TSTP Solution File: SEU028+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 3.63s 1.13s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 105 ( 10 unt; 0 def)
% Number of atoms : 432 ( 137 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 573 ( 246 ~; 239 |; 66 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn; 76 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f37,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_dom(X1))
& one_to_one(X1) )
=> ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
& apply(function_inverse(X1),apply(X1,X0)) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
fof(f38,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f39,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
& relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).
fof(f40,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
& relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).
fof(f42,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
inference(negated_conjecture,[],[f42]) ).
fof(f56,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f63,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f62]) ).
fof(f76,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f77,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f76]) ).
fof(f81,plain,
! [X0,X1] :
( ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
& apply(function_inverse(X1),apply(X1,X0)) = X0 )
| ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f82,plain,
! [X0,X1] :
( ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
& apply(function_inverse(X1),apply(X1,X0)) = X0 )
| ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f84,plain,
! [X0,X1] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
& relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f86,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
& relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
& relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f88,plain,
! [X0] :
( ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
& relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f87]) ).
fof(f90,plain,
? [X0] :
( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
| relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f91,plain,
? [X0] :
( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
| relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(flattening,[],[f90]) ).
fof(f117,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f118,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK11(X0,X1) != apply(X1,sK11(X0,X1))
& in(sK11(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK11(X0,X1) != apply(X1,sK11(X0,X1))
& in(sK11(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f119,f120]) ).
fof(f122,plain,
( ? [X0] :
( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
| relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) )
& one_to_one(sK12)
& function(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
( ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) )
& one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f91,f122]) ).
fof(f130,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f131,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f132,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f140,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f179,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK11(X0,X1),X0)
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f180,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK11(X0,X1) != apply(X1,sK11(X0,X1))
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f184,plain,
! [X0,X1] :
( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
| ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f186,plain,
! [X0,X1] :
( apply(relation_composition(function_inverse(X1),X1),X0) = X0
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f187,plain,
! [X0] :
( relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0)))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f189,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f192,plain,
relation(sK12),
inference(cnf_transformation,[],[f123]) ).
fof(f193,plain,
function(sK12),
inference(cnf_transformation,[],[f123]) ).
fof(f194,plain,
one_to_one(sK12),
inference(cnf_transformation,[],[f123]) ).
fof(f195,plain,
( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f199,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK11(relation_dom(X1),X1) != apply(X1,sK11(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f180]) ).
fof(f200,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK11(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f179]) ).
cnf(c_53,plain,
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_54,plain,
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_55,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_62,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| function(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_100,plain,
( apply(X0,sK11(relation_dom(X0),X0)) != sK11(relation_dom(X0),X0)
| ~ function(X0)
| ~ relation(X0)
| identity_relation(relation_dom(X0)) = X0 ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_101,plain,
( ~ function(X0)
| ~ relation(X0)
| identity_relation(relation_dom(X0)) = X0
| in(sK11(relation_dom(X0),X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_106,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(relation_composition(X1,function_inverse(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_108,plain,
( ~ in(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(relation_composition(function_inverse(X1),X1),X0) = X0 ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_111,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ),
inference(cnf_transformation,[],[f187]) ).
cnf(c_113,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_115,negated_conjecture,
( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_116,negated_conjecture,
one_to_one(sK12),
inference(cnf_transformation,[],[f194]) ).
cnf(c_117,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f193]) ).
cnf(c_118,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f192]) ).
cnf(c_143,plain,
( ~ function(sK12)
| ~ relation(sK12)
| relation(function_inverse(sK12)) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_144,plain,
( ~ function(sK12)
| ~ relation(sK12)
| function(function_inverse(sK12)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_151,plain,
( ~ function(sK12)
| ~ relation(sK12)
| ~ one_to_one(sK12)
| relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) ),
inference(instantiation,[status(thm)],[c_113]) ).
cnf(c_153,plain,
( ~ function(sK12)
| ~ relation(sK12)
| ~ one_to_one(sK12)
| relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12) ),
inference(instantiation,[status(thm)],[c_111]) ).
cnf(c_907,plain,
( X0 != sK12
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0)
| apply(relation_composition(function_inverse(X0),X0),X1) = X1 ),
inference(resolution_lifted,[status(thm)],[c_108,c_116]) ).
cnf(c_908,plain,
( ~ in(X0,relation_rng(sK12))
| ~ function(sK12)
| ~ relation(sK12)
| apply(relation_composition(function_inverse(sK12),sK12),X0) = X0 ),
inference(unflattening,[status(thm)],[c_907]) ).
cnf(c_910,plain,
( ~ in(X0,relation_rng(sK12))
| apply(relation_composition(function_inverse(sK12),sK12),X0) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_908,c_118,c_117,c_908]) ).
cnf(c_931,plain,
( X0 != sK12
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| apply(relation_composition(X0,function_inverse(X0)),X1) = X1 ),
inference(resolution_lifted,[status(thm)],[c_106,c_116]) ).
cnf(c_932,plain,
( ~ in(X0,relation_dom(sK12))
| ~ function(sK12)
| ~ relation(sK12)
| apply(relation_composition(sK12,function_inverse(sK12)),X0) = X0 ),
inference(unflattening,[status(thm)],[c_931]) ).
cnf(c_934,plain,
( ~ in(X0,relation_dom(sK12))
| apply(relation_composition(sK12,function_inverse(sK12)),X0) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_932,c_118,c_117,c_932]) ).
cnf(c_971,plain,
( X0 != sK12
| ~ function(X0)
| ~ relation(X0)
| relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ),
inference(resolution_lifted,[status(thm)],[c_113,c_116]) ).
cnf(c_972,plain,
( ~ function(sK12)
| ~ relation(sK12)
| relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) ),
inference(unflattening,[status(thm)],[c_971]) ).
cnf(c_973,plain,
relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12),
inference(global_subsumption_just,[status(thm)],[c_972,c_118,c_117,c_116,c_151]) ).
cnf(c_985,plain,
( X0 != sK12
| ~ function(X0)
| ~ relation(X0)
| relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ),
inference(resolution_lifted,[status(thm)],[c_111,c_116]) ).
cnf(c_986,plain,
( ~ function(sK12)
| ~ relation(sK12)
| relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12) ),
inference(unflattening,[status(thm)],[c_985]) ).
cnf(c_987,plain,
relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12),
inference(global_subsumption_just,[status(thm)],[c_986,c_118,c_117,c_116,c_153]) ).
cnf(c_2802,plain,
( apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))) != sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))
| ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| identity_relation(relation_dom(relation_composition(function_inverse(sK12),sK12))) = relation_composition(function_inverse(sK12),sK12) ),
inference(superposition,[status(thm)],[c_973,c_100]) ).
cnf(c_2803,plain,
( apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))) != sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))
| ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| identity_relation(relation_dom(relation_composition(sK12,function_inverse(sK12)))) = relation_composition(sK12,function_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_987,c_100]) ).
cnf(c_2819,plain,
( apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))) != sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))
| ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(light_normalisation,[status(thm)],[c_2803,c_987]) ).
cnf(c_2824,plain,
( apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))) != sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))
| ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12)) ),
inference(light_normalisation,[status(thm)],[c_2802,c_973]) ).
cnf(c_7946,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| identity_relation(relation_dom(relation_composition(function_inverse(sK12),sK12))) = relation_composition(function_inverse(sK12),sK12)
| in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_973,c_101]) ).
cnf(c_7947,plain,
( ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| identity_relation(relation_dom(relation_composition(sK12,function_inverse(sK12)))) = relation_composition(sK12,function_inverse(sK12))
| in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_987,c_101]) ).
cnf(c_7993,plain,
( ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
| in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12)) ),
inference(light_normalisation,[status(thm)],[c_7947,c_987]) ).
cnf(c_7998,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12))
| in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12)) ),
inference(light_normalisation,[status(thm)],[c_7946,c_973]) ).
cnf(c_10977,plain,
( ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))) = sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_7993,c_934]) ).
cnf(c_11011,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))) = sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_7998,c_910]) ).
cnf(c_11057,plain,
( ~ relation(relation_composition(sK12,function_inverse(sK12)))
| ~ function(relation_composition(sK12,function_inverse(sK12)))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_10977,c_2819,c_10977]) ).
cnf(c_11058,plain,
( ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(renaming,[status(thm)],[c_11057]) ).
cnf(c_11066,plain,
( ~ relation(relation_composition(sK12,function_inverse(sK12)))
| ~ function(function_inverse(sK12))
| ~ relation(function_inverse(sK12))
| ~ function(sK12)
| ~ relation(sK12)
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_62,c_11058]) ).
cnf(c_11068,plain,
( ~ relation(relation_composition(sK12,function_inverse(sK12)))
| ~ function(function_inverse(sK12))
| ~ relation(function_inverse(sK12))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11066,c_118,c_117]) ).
cnf(c_11073,plain,
( ~ relation(relation_composition(sK12,function_inverse(sK12)))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_11068,c_118,c_117,c_143,c_144,c_11068]) ).
cnf(c_11080,plain,
( ~ relation(function_inverse(sK12))
| ~ relation(sK12)
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_55,c_11073]) ).
cnf(c_11082,plain,
( ~ relation(function_inverse(sK12))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11080,c_118]) ).
cnf(c_11251,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_11011,c_118,c_117,c_143,c_115,c_2824,c_11011,c_11082]) ).
cnf(c_11258,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(function_inverse(sK12))
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_55,c_11251]) ).
cnf(c_11260,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ relation(function_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11258,c_118]) ).
cnf(c_11263,plain,
~ function(relation_composition(function_inverse(sK12),sK12)),
inference(global_subsumption_just,[status(thm)],[c_11260,c_118,c_117,c_143,c_11260]) ).
cnf(c_11266,plain,
( ~ function(function_inverse(sK12))
| ~ relation(function_inverse(sK12))
| ~ function(sK12)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_62,c_11263]) ).
cnf(c_11268,plain,
( ~ function(function_inverse(sK12))
| ~ relation(function_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11266,c_118,c_117]) ).
cnf(c_11271,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11268,c_144,c_143,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n011.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 23:28:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.63/1.13 % SZS status Started for theBenchmark.p
% 3.63/1.13 % SZS status Theorem for theBenchmark.p
% 3.63/1.13
% 3.63/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.63/1.13
% 3.63/1.13 ------ iProver source info
% 3.63/1.13
% 3.63/1.13 git: date: 2023-05-31 18:12:56 +0000
% 3.63/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.63/1.13 git: non_committed_changes: false
% 3.63/1.13 git: last_make_outside_of_git: false
% 3.63/1.13
% 3.63/1.13 ------ Parsing...
% 3.63/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.63/1.13
% 3.63/1.13 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e
% 3.63/1.13
% 3.63/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.63/1.13
% 3.63/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.63/1.13 ------ Proving...
% 3.63/1.13 ------ Problem Properties
% 3.63/1.13
% 3.63/1.13
% 3.63/1.13 clauses 80
% 3.63/1.13 conjectures 3
% 3.63/1.13 EPR 26
% 3.63/1.13 Horn 77
% 3.63/1.13 unary 34
% 3.63/1.13 binary 26
% 3.63/1.13 lits 150
% 3.63/1.13 lits eq 33
% 3.63/1.13 fd_pure 0
% 3.63/1.13 fd_pseudo 0
% 3.63/1.13 fd_cond 1
% 3.63/1.13 fd_pseudo_cond 1
% 3.63/1.13 AC symbols 0
% 3.63/1.13
% 3.63/1.13 ------ Schedule dynamic 5 is on
% 3.63/1.13
% 3.63/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.63/1.13
% 3.63/1.13
% 3.63/1.13 ------
% 3.63/1.13 Current options:
% 3.63/1.13 ------
% 3.63/1.13
% 3.63/1.13
% 3.63/1.13
% 3.63/1.13
% 3.63/1.13 ------ Proving...
% 3.63/1.13
% 3.63/1.13
% 3.63/1.13 % SZS status Theorem for theBenchmark.p
% 3.63/1.13
% 3.63/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.63/1.13
% 3.63/1.14
%------------------------------------------------------------------------------