rng(sK17)
& relation_rng(X1) = relation_dom(sK17)
& one_to_one(sK17)
& function(X1)
& relation(X1) )
& function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
( ? [X1] :
( function_inverse(sK17) != X1
& ! [X3,X2] :
( ( ( apply(sK17,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(sK17,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(sK17)) )
& relation_dom(X1) = relation_rng(sK17)
& relation_rng(X1) = relation_dom(sK17)
& one_to_one(sK17)
& function(X1)
& relation(X1) )
=> ( function_inverse(sK17) != sK18
& ! [X3,X2] :
( ( ( apply(sK17,X2) = X3
| apply(sK18,X3) != X2 )
& ( apply(sK18,X3) = X2
| apply(sK17,X2) != X3 ) )
| ~ in(X3,relation_dom(sK18))
| ~ in(X2,relation_dom(sK17)) )
& relation_rng(sK17) = relation_dom(sK18)
& relation_dom(sK17) = relation_rng(sK18)
& one_to_one(sK17)
& function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
( function_inverse(sK17) != sK18
& ! [X2,X3] :
( ( ( apply(sK17,X2) = X3
| apply(sK18,X3) != X2 )
& ( apply(sK18,X3) = X2
| apply(sK17,X2) != X3 ) )
| ~ in(X3,relation_dom(sK18))
| ~ in(X2,relation_dom(sK17)) )
& relation_rng(sK17) = relation_dom(sK18)
& relation_dom(sK17) = relation_rng(sK18)
& one_to_one(sK17)
& function(sK18)
& relation(sK18)
& function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f113,f115,f114]) ).
fof(f117,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
=> ( apply(X1,sK19(X0,X1)) != apply(X0,sK19(X0,X1))
& in(sK19(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( apply(X1,sK19(X0,X1)) != apply(X0,sK19(X0,X1))
& in(sK19(X0,X1),relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f74,f117]) ).
fof(f127,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f131,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f132,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f175,plain,
! [X0,X1] :
( relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f178,plain,
! [X0,X1,X4,X5] :
( apply(X1,X4) = X5
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0))
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f183,plain,
relation(sK17),
inference(cnf_transformation,[],[f116]) ).
fof(f184,plain,
function(sK17),
inference(cnf_transformation,[],[f116]) ).
fof(f185,plain,
relation(sK18),
inference(cnf_transformation,[],[f116]) ).
fof(f186,plain,
function(sK18),
inference(cnf_transformation,[],[f116]) ).
fof(f187,plain,
one_to_one(sK17),
inference(cnf_transformation,[],[f116]) ).
fof(f188,plain,
relation_dom(sK17) = relation_rng(sK18),
inference(cnf_transformation,[],[f116]) ).
fof(f189,plain,
relation_rng(sK17) = relation_dom(sK18),
inference(cnf_transformation,[],[f116]) ).
fof(f191,plain,
! [X2,X3] :
( apply(sK17,X2) = X3
| apply(sK18,X3) != X2
| ~ in(X3,relation_dom(sK18))
| ~ in(X2,relation_dom(sK17)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f192,plain,
function_inverse(sK17) != sK18,
inference(cnf_transformation,[],[f116]) ).
fof(f196,plain,
! [X0,X1] :
( X0 = X1
| in(sK19(X0,X1),relation_dom(X0))
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f197,plain,
! [X0,X1] :
( X0 = X1
| apply(X1,sK19(X0,X1)) != apply(X0,sK19(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f198,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f199,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f198]) ).
fof(f205,plain,
! [X0,X1,X5] :
( apply(X1,apply(X0,X5)) = X5
| ~ in(X5,relation_dom(X0))
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f178]) ).
fof(f206,plain,
! [X0,X5] :
( apply(function_inverse(X0),apply(X0,X5)) = X5
| ~ in(X5,relation_dom(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f205]) ).
fof(f210,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f175]) ).
fof(f211,plain,
! [X3] :
( apply(sK17,apply(sK18,X3)) = X3
| ~ in(X3,relation_dom(sK18))
| ~ in(apply(sK18,X3),relation_dom(sK17)) ),
inference(equality_resolution,[],[f191]) ).
cnf(c_56,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_59,plain,
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_60,plain,
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_106,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(function_inverse(X1),apply(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_109,plain,
( ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_111,negated_conjecture,
function_inverse(sK17) != sK18,
inference(cnf_transformation,[],[f192]) ).
cnf(c_112,negated_conjecture,
( ~ in(apply(sK18,X0),relation_dom(sK17))
| ~ in(X0,relation_dom(sK18))
| apply(sK17,apply(sK18,X0)) = X0 ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_114,negated_conjecture,
relation_rng(sK17) = relation_dom(sK18),
inference(cnf_transformation,[],[f189]) ).
cnf(c_115,negated_conjecture,
relation_rng(sK18) = relation_dom(sK17),
inference(cnf_transformation,[],[f188]) ).
cnf(c_116,negated_conjecture,
one_to_one(sK17),
inference(cnf_transformation,[],[f187]) ).
cnf(c_117,negated_conjecture,
function(sK18),
inference(cnf_transformation,[],[f186]) ).
cnf(c_118,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f185]) ).
cnf(c_119,negated_conjecture,
function(sK17),
inference(cnf_transformation,[],[f184]) ).
cnf(c_120,negated_conjecture,
relation(sK17),
inference(cnf_transformation,[],[f183]) ).
cnf(c_124,plain,
( apply(X0,sK19(X0,X1)) != apply(X1,sK19(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_125,plain,
( relation_dom(X0) != relation_dom(X1)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| X0 = X1
| in(sK19(X0,X1),relation_dom(X0)) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_146,plain,
( ~ function(sK17)
| ~ relation(sK17)
| relation(function_inverse(sK17)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_147,plain,
( ~ function(sK17)
| ~ relation(sK17)
| function(function_inverse(sK17)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_175,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(global_subsumption_just,[status(thm)],[c_109,c_60,c_59,c_109]) ).
cnf(c_314,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(function_inverse(X1),apply(X1,X0)) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_106,c_59]) ).
cnf(c_322,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(function_inverse(X1),apply(X1,X0)) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_314,c_60]) ).
cnf(c_3598,plain,
( ~ function(sK17)
| ~ relation(sK17)
| relation_dom(function_inverse(sK17)) = relation_rng(sK17) ),
inference(superposition,[status(thm)],[c_116,c_175]) ).
cnf(c_3599,plain,
relation_dom(function_inverse(sK17)) = relation_rng(sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_3598,c_120,c_119]) ).
cnf(c_3600,plain,
relation_dom(function_inverse(sK17)) = relation_dom(sK18),
inference(light_normalisation,[status(thm)],[c_3599,c_114]) ).
cnf(c_3609,plain,
( ~ in(X0,relation_dom(sK18))
| ~ function(sK18)
| ~ relation(sK18)
| in(apply(sK18,X0),relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_115,c_56]) ).
cnf(c_3613,plain,
( ~ in(X0,relation_dom(sK18))
| in(apply(sK18,X0),relation_dom(sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3609,c_118,c_117]) ).
cnf(c_3638,negated_conjecture,
( ~ in(X0,relation_dom(sK18))
| apply(sK17,apply(sK18,X0)) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_112,c_112,c_3613]) ).
cnf(c_3957,plain,
( relation_dom(X0) != relation_dom(sK18)
| ~ function(function_inverse(sK17))
| ~ relation(function_inverse(sK17))
| ~ function(X0)
| ~ relation(X0)
| function_inverse(sK17) = X0
| in(sK19(function_inverse(sK17),X0),relation_dom(function_inverse(sK17))) ),
inference(superposition,[status(thm)],[c_3600,c_125]) ).
cnf(c_3962,plain,
( relation_dom(X0) != relation_dom(sK18)
| ~ function(function_inverse(sK17))
| ~ relation(function_inverse(sK17))
| ~ function(X0)
| ~ relation(X0)
| function_inverse(sK17) = X0
| in(sK19(function_inverse(sK17),X0),relation_dom(sK18)) ),
inference(light_normalisation,[status(thm)],[c_3957,c_3600]) ).
cnf(c_4052,plain,
( ~ in(X0,relation_dom(sK18))
| ~ function(sK17)
| ~ relation(sK17)
| ~ one_to_one(sK17)
| apply(function_inverse(sK17),apply(sK17,apply(sK18,X0))) = apply(sK18,X0) ),
inference(superposition,[status(thm)],[c_3613,c_322]) ).
cnf(c_4054,plain,
( ~ in(X0,relation_dom(sK18))
| apply(function_inverse(sK17),apply(sK17,apply(sK18,X0))) = apply(sK18,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4052,c_116,c_120,c_119]) ).
cnf(c_4084,plain,
( apply(function_inverse(sK17),sK19(function_inverse(sK17),sK18)) != apply(sK18,sK19(function_inverse(sK17),sK18))
| relation_dom(function_inverse(sK17)) != relation_dom(sK18)
| ~ function(function_inverse(sK17))
| ~ relation(function_inverse(sK17))
| ~ function(sK18)
| ~ relation(sK18)
| function_inverse(sK17) = sK18 ),
inference(instantiation,[status(thm)],[c_124]) ).
cnf(c_6890,plain,
( relation_dom(X0) != relation_dom(sK18)
| ~ function(X0)
| ~ relation(X0)
| function_inverse(sK17) = X0
| in(sK19(function_inverse(sK17),X0),relation_dom(sK18)) ),
inference(global_subsumption_just,[status(thm)],[c_3962,c_120,c_119,c_146,c_147,c_3962]) ).
cnf(c_6900,plain,
( ~ function(sK18)
| ~ relation(sK18)
| function_inverse(sK17) = sK18
| in(sK19(function_inverse(sK17),sK18),relation_dom(sK18)) ),
inference(equality_resolution,[status(thm)],[c_6890]) ).
cnf(c_6901,plain,
in(sK19(function_inverse(sK17),sK18),relation_dom(sK18)),
inference(forward_subsumption_resolution,[status(thm)],[c_6900,c_111,c_118,c_117]) ).
cnf(c_42519,plain,
apply(function_inverse(sK17),apply(sK17,apply(sK18,sK19(function_inverse(sK17),sK18)))) = apply(sK18,sK19(function_inverse(sK17),sK18)),
inference(superposition,[status(thm)],[c_6901,c_4054]) ).
cnf(c_42524,plain,
apply(sK17,apply(sK18,sK19(function_inverse(sK17),sK18))) = sK19(function_inverse(sK17),sK18),
inference(superposition,[status(thm)],[c_6901,c_3638]) ).
cnf(c_42530,plain,
apply(function_inverse(sK17),sK19(function_inverse(sK17),sK18)) = apply(sK18,sK19(function_inverse(sK17),sK18)),
inference(light_normalisation,[status(thm)],[c_42519,c_42524]) ).
cnf(c_42544,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_42530,c_4084,c_3600,c_147,c_146,c_111,c_117,c_118,c_119,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Thu Aug 24 02:07:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 84.58/12.24 % SZS status Started for theBenchmark.p
% 84.58/12.24 % SZS status Theorem for theBenchmark.p
% 84.58/12.24
% 84.58/12.24 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 84.58/12.24
% 84.58/12.24 ------ iProver source info
% 84.58/12.24
% 84.58/12.24 git: date: 2023-05-31 18:12:56 +0000
% 84.58/12.24 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 84.58/12.24 git: non_committed_changes: false
% 84.58/12.24 git: last_make_outside_of_git: false
% 84.58/12.24
% 84.58/12.24 ------ Parsing...
% 84.58/12.24 ------ Clausification by vclausify_rel & Parsing by iProver...
% 84.58/12.24
% 84.58/12.24 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 84.58/12.24
% 84.58/12.24 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 84.58/12.24
% 84.58/12.24 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 84.58/12.24 ------ Proving...
% 84.58/12.24 ------ Problem Properties
% 84.58/12.24
% 84.58/12.24
% 84.58/12.24 clauses 72
% 84.58/12.24 conjectures 10
% 84.58/12.24 EPR 31
% 84.58/12.24 Horn 63
% 84.58/12.24 unary 30
% 84.58/12.24 binary 16
% 84.58/12.24 lits 181
% 84.58/12.24 lits eq 30
% 84.58/12.24 fd_pure 0
% 84.58/12.24 fd_pseudo 0
% 84.58/12.24 fd_cond 1
% 84.58/12.24 fd_pseudo_cond 10
% 84.58/12.24 AC symbols 0
% 84.58/12.24
% 84.58/12.24 ------ Input Options Time Limit: Unbounded
% 84.58/12.24
% 84.58/12.24
% 84.58/12.24 ------
% 84.58/12.24 Current options:
% 84.58/12.24 ------
% 84.58/12.24
% 84.58/12.24
% 84.58/12.24
% 84.58/12.24
% 84.58/12.24 ------ Proving...
% 84.58/12.24
% 84.58/12.24
% 84.58/12.24 % SZS status Theorem for theBenchmark.p
% 84.58/12.24
% 84.58/12.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 84.58/12.24
% 84.58/12.26
%------------------------------------------------------------------------------