TSTP Solution File: SEU220+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU220+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 17:04:51 EDT 2023
% Result : Theorem 3.92s 1.16s
% Output : CNFRefutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 12 unt; 0 def)
% Number of atoms : 400 ( 136 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 546 ( 219 ~; 209 |; 96 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 131 ( 4 sgn; 89 !; 14 ?)
% 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(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f35,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/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f36,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,conjecture,
! [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(f38,negated_conjecture,
~ ! [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 ) ) ),
inference(negated_conjecture,[],[f37]) ).
fof(f52,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f52]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f70]) ).
fof(f77,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,[],[f35]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f80,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f79]) ).
fof(f81,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(f82,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,[],[f81]) ).
fof(f87,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(f88,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,[],[f78,f87]) ).
fof(f111,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)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP0(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f112,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)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP0(X2,X3,X0,X1) ) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( ( sP0(X0,X1,X2,X3)
| ( ( apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) )
& apply(X3,X0) = X1
& in(X0,relation_rng(X2)) ) )
& ( ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) )
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f112]) ).
fof(f114,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,[],[f88]) ).
fof(f115,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,[],[f114]) ).
fof(f116,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,[],[f115]) ).
fof(f117,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) )
=> ( ( ( sK13(X0,X1) != apply(X1,sK12(X0,X1))
| ~ in(sK12(X0,X1),relation_rng(X0)) )
& sK12(X0,X1) = apply(X0,sK13(X0,X1))
& in(sK13(X0,X1),relation_dom(X0)) )
| ~ sP0(sK12(X0,X1),sK13(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ( ( sK13(X0,X1) != apply(X1,sK12(X0,X1))
| ~ in(sK12(X0,X1),relation_rng(X0)) )
& sK12(X0,X1) = apply(X0,sK13(X0,X1))
& in(sK13(X0,X1),relation_dom(X0)) )
| ~ sP0(sK12(X0,X1),sK13(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,[sK12,sK13])],[f116,f117]) ).
fof(f119,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) )
=> ( ( sK14 != apply(relation_composition(function_inverse(sK15),sK15),sK14)
| sK14 != apply(sK15,apply(function_inverse(sK15),sK14)) )
& in(sK14,relation_rng(sK15))
& one_to_one(sK15)
& function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
( ( sK14 != apply(relation_composition(function_inverse(sK15),sK15),sK14)
| sK14 != apply(sK15,apply(function_inverse(sK15),sK14)) )
& in(sK14,relation_rng(sK15))
& one_to_one(sK15)
& function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f82,f119]) ).
fof(f127,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f128,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f170,plain,
! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( apply(X2,X1) = X0
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f113]) ).
fof(f180,plain,
! [X0,X1,X4,X5] :
( sP0(X4,X5,X0,X1)
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f186,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f188,plain,
relation(sK15),
inference(cnf_transformation,[],[f120]) ).
fof(f189,plain,
function(sK15),
inference(cnf_transformation,[],[f120]) ).
fof(f190,plain,
one_to_one(sK15),
inference(cnf_transformation,[],[f120]) ).
fof(f191,plain,
in(sK14,relation_rng(sK15)),
inference(cnf_transformation,[],[f120]) ).
fof(f192,plain,
( sK14 != apply(relation_composition(function_inverse(sK15),sK15),sK14)
| sK14 != apply(sK15,apply(function_inverse(sK15),sK14)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f198,plain,
! [X2,X3,X0] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f175]) ).
fof(f204,plain,
! [X0,X4,X5] :
( sP0(X4,X5,X0,function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f180]) ).
cnf(c_53,plain,
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_54,plain,
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_96,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_103,plain,
( ~ sP0(X0,apply(X1,X0),X2,X1)
| ~ in(X0,relation_rng(X2))
| apply(X2,apply(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_110,plain,
( ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| sP0(X1,X2,X0,function_inverse(X0)) ),
inference(cnf_transformation,[],[f204]) ).
cnf(c_113,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_114,negated_conjecture,
( apply(relation_composition(function_inverse(sK15),sK15),sK14) != sK14
| apply(sK15,apply(function_inverse(sK15),sK14)) != sK14 ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_115,negated_conjecture,
in(sK14,relation_rng(sK15)),
inference(cnf_transformation,[],[f191]) ).
cnf(c_116,negated_conjecture,
one_to_one(sK15),
inference(cnf_transformation,[],[f190]) ).
cnf(c_117,negated_conjecture,
function(sK15),
inference(cnf_transformation,[],[f189]) ).
cnf(c_118,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f188]) ).
cnf(c_143,plain,
( ~ function(sK15)
| ~ relation(sK15)
| relation(function_inverse(sK15)) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_144,plain,
( ~ function(sK15)
| ~ relation(sK15)
| function(function_inverse(sK15)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_151,plain,
( ~ function(sK15)
| ~ relation(sK15)
| ~ one_to_one(sK15)
| relation_dom(function_inverse(sK15)) = relation_rng(sK15) ),
inference(instantiation,[status(thm)],[c_113]) ).
cnf(c_168,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| sP0(X1,X2,X0,function_inverse(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_110,c_54,c_53,c_110]) ).
cnf(c_2402,plain,
X0 = X0,
theory(equality) ).
cnf(c_2404,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_3255,plain,
( ~ sP0(sK14,apply(function_inverse(sK15),sK14),sK15,function_inverse(sK15))
| ~ in(sK14,relation_rng(sK15))
| apply(sK15,apply(function_inverse(sK15),sK14)) = sK14 ),
inference(instantiation,[status(thm)],[c_103]) ).
cnf(c_3272,plain,
( ~ function(sK15)
| ~ relation(sK15)
| ~ one_to_one(sK15)
| sP0(sK14,apply(function_inverse(sK15),sK14),sK15,function_inverse(sK15)) ),
inference(instantiation,[status(thm)],[c_168]) ).
cnf(c_3287,plain,
( X0 != X1
| sK14 != X1
| sK14 = X0 ),
inference(instantiation,[status(thm)],[c_2404]) ).
cnf(c_3306,plain,
( X0 != sK14
| sK14 != sK14
| sK14 = X0 ),
inference(instantiation,[status(thm)],[c_3287]) ).
cnf(c_3321,plain,
( apply(relation_composition(function_inverse(sK15),sK15),sK14) != X0
| sK14 != X0
| apply(relation_composition(function_inverse(sK15),sK15),sK14) = sK14 ),
inference(instantiation,[status(thm)],[c_2404]) ).
cnf(c_3422,plain,
sK14 = sK14,
inference(instantiation,[status(thm)],[c_2402]) ).
cnf(c_4323,plain,
( apply(sK15,apply(function_inverse(sK15),sK14)) != sK14
| sK14 != sK14
| sK14 = apply(sK15,apply(function_inverse(sK15),sK14)) ),
inference(instantiation,[status(thm)],[c_3306]) ).
cnf(c_6043,plain,
( apply(relation_composition(function_inverse(sK15),sK15),sK14) != apply(sK15,apply(function_inverse(sK15),sK14))
| sK14 != apply(sK15,apply(function_inverse(sK15),sK14))
| apply(relation_composition(function_inverse(sK15),sK15),sK14) = sK14 ),
inference(instantiation,[status(thm)],[c_3321]) ).
cnf(c_6808,plain,
( ~ function(sK15)
| ~ relation(sK15)
| relation_dom(function_inverse(sK15)) = relation_rng(sK15) ),
inference(superposition,[status(thm)],[c_116,c_113]) ).
cnf(c_6851,plain,
relation_dom(function_inverse(sK15)) = relation_rng(sK15),
inference(global_subsumption_just,[status(thm)],[c_6808,c_118,c_117,c_116,c_151]) ).
cnf(c_6925,plain,
( ~ in(X0,relation_rng(sK15))
| ~ function(function_inverse(sK15))
| ~ relation(function_inverse(sK15))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_composition(function_inverse(sK15),X1),X0) = apply(X1,apply(function_inverse(sK15),X0)) ),
inference(superposition,[status(thm)],[c_6851,c_96]) ).
cnf(c_7002,plain,
( ~ in(X0,relation_rng(sK15))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_composition(function_inverse(sK15),X1),X0) = apply(X1,apply(function_inverse(sK15),X0)) ),
inference(global_subsumption_just,[status(thm)],[c_6925,c_118,c_117,c_143,c_144,c_6925]) ).
cnf(c_7006,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(relation_composition(function_inverse(sK15),X0),sK14) = apply(X0,apply(function_inverse(sK15),sK14)) ),
inference(superposition,[status(thm)],[c_115,c_7002]) ).
cnf(c_7008,plain,
( ~ function(sK15)
| ~ relation(sK15)
| apply(relation_composition(function_inverse(sK15),sK15),sK14) = apply(sK15,apply(function_inverse(sK15),sK14)) ),
inference(instantiation,[status(thm)],[c_7006]) ).
cnf(c_7009,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7008,c_6043,c_4323,c_3422,c_3272,c_3255,c_114,c_115,c_116,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU220+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n010.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 : Wed Aug 23 13:58:21 EDT 2023
% 0.13/0.34 % 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
% 3.92/1.16 % SZS status Started for theBenchmark.p
% 3.92/1.16 % SZS status Theorem for theBenchmark.p
% 3.92/1.16
% 3.92/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.92/1.16
% 3.92/1.16 ------ iProver source info
% 3.92/1.16
% 3.92/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.92/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.92/1.16 git: non_committed_changes: false
% 3.92/1.16 git: last_make_outside_of_git: false
% 3.92/1.16
% 3.92/1.16 ------ Parsing...
% 3.92/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.92/1.16
% 3.92/1.16 ------ 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
% 3.92/1.16
% 3.92/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.92/1.16
% 3.92/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.92/1.16 ------ Proving...
% 3.92/1.16 ------ Problem Properties
% 3.92/1.16
% 3.92/1.16
% 3.92/1.16 clauses 68
% 3.92/1.16 conjectures 5
% 3.92/1.16 EPR 29
% 3.92/1.16 Horn 62
% 3.92/1.16 unary 26
% 3.92/1.16 binary 17
% 3.92/1.16 lits 166
% 3.92/1.16 lits eq 18
% 3.92/1.16 fd_pure 0
% 3.92/1.16 fd_pseudo 0
% 3.92/1.16 fd_cond 1
% 3.92/1.16 fd_pseudo_cond 5
% 3.92/1.16 AC symbols 0
% 3.92/1.16
% 3.92/1.16 ------ Input Options Time Limit: Unbounded
% 3.92/1.16
% 3.92/1.16
% 3.92/1.16 ------
% 3.92/1.16 Current options:
% 3.92/1.16 ------
% 3.92/1.16
% 3.92/1.16
% 3.92/1.16
% 3.92/1.16
% 3.92/1.16 ------ Proving...
% 3.92/1.16
% 3.92/1.16
% 3.92/1.16 % SZS status Theorem for theBenchmark.p
% 3.92/1.16
% 3.92/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.92/1.16
% 3.92/1.16
%------------------------------------------------------------------------------