TSTP Solution File: SEU419+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU419+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:07:07 EDT 2023
% Result : Theorem 4.05s 1.14s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 70 ( 12 unt; 0 def)
% Number of atoms : 243 ( 36 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 289 ( 116 ~; 123 |; 37 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 144 ( 3 sgn; 96 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> k9_relat_1(k4_xboole_0(X1,X2),k1_tarski(X0)) = k4_xboole_0(k9_relat_1(X1,k1_tarski(X0)),k9_relat_1(X2,k1_tarski(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> k9_relat_1(k4_xboole_0(X1,X2),k1_tarski(X0)) = k4_xboole_0(k9_relat_1(X1,k1_tarski(X0)),k9_relat_1(X2,k1_tarski(X0))) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f5,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( k4_xboole_0(X0,X1) = X2
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f9,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f22,axiom,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_relat_1(X0) )
=> v1_relat_1(k4_xboole_0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(f41,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
<=> r2_hidden(k4_tarski(X1,X0),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_2) ).
fof(f45,plain,
? [X0,X1] :
( ? [X2] :
( k9_relat_1(k4_xboole_0(X1,X2),k1_tarski(X0)) != k4_xboole_0(k9_relat_1(X1,k1_tarski(X0)),k9_relat_1(X2,k1_tarski(X0)))
& v1_relat_1(X2) )
& v1_relat_1(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f49,plain,
! [X0,X1] :
( v1_relat_1(k4_xboole_0(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f50,plain,
! [X0,X1] :
( v1_relat_1(k4_xboole_0(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(flattening,[],[f49]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
<=> r2_hidden(k4_tarski(X1,X0),X2) )
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f62,plain,
( ? [X0,X1] :
( ? [X2] :
( k9_relat_1(k4_xboole_0(X1,X2),k1_tarski(X0)) != k4_xboole_0(k9_relat_1(X1,k1_tarski(X0)),k9_relat_1(X2,k1_tarski(X0)))
& v1_relat_1(X2) )
& v1_relat_1(X1) )
=> ( ? [X2] :
( k9_relat_1(k4_xboole_0(sK1,X2),k1_tarski(sK0)) != k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(X2,k1_tarski(sK0)))
& v1_relat_1(X2) )
& v1_relat_1(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
( ? [X2] :
( k9_relat_1(k4_xboole_0(sK1,X2),k1_tarski(sK0)) != k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(X2,k1_tarski(sK0)))
& v1_relat_1(X2) )
=> ( k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0)) != k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)))
& v1_relat_1(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
( k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0)) != k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)))
& v1_relat_1(sK2)
& v1_relat_1(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f45,f63,f62]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) = X2
| ? [X3] :
( ( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
& ( ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X3,X2) ) )
| k4_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) = X2
| ? [X3] :
( ( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
& ( ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X3,X2) ) )
| k4_xboole_0(X0,X1) != X2 ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) = X2
| ? [X3] :
( ( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0) )
& ( ( ~ r2_hidden(X4,X1)
& r2_hidden(X4,X0) )
| ~ r2_hidden(X4,X2) ) )
| k4_xboole_0(X0,X1) != X2 ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) )
=> ( ( r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X0)
| ~ r2_hidden(sK4(X0,X1,X2),X2) )
& ( ( ~ r2_hidden(sK4(X0,X1,X2),X1)
& r2_hidden(sK4(X0,X1,X2),X0) )
| r2_hidden(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) = X2
| ( ( r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X0)
| ~ r2_hidden(sK4(X0,X1,X2),X2) )
& ( ( ~ r2_hidden(sK4(X0,X1,X2),X1)
& r2_hidden(sK4(X0,X1,X2),X0) )
| r2_hidden(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0) )
& ( ( ~ r2_hidden(X4,X1)
& r2_hidden(X4,X0) )
| ~ r2_hidden(X4,X2) ) )
| k4_xboole_0(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f73,f74]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| ~ r2_hidden(k4_tarski(X1,X0),X2) )
& ( r2_hidden(k4_tarski(X1,X0),X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1))) ) )
| ~ v1_relat_1(X2) ),
inference(nnf_transformation,[],[f61]) ).
fof(f90,plain,
v1_relat_1(sK1),
inference(cnf_transformation,[],[f64]) ).
fof(f91,plain,
v1_relat_1(sK2),
inference(cnf_transformation,[],[f64]) ).
fof(f92,plain,
k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0)) != k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0))),
inference(cnf_transformation,[],[f64]) ).
fof(f95,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f102,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X0)
| ~ r2_hidden(X4,X2)
| k4_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X2,X0,X1,X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2)
| k4_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f104,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| k4_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f105,plain,
! [X2,X0,X1] :
( k4_xboole_0(X0,X1) = X2
| r2_hidden(sK4(X0,X1,X2),X0)
| r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f106,plain,
! [X2,X0,X1] :
( k4_xboole_0(X0,X1) = X2
| ~ r2_hidden(sK4(X0,X1,X2),X1)
| r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f107,plain,
! [X2,X0,X1] :
( k4_xboole_0(X0,X1) = X2
| r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X0)
| ~ r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f108,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f114,plain,
! [X0,X1] :
( v1_relat_1(k4_xboole_0(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f139,plain,
! [X2,X0,X1] :
( r2_hidden(k4_tarski(X1,X0),X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f140,plain,
! [X2,X0,X1] :
( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| ~ r2_hidden(k4_tarski(X1,X0),X2)
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f141,plain,
! [X2,X0,X1] :
( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),X2)
| ~ v1_relat_1(X2) ),
inference(definition_unfolding,[],[f140,f108]) ).
fof(f142,plain,
! [X2,X0,X1] :
( r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| ~ v1_relat_1(X2) ),
inference(definition_unfolding,[],[f139,f108]) ).
fof(f145,plain,
! [X0,X1,X4] :
( r2_hidden(X4,k4_xboole_0(X0,X1))
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f104]) ).
fof(f146,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,k4_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f103]) ).
fof(f147,plain,
! [X0,X1,X4] :
( r2_hidden(X4,X0)
| ~ r2_hidden(X4,k4_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f102]) ).
cnf(c_49,negated_conjecture,
k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0))) != k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0)),
inference(cnf_transformation,[],[f92]) ).
cnf(c_50,negated_conjecture,
v1_relat_1(sK2),
inference(cnf_transformation,[],[f91]) ).
cnf(c_51,negated_conjecture,
v1_relat_1(sK1),
inference(cnf_transformation,[],[f90]) ).
cnf(c_54,plain,
k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f95]) ).
cnf(c_61,plain,
( ~ r2_hidden(sK4(X0,X1,X2),X0)
| ~ r2_hidden(sK4(X0,X1,X2),X2)
| k4_xboole_0(X0,X1) = X2
| r2_hidden(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_62,plain,
( ~ r2_hidden(sK4(X0,X1,X2),X1)
| k4_xboole_0(X0,X1) = X2
| r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_63,plain,
( k4_xboole_0(X0,X1) = X2
| r2_hidden(sK4(X0,X1,X2),X0)
| r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_64,plain,
( ~ r2_hidden(X0,X1)
| r2_hidden(X0,k4_xboole_0(X1,X2))
| r2_hidden(X0,X2) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_65,plain,
( ~ r2_hidden(X0,k4_xboole_0(X1,X2))
| ~ r2_hidden(X0,X2) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_66,plain,
( ~ r2_hidden(X0,k4_xboole_0(X1,X2))
| r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_72,plain,
( ~ v1_relat_1(X0)
| ~ v1_relat_1(X1)
| v1_relat_1(k4_xboole_0(X1,X0)) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_97,plain,
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),X2)
| ~ v1_relat_1(X2)
| r2_hidden(X1,k9_relat_1(X2,k1_tarski(X0))) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_98,plain,
( ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2)))
| ~ v1_relat_1(X1)
| r2_hidden(k2_tarski(k2_tarski(X2,X0),k1_tarski(X2)),X1) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_405,plain,
( ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2)))
| ~ v1_relat_1(X1)
| r2_hidden(k2_tarski(k1_tarski(X2),k2_tarski(X2,X0)),X1) ),
inference(demodulation,[status(thm)],[c_98,c_54]) ).
cnf(c_406,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),X2)
| ~ v1_relat_1(X2)
| r2_hidden(X1,k9_relat_1(X2,k1_tarski(X0))) ),
inference(demodulation,[status(thm)],[c_97,c_54]) ).
cnf(c_1688,plain,
( ~ r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0)))
| ~ r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK1,k1_tarski(sK0)))
| k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0))) = k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))
| r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK2,k1_tarski(sK0))) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1689,plain,
( ~ r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK2,k1_tarski(sK0)))
| k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0))) = k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))
| r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_1690,plain,
( k4_xboole_0(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0))) = k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))
| r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0)))
| r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK1,k1_tarski(sK0))) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_1718,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK1)
| ~ v1_relat_1(sK1)
| r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK1,k1_tarski(sK0))) ),
inference(instantiation,[status(thm)],[c_406]) ).
cnf(c_1740,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),k4_xboole_0(sK1,sK2))
| ~ v1_relat_1(k4_xboole_0(sK1,sK2))
| r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))) ),
inference(instantiation,[status(thm)],[c_406]) ).
cnf(c_1748,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK2)
| ~ v1_relat_1(sK2)
| r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK2,k1_tarski(sK0))) ),
inference(instantiation,[status(thm)],[c_406]) ).
cnf(c_1828,plain,
( ~ v1_relat_1(sK1)
| ~ v1_relat_1(sK2)
| v1_relat_1(k4_xboole_0(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_1854,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),X0)
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),k4_xboole_0(X0,sK2))
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK2) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_1858,plain,
( ~ r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK2,k1_tarski(sK0)))
| ~ v1_relat_1(sK2)
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK2) ),
inference(instantiation,[status(thm)],[c_405]) ).
cnf(c_1918,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),k4_xboole_0(sK1,X0))
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK1) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_1925,plain,
( ~ r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(sK1,k1_tarski(sK0)))
| ~ v1_relat_1(sK1)
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK1) ),
inference(instantiation,[status(thm)],[c_405]) ).
cnf(c_2050,plain,
( ~ r2_hidden(sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0)))
| ~ v1_relat_1(k4_xboole_0(sK1,sK2))
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),k4_xboole_0(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_405]) ).
cnf(c_2478,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK1)
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),k4_xboole_0(sK1,sK2))
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK2) ),
inference(instantiation,[status(thm)],[c_1854]) ).
cnf(c_3107,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),k4_xboole_0(sK1,sK2))
| r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK1) ),
inference(instantiation,[status(thm)],[c_1918]) ).
cnf(c_3113,plain,
( ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),k4_xboole_0(sK1,sK2))
| ~ r2_hidden(k2_tarski(k1_tarski(sK0),k2_tarski(sK0,sK4(k9_relat_1(sK1,k1_tarski(sK0)),k9_relat_1(sK2,k1_tarski(sK0)),k9_relat_1(k4_xboole_0(sK1,sK2),k1_tarski(sK0))))),sK2) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_3534,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3113,c_3107,c_2478,c_2050,c_1925,c_1858,c_1828,c_1748,c_1740,c_1718,c_1688,c_1689,c_1690,c_49,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU419+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Wed Aug 23 18:34:41 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.21/0.46 Running first-order theorem proving
% 0.21/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.05/1.14 % SZS status Started for theBenchmark.p
% 4.05/1.14 % SZS status Theorem for theBenchmark.p
% 4.05/1.14
% 4.05/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.05/1.14
% 4.05/1.14 ------ iProver source info
% 4.05/1.14
% 4.05/1.14 git: date: 2023-05-31 18:12:56 +0000
% 4.05/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.05/1.14 git: non_committed_changes: false
% 4.05/1.14 git: last_make_outside_of_git: false
% 4.05/1.14
% 4.05/1.14 ------ Parsing...
% 4.05/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.05/1.14
% 4.05/1.14 ------ Preprocessing... sup_sim: 2 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
% 4.05/1.14
% 4.05/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.05/1.14
% 4.05/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.05/1.14 ------ Proving...
% 4.05/1.14 ------ Problem Properties
% 4.05/1.14
% 4.05/1.14
% 4.05/1.14 clauses 46
% 4.05/1.14 conjectures 3
% 4.05/1.14 EPR 21
% 4.05/1.14 Horn 39
% 4.05/1.14 unary 20
% 4.05/1.14 binary 13
% 4.05/1.14 lits 86
% 4.05/1.14 lits eq 10
% 4.05/1.14 fd_pure 0
% 4.05/1.14 fd_pseudo 0
% 4.05/1.14 fd_cond 1
% 4.05/1.14 fd_pseudo_cond 5
% 4.05/1.14 AC symbols 0
% 4.05/1.14
% 4.05/1.14 ------ Input Options Time Limit: Unbounded
% 4.05/1.14
% 4.05/1.14
% 4.05/1.14 ------
% 4.05/1.14 Current options:
% 4.05/1.14 ------
% 4.05/1.14
% 4.05/1.14
% 4.05/1.14
% 4.05/1.14
% 4.05/1.14 ------ Proving...
% 4.05/1.14
% 4.05/1.14
% 4.05/1.14 % SZS status Theorem for theBenchmark.p
% 4.05/1.14
% 4.05/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.05/1.14
% 4.05/1.14
%------------------------------------------------------------------------------