%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU419+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:57:26 PM UTC 2026
% Result : Theorem 1.95s 1.40s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 67 ( 12 unt; 0 def)
% Number of atoms : 221 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 260 ( 106 ~; 117 |; 27 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 135 ( 0 sgn 129 !; 6 ?; 36 :)
% 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,[status(cth)],[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] :
( X2 = k4_xboole_0(X0,X1)
<=> ! [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] :
( 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(ennf_transformation,[],[f2]) ).
fof(f49,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| v1_relat_1(k4_xboole_0(X0,X1)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f50,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| v1_relat_1(k4_xboole_0(X0,X1)) ),
inference(flattening,[],[f49]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
<=> r2_hidden(k4_tarski(X1,X0),X2) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f62,plain,
( v1_relat_1(sK1)
& v1_relat_1(sK2)
& 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f45]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) != 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) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k4_xboole_0(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) != 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) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k4_xboole_0(X0,X1) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) != 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) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k4_xboole_0(X0,X1) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( k4_xboole_0(X0,X1) != 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) ) ) )
& ( ( ( 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)
| r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X0) ) )
| X2 = k4_xboole_0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f70]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(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))) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f80,plain,
v1_relat_1(sK1),
inference(cnf_transformation,[],[f62]) ).
fof(f81,plain,
v1_relat_1(sK2),
inference(cnf_transformation,[],[f62]) ).
fof(f82,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,[],[f62]) ).
fof(f85,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f92,plain,
! [X2,X0,X1,X4] :
( k4_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| ~ r2_hidden(X4,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f93,plain,
! [X2,X0,X1,X4] :
( k4_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f94,plain,
! [X2,X0,X1,X4] :
( k4_xboole_0(X0,X1) != X2
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f95,plain,
! [X2,X0,X1] :
( r2_hidden(sK4(X0,X1,X2),X2)
| ~ r2_hidden(sK4(X0,X1,X2),X1)
| k4_xboole_0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f96,plain,
! [X2,X0,X1] :
( r2_hidden(sK4(X0,X1,X2),X2)
| r2_hidden(sK4(X0,X1,X2),X0)
| k4_xboole_0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ r2_hidden(sK4(X0,X1,X2),X2)
| r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X0)
| k4_xboole_0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f98,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f104,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| v1_relat_1(k4_xboole_0(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k4_tarski(X1,X0),X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(k4_tarski(X1,X0),X2)
| r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1))) ),
inference(cnf_transformation,[],[f79]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),X2)
| r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1))) ),
inference(definition_unfolding,[],[f130,f98]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),X2) ),
inference(definition_unfolding,[],[f129,f98]) ).
fof(f135,plain,
! [X0,X1,X4] :
( r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,k4_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f94]) ).
fof(f136,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k4_xboole_0(X0,X1))
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f93]) ).
fof(f137,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k4_xboole_0(X0,X1))
| ~ r2_hidden(X4,X1) ),
inference(equality_resolution,[],[f92]) ).
tcf(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,[],[f82]) ).
tcf(c_50,negated_conjecture,
v1_relat_1(sK2),
inference(cnf_transformation,[],[f81]) ).
tcf(c_51,negated_conjecture,
v1_relat_1(sK1),
inference(cnf_transformation,[],[f80]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f85]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(sK4(X0,X1,X2),X1)
| ( k4_xboole_0(X0,X1) = X2 )
| ~ r2_hidden(sK4(X0,X1,X2),X2)
| ~ r2_hidden(sK4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(sK4(X0,X1,X2),X2)
| r2_hidden(sK4(X0,X1,X2),X0)
| ( k4_xboole_0(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(sK4(X0,X1,X2),X2)
| ( k4_xboole_0(X0,X1) = X2 )
| ~ r2_hidden(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X2)
| r2_hidden(X0,k4_xboole_0(X1,X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X1)
| ~ r2_hidden(X0,k4_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ r2_hidden(X0,X2)
| ~ r2_hidden(X0,k4_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(k4_xboole_0(X1,X0))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,k9_relat_1(X2,k1_tarski(X0)))
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),X2) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k2_tarski(k2_tarski(X2,X0),k1_tarski(X2)),X1)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2))) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k2_tarski(k1_tarski(X2),k2_tarski(X2,X0)),X1)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2))) ),
inference(demodulation,[status(thm)],[c_98,c_54]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,k9_relat_1(X2,k1_tarski(X0)))
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_97,c_54]) ).
tcf(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(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(sK1,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_61]) ).
tcf(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(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))) = 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_63]) ).
tcf(c_1690,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)))
| 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)))
| ( 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(instantiation,[status(thm)],[c_62]) ).
tcf(c_1718,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_406]) ).
tcf(c_1740,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_406]) ).
tcf(c_1748,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_406]) ).
tcf(c_1828,plain,
( v1_relat_1(k4_xboole_0(sK1,sK2))
| ~ v1_relat_1(sK2)
| ~ v1_relat_1(sK1) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_1854,plain,
! [X0: $i] :
( 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)
| 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))))),X0) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1858,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_405]) ).
tcf(c_1918,plain,
! [X0: $i] :
( 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,X0)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1925,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_405]) ).
tcf(c_2050,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_405]) ).
tcf(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))))),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))
| ~ 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_1854]) ).
tcf(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))))),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)) ),
inference(instantiation,[status(thm)],[c_1918]) ).
tcf(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))))),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_66]) ).
tcf(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
% 0.00/0.03 % Problem : SEU419+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.56 % Computer : n016.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Thu Sep 24 14:12:00 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.61 Running first-order theorem proving
% 0.09/0.61 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.62
% 0.09/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.62
% 0.09/0.62 % Detected problem language: tptp
% 0.14/0.63 % Proving...
% 1.95/1.40 % SZS status Started for theBenchmark.p
% 1.95/1.40 % SZS status Theorem for theBenchmark.p
% 1.95/1.40
% 1.95/1.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.95/1.40
% 1.95/1.40 % ------ iProver source info
% 1.95/1.40
% 1.95/1.40 % git: date: 2026-07-19 20:42:38 +0200
% 1.95/1.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.95/1.40 % git: non_committed_changes: false
% 1.95/1.40
% 1.95/1.40 % ------ Parsing...
% 1.95/1.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.95/1.40
% 1.95/1.40 % ------ 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 %
% 1.95/1.40
% 1.95/1.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.95/1.40
% 1.95/1.40 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.95/1.40 % ------ Proving...
% 1.95/1.40 % ------ Problem Properties
% 1.95/1.40
% 1.95/1.40 %
% 1.95/1.40 % clauses 46
% 1.95/1.40 % conjectures 3
% 1.95/1.40 % EPR 21
% 1.95/1.40 % Horn 39
% 1.95/1.40 % unary 20
% 1.95/1.40 % binary 13
% 1.95/1.40 % lits 86
% 1.95/1.40 % lits eq 10
% 1.95/1.40 % fd_pure 0
% 1.95/1.40 % fd_pseudo 0
% 1.95/1.40 % fd_cond 1
% 1.95/1.40 % fd_pseudo_cond 5
% 1.95/1.40 % AC symbols 0
% 1.95/1.40
% 1.95/1.40 % ------ Input Options Time Limit: Unbounded
% 1.95/1.40
% 1.95/1.40
% 1.95/1.40 % ------
% 1.95/1.40 % Current options:
% 1.95/1.40 % ------
% 1.95/1.40
% 1.95/1.40
% 1.95/1.40 %
% 1.95/1.40
% 1.95/1.40 % ------ Proving...
% 1.95/1.40 %
% 1.95/1.40
% 1.95/1.40 % SZS status Theorem for theBenchmark.p
% 1.95/1.40
% 1.95/1.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.95/1.40
% 1.95/1.40
%------------------------------------------------------------------------------