%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU418+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Tue Sep 29 12:48:51 PM UTC 2026
% Result : Theorem 10.65s 2.33s
% Output : Refutation 11.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 146 ( 28 unt; 8 def)
% Number of atoms : 546 ( 53 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 709 ( 309 ~; 316 |; 59 &)
% ( 13 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-4 aty)
% Number of variables : 315 ( 1 sgn 289 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> r1_tarski(k5_relat_1(k3_xboole_0(X0,X1),X2),k3_xboole_0(k5_relat_1(X0,X2),k5_relat_1(X1,X2))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> r1_tarski(k5_relat_1(k3_xboole_0(X0,X1),X2),k3_xboole_0(k5_relat_1(X0,X2),k5_relat_1(X1,X2))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0] :
( v1_relat_1(X0)
<=> ! [X1] :
~ ( r2_hidden(X1,X0)
& ! [X2,X3] : X1 != k4_tarski(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = k3_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ( X2 = k5_relat_1(X0,X1)
<=> ! [X3,X4] :
( r2_hidden(k4_tarski(X3,X4),X2)
<=> ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f18,axiom,
! [X0,X1] :
( ( v1_relat_1(X0)
& v1_relat_1(X1) )
=> v1_relat_1(k5_relat_1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f23,axiom,
! [X0,X1] :
( ( v1_relat_1(X0)
& v1_relat_1(X1) )
=> v1_relat_1(k3_xboole_0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f35,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f46,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f35]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r1_tarski(k5_relat_1(k3_xboole_0(X0,X1),X2),k3_xboole_0(k5_relat_1(X0,X2),k5_relat_1(X1,X2)))
& v1_relat_1(X2) )
& v1_relat_1(X1) )
& v1_relat_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
! [X0] :
( v1_relat_1(X0)
<=> ! [X1] :
( ~ r2_hidden(X1,X0)
| ? [X2,X3] : k4_tarski(X2,X3) = X1 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k5_relat_1(X0,X1)
<=> ! [X3,X4] :
( r2_hidden(k4_tarski(X3,X4),X2)
<=> ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) ) ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f55,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f56,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( v1_relat_1(k3_xboole_0(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f60,plain,
! [X0,X1] :
( v1_relat_1(k3_xboole_0(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f59]) ).
fof(f73,plain,
( ~ r1_tarski(k5_relat_1(k3_xboole_0(sK0,sK1),sK2),k3_xboole_0(k5_relat_1(sK0,sK2),k5_relat_1(sK1,sK2)))
& v1_relat_1(sK2)
& v1_relat_1(sK1)
& v1_relat_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f49]) ).
fof(f74,plain,
! [X0] :
( ( v1_relat_1(X0)
| ? [X1] :
( r2_hidden(X1,X0)
& ! [X2,X3] : k4_tarski(X2,X3) != X1 ) )
& ( ! [X1] :
( ~ r2_hidden(X1,X0)
| ? [X2,X3] : k4_tarski(X2,X3) = X1 )
| ~ v1_relat_1(X0) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0] :
( ( v1_relat_1(X0)
| ? [X1] :
( r2_hidden(X1,X0)
& ! [X2,X3] : k4_tarski(X2,X3) != X1 ) )
& ( ! [X4] :
( ~ r2_hidden(X4,X0)
| ? [X5,X6] : k4_tarski(X5,X6) = X4 )
| ~ v1_relat_1(X0) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ( v1_relat_1(X0)
| ( r2_hidden(sK3(X0),X0)
& ! [X2,X3] : k4_tarski(X2,X3) != sK3(X0) ) )
& ( ! [X4] :
( ~ r2_hidden(X4,X0)
| k4_tarski(sK4(X4),sK5(X4)) = X4 )
| ~ v1_relat_1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X1,sK3(X0)),skolemize(X5,sK4(X4)),skolemize(X6,sK5(X4))],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f78,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK6(X0,X1),X1)
& r2_hidden(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ? [X3] :
( ( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ? [X3] :
( ( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ? [X3] :
( ( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| ~ r2_hidden(X4,X1) )
& ( ( r2_hidden(X4,X0)
& r2_hidden(X4,X1) )
| ~ r2_hidden(X4,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ( ( ~ r2_hidden(sK7(X0,X1,X2),X0)
| ~ r2_hidden(sK7(X0,X1,X2),X1)
| ~ r2_hidden(sK7(X0,X1,X2),X2) )
& ( ( r2_hidden(sK7(X0,X1,X2),X0)
& r2_hidden(sK7(X0,X1,X2),X1) )
| r2_hidden(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| ~ r2_hidden(X4,X1) )
& ( ( r2_hidden(X4,X0)
& r2_hidden(X4,X1) )
| ~ r2_hidden(X4,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f82]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) )
| r2_hidden(k4_tarski(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( r2_hidden(k4_tarski(X3,X4),X2)
| ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) ) )
& ( ? [X5] :
( r2_hidden(k4_tarski(X3,X5),X0)
& r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(nnf_transformation,[],[f54]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ r2_hidden(k4_tarski(X3,X5),X0)
| ~ r2_hidden(k4_tarski(X5,X4),X1) )
| ~ r2_hidden(k4_tarski(X3,X4),X2) )
& ( ? [X6] :
( r2_hidden(k4_tarski(X3,X6),X0)
& r2_hidden(k4_tarski(X6,X4),X1) )
| r2_hidden(k4_tarski(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( r2_hidden(k4_tarski(X7,X8),X2)
| ! [X9] :
( ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1) ) )
& ( ? [X10] :
( r2_hidden(k4_tarski(X7,X10),X0)
& r2_hidden(k4_tarski(X10,X8),X1) )
| ~ r2_hidden(k4_tarski(X7,X8),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_relat_1(X0,X1)
| ( ( ! [X5] :
( ~ r2_hidden(k4_tarski(sK8(X0,X1,X2),X5),X0)
| ~ r2_hidden(k4_tarski(X5,sK9(X0,X1,X2)),X1) )
| ~ r2_hidden(k4_tarski(sK8(X0,X1,X2),sK9(X0,X1,X2)),X2) )
& ( ( r2_hidden(k4_tarski(sK8(X0,X1,X2),sK10(X0,X1,X2)),X0)
& r2_hidden(k4_tarski(sK10(X0,X1,X2),sK9(X0,X1,X2)),X1) )
| r2_hidden(k4_tarski(sK8(X0,X1,X2),sK9(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( r2_hidden(k4_tarski(X7,X8),X2)
| ! [X9] :
( ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1) ) )
& ( ( r2_hidden(k4_tarski(X7,sK11(X0,X1,X7,X8)),X0)
& r2_hidden(k4_tarski(sK11(X0,X1,X7,X8),X8),X1) )
| ~ r2_hidden(k4_tarski(X7,X8),X2) ) )
| k5_relat_1(X0,X1) != X2 ) )
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) )
| ~ v1_relat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X3,sK8(X0,X1,X2)),skolemize(X4,sK9(X0,X1,X2)),skolemize(X6,sK10(X0,X1,X2)),skolemize(X10,sK11(X0,X1,X7,X8))],[f85]) ).
fof(f94,plain,
v1_relat_1(sK0),
inference(cnf_transformation,[],[f73]) ).
fof(f95,plain,
v1_relat_1(sK1),
inference(cnf_transformation,[],[f73]) ).
fof(f96,plain,
v1_relat_1(sK2),
inference(cnf_transformation,[],[f73]) ).
fof(f97,plain,
~ r1_tarski(k5_relat_1(k3_xboole_0(sK0,sK1),sK2),k3_xboole_0(k5_relat_1(sK0,sK2),k5_relat_1(sK1,sK2))),
inference(cnf_transformation,[],[f73]) ).
fof(f100,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f102,plain,
! [X0,X4] :
( ~ r2_hidden(X4,X0)
| k4_tarski(sK4(X4),sK5(X4)) = X4
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f105,plain,
! [X3,X0,X1] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f106,plain,
! [X0,X1] :
( r2_hidden(sK6(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f107,plain,
! [X0,X1] :
( ~ r2_hidden(sK6(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f108,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X0)
| ~ r2_hidden(X4,X2)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| ~ r2_hidden(X4,X1)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f114,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f115,plain,
! [X2,X0,X1,X8,X7] :
( r2_hidden(k4_tarski(sK11(X0,X1,X7,X8),X8),X1)
| ~ r2_hidden(k4_tarski(X7,X8),X2)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f116,plain,
! [X2,X0,X1,X8,X7] :
( r2_hidden(k4_tarski(X7,sK11(X0,X1,X7,X8)),X0)
| ~ r2_hidden(k4_tarski(X7,X8),X2)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f117,plain,
! [X2,X0,X1,X8,X9,X7] :
( r2_hidden(k4_tarski(X7,X8),X2)
| ~ r2_hidden(k4_tarski(X7,X9),X0)
| ~ r2_hidden(k4_tarski(X9,X8),X1)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f121,plain,
! [X0,X1] :
( v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f127,plain,
! [X0,X1] :
( v1_relat_1(k3_xboole_0(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f145,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f157,plain,
! [X0,X4] :
( ~ r2_hidden(X4,X0)
| k2_tarski(k2_tarski(sK4(X4),sK5(X4)),k1_tarski(sK4(X4))) = X4
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f102,f114]) ).
fof(f161,plain,
! [X2,X0,X1,X8,X9,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f117,f114,f114,f114]) ).
fof(f162,plain,
! [X2,X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,sK11(X0,X1,X7,X8)),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),X2)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f116,f114,f114]) ).
fof(f163,plain,
! [X2,X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(sK11(X0,X1,X7,X8),X8),k1_tarski(sK11(X0,X1,X7,X8))),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),X2)
| k5_relat_1(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(definition_unfolding,[],[f115,f114,f114]) ).
fof(f164,plain,
! [X0,X1,X4] :
( r2_hidden(X4,k3_xboole_0(X0,X1))
| ~ r2_hidden(X4,X0)
| ~ r2_hidden(X4,X1) ),
inference(equality_resolution,[],[f110]) ).
fof(f165,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k3_xboole_0(X0,X1))
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f109]) ).
fof(f166,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k3_xboole_0(X0,X1))
| r2_hidden(X4,X1) ),
inference(equality_resolution,[],[f108]) ).
fof(f167,plain,
! [X0,X1,X8,X9,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| ~ v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f161]) ).
fof(f168,plain,
! [X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,sK11(X0,X1,X7,X8)),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f162]) ).
fof(f169,plain,
! [X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(sK11(X0,X1,X7,X8),X8),k1_tarski(sK11(X0,X1,X7,X8))),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(equality_resolution,[],[f163]) ).
fof(f170,definition,
sF18 = k3_xboole_0(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f171,plain,
k3_xboole_0(sK0,sK1) = sF18,
inference(reorient_equations,[],[f170]) ).
fof(f172,definition,
sF19 = k5_relat_1(sF18,sK2),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f173,plain,
k5_relat_1(sF18,sK2) = sF19,
inference(reorient_equations,[],[f172]) ).
fof(f174,definition,
sF20 = k5_relat_1(sK0,sK2),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f175,plain,
k5_relat_1(sK0,sK2) = sF20,
inference(reorient_equations,[],[f174]) ).
fof(f176,definition,
sF21 = k5_relat_1(sK1,sK2),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f177,plain,
k5_relat_1(sK1,sK2) = sF21,
inference(reorient_equations,[],[f176]) ).
fof(f178,definition,
sF22 = k3_xboole_0(sF20,sF21),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f179,plain,
k3_xboole_0(sF20,sF21) = sF22,
inference(reorient_equations,[],[f178]) ).
fof(f180,plain,
~ r1_tarski(sF19,sF22),
inference(definition_folding,[],[f97,f179,f177,f175,f173,f171]) ).
fof(f181,plain,
! [X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(sK11(X0,X1,X7,X8),X8),k1_tarski(sK11(X0,X1,X7,X8))),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f169,f121]) ).
fof(f182,plain,
! [X0,X1,X8,X7] :
( r2_hidden(k2_tarski(k2_tarski(X7,sK11(X0,X1,X7,X8)),k1_tarski(X7)),X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f168,f121]) ).
fof(f183,plain,
! [X0,X1,X8,X9,X7] :
( ~ r2_hidden(k2_tarski(k2_tarski(X9,X8),k1_tarski(X9)),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X9),k1_tarski(X7)),X0)
| r2_hidden(k2_tarski(k2_tarski(X7,X8),k1_tarski(X7)),k5_relat_1(X0,X1))
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0) ),
inference(forward_subsumption_resolution,[],[f167,f121]) ).
fof(f192,plain,
! [X0] :
( ~ r2_hidden(X0,sF18)
| r2_hidden(X0,sK0) ),
inference(superposition,[],[f165,f171]) ).
fof(f198,plain,
! [X0] :
( ~ r2_hidden(X0,sF18)
| r2_hidden(X0,sK1) ),
inference(superposition,[],[f166,f171]) ).
fof(f204,plain,
! [X2,X0,X1] :
( ~ r2_hidden(sK6(X0,k3_xboole_0(X1,X2)),X2)
| ~ r2_hidden(sK6(X0,k3_xboole_0(X1,X2)),X1)
| r1_tarski(X0,k3_xboole_0(X1,X2)) ),
inference(resolution,[],[f164,f107]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK11(X1,X2,X0,X3))),X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X3),k1_tarski(X0)),k5_relat_1(X1,X2))
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1) ),
inference(superposition,[],[f182,f100]) ).
fof(f246,definition,
( spl23_6
<=> v1_relat_1(sF18) ),
introduced(definition,[new_symbols(definition,[spl23_6])],[avatar_definition]) ).
fof(f247,plain,
( v1_relat_1(sF18)
| ~ spl23_6 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( ~ v1_relat_1(sF18)
| spl23_6 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f259,plain,
( v1_relat_1(sF18)
| ~ v1_relat_1(sK0)
| ~ v1_relat_1(sK1) ),
inference(superposition,[],[f127,f171]) ).
fof(f260,plain,
( ~ v1_relat_1(sK0)
| ~ v1_relat_1(sK1)
| spl23_6 ),
inference(forward_subsumption_resolution,[],[f259,f248]) ).
fof(f261,plain,
( ~ v1_relat_1(sK1)
| spl23_6 ),
inference(forward_subsumption_resolution,[],[f260,f94]) ).
fof(f262,plain,
( $false
| spl23_6 ),
inference(forward_subsumption_resolution,[],[f261,f95]) ).
fof(f263,plain,
spl23_6,
inference(avatar_contradiction_clause,[],[f262]) ).
fof(f264,plain,
( v1_relat_1(sF19)
| ~ v1_relat_1(sF18)
| ~ v1_relat_1(sK2) ),
inference(superposition,[],[f121,f173]) ).
fof(f269,plain,
( v1_relat_1(sF19)
| ~ v1_relat_1(sK2)
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f264,f247]) ).
fof(f272,plain,
( v1_relat_1(sF19)
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f269,f96]) ).
fof(f279,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(X2,X3))
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X4,sK11(X2,X3,X0,X1)),k1_tarski(X4)),X5)
| r2_hidden(k2_tarski(k2_tarski(X4,X1),k1_tarski(X4)),k5_relat_1(X5,X3))
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X5) ),
inference(resolution,[],[f181,f183]) ).
fof(f292,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2_hidden(k2_tarski(k2_tarski(X4,sK11(X2,X3,X0,X1)),k1_tarski(X4)),X5)
| ~ v1_relat_1(X3)
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(X2,X3))
| r2_hidden(k2_tarski(k2_tarski(X4,X1),k1_tarski(X4)),k5_relat_1(X5,X3))
| ~ v1_relat_1(X5) ),
inference(duplicate_literal_removal,[],[f279]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sF18,X2))
| ~ v1_relat_1(X2)
| ~ v1_relat_1(sF18)
| r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK11(sF18,X2,X0,X1))),sK1) ),
inference(resolution,[],[f223,f198]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sF18,X2))
| ~ v1_relat_1(X2)
| ~ v1_relat_1(sF18)
| r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK11(sF18,X2,X0,X1))),sK0) ),
inference(resolution,[],[f223,f192]) ).
fof(f319,plain,
( ! [X2,X0,X1] :
( r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK11(sF18,X2,X0,X1))),sK0)
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sF18,X2)) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f312,f247]) ).
fof(f320,plain,
( ! [X2,X0,X1] :
( r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK11(sF18,X2,X0,X1))),sK1)
| ~ v1_relat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sF18,X2)) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f311,f247]) ).
fof(f386,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK11(X1,X2,X3,X4))),X5)
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X3,X4),k1_tarski(X3)),k5_relat_1(X1,X2))
| r2_hidden(k2_tarski(k2_tarski(X0,X4),k1_tarski(X0)),k5_relat_1(X5,X2))
| ~ v1_relat_1(X5) ),
inference(superposition,[],[f292,f100]) ).
fof(f568,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ v1_relat_1(X0)
| sK6(X0,X1) = k2_tarski(k2_tarski(sK4(sK6(X0,X1)),sK5(sK6(X0,X1))),k1_tarski(sK4(sK6(X0,X1)))) ),
inference(resolution,[],[f157,f106]) ).
fof(f596,plain,
( ~ v1_relat_1(sF19)
| sK6(sF19,sF22) = k2_tarski(k2_tarski(sK4(sK6(sF19,sF22)),sK5(sK6(sF19,sF22))),k1_tarski(sK4(sK6(sF19,sF22)))) ),
inference(resolution,[],[f568,f180]) ).
fof(f597,plain,
( sK6(sF19,sF22) = k2_tarski(k2_tarski(sK4(sK6(sF19,sF22)),sK5(sK6(sF19,sF22))),k1_tarski(sK4(sK6(sF19,sF22))))
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f596,f272]) ).
fof(f713,plain,
! [X2,X0,X1] :
( r2_hidden(sK6(X0,X1),X2)
| ~ r1_tarski(X0,X2)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f105,f106]) ).
fof(f799,plain,
! [X0] :
( ~ r2_hidden(sK6(X0,sF22),sF21)
| ~ r2_hidden(sK6(X0,sF22),sF20)
| r1_tarski(X0,sF22) ),
inference(superposition,[],[f204,f179]) ).
fof(f1119,plain,
( ! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(sF18)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK0,X0))
| ~ v1_relat_1(sK0) )
| ~ spl23_6 ),
inference(resolution,[],[f319,f386]) ).
fof(f1122,plain,
( ! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| ~ v1_relat_1(sF18)
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK0,X0))
| ~ v1_relat_1(sK0) )
| ~ spl23_6 ),
inference(duplicate_literal_removal,[],[f1119]) ).
fof(f1124,plain,
( ! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK0,X0))
| ~ v1_relat_1(sK0) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f1122,f247]) ).
fof(f1127,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| ~ v1_relat_1(X0)
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK0,X0)) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f1124,f94]) ).
fof(f1167,definition,
( spl23_30
<=> r2_hidden(sK6(sF19,sF22),sF21) ),
introduced(definition,[new_symbols(definition,[spl23_30])],[avatar_definition]) ).
fof(f1168,plain,
( r2_hidden(sK6(sF19,sF22),sF21)
| ~ spl23_30 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f1169,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF21)
| spl23_30 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f1171,definition,
( spl23_31
<=> r2_hidden(sK6(sF19,sF22),sF20) ),
introduced(definition,[new_symbols(definition,[spl23_31])],[avatar_definition]) ).
fof(f1173,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF20)
| spl23_31 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f1233,plain,
( ! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| ~ v1_relat_1(X0)
| ~ v1_relat_1(sF18)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK1,X0))
| ~ v1_relat_1(sK1) )
| ~ spl23_6 ),
inference(resolution,[],[f320,f386]) ).
fof(f1238,plain,
( ! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| ~ v1_relat_1(sF18)
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK1,X0))
| ~ v1_relat_1(sK1) )
| ~ spl23_6 ),
inference(duplicate_literal_removal,[],[f1233]) ).
fof(f1240,plain,
( ! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK1,X0))
| ~ v1_relat_1(sK1) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f1238,f247]) ).
fof(f1243,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sF18,X0))
| ~ v1_relat_1(X0)
| r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),k5_relat_1(sK1,X0)) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f1240,f95]) ).
fof(f1863,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF19)
| ~ v1_relat_1(sK2)
| r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sK1,sK2)) )
| ~ spl23_6 ),
inference(superposition,[],[f1243,f173]) ).
fof(f1870,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF19)
| r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sK1,sK2)) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f1863,f96]) ).
fof(f1873,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF19)
| r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF21) )
| ~ spl23_6 ),
inference(forward_demodulation,[],[f1870,f177]) ).
fof(f1898,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF19)
| r2_hidden(sK6(sF19,sF22),sF21)
| ~ spl23_6 ),
inference(superposition,[],[f1873,f597]) ).
fof(f1911,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF19)
| ~ spl23_6
| spl23_30 ),
inference(forward_subsumption_resolution,[],[f1898,f1169]) ).
fof(f1996,plain,
( ~ r1_tarski(sF19,sF19)
| r1_tarski(sF19,sF22)
| ~ spl23_6
| spl23_30 ),
inference(resolution,[],[f1911,f713]) ).
fof(f1997,plain,
( r1_tarski(sF19,sF22)
| ~ spl23_6
| spl23_30 ),
inference(forward_subsumption_resolution,[],[f1996,f145]) ).
fof(f2000,plain,
( $false
| ~ spl23_6
| spl23_30 ),
inference(forward_subsumption_resolution,[],[f1997,f180]) ).
fof(f2001,plain,
( ~ spl23_6
| spl23_30 ),
inference(avatar_contradiction_clause,[],[f2000]) ).
fof(f2002,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF20)
| r1_tarski(sF19,sF22)
| ~ spl23_30 ),
inference(resolution,[],[f1168,f799]) ).
fof(f2011,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF20)
| ~ spl23_30 ),
inference(forward_subsumption_resolution,[],[f2002,f180]) ).
fof(f2012,plain,
( ~ spl23_31
| ~ spl23_30 ),
inference(avatar_split_clause,[],[f2011,f1167,f1171]) ).
fof(f2478,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF19)
| ~ v1_relat_1(sK2)
| r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sK0,sK2)) )
| ~ spl23_6 ),
inference(superposition,[],[f1127,f173]) ).
fof(f2485,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF19)
| r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k5_relat_1(sK0,sK2)) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f2478,f96]) ).
fof(f2487,plain,
( ! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF19)
| r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),sF20) )
| ~ spl23_6 ),
inference(forward_demodulation,[],[f2485,f175]) ).
fof(f2500,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF19)
| r2_hidden(sK6(sF19,sF22),sF20)
| ~ spl23_6 ),
inference(superposition,[],[f2487,f597]) ).
fof(f2504,plain,
( ~ r2_hidden(sK6(sF19,sF22),sF19)
| ~ spl23_6
| spl23_31 ),
inference(forward_subsumption_resolution,[],[f2500,f1173]) ).
fof(f2535,plain,
( ~ r1_tarski(sF19,sF19)
| r1_tarski(sF19,sF22)
| ~ spl23_6
| spl23_31 ),
inference(resolution,[],[f2504,f713]) ).
fof(f2536,plain,
( r1_tarski(sF19,sF22)
| ~ spl23_6
| spl23_31 ),
inference(forward_subsumption_resolution,[],[f2535,f145]) ).
fof(f2539,plain,
( $false
| ~ spl23_6
| spl23_31 ),
inference(forward_subsumption_resolution,[],[f2536,f180]) ).
fof(f2540,plain,
( ~ spl23_6
| spl23_31 ),
inference(avatar_contradiction_clause,[],[f2539]) ).
cnf(s6,plain,
spl23_6,
inference(sat_conversion,[],[f263]) ).
cnf(s62,plain,
( ~ spl23_6
| spl23_30 ),
inference(sat_conversion,[],[f2001]) ).
cnf(s64,plain,
( ~ spl23_30
| ~ spl23_31 ),
inference(sat_conversion,[],[f2012]) ).
cnf(s82,plain,
( ~ spl23_6
| spl23_31 ),
inference(sat_conversion,[],[f2540]) ).
cnf(s84,plain,
spl23_31,
inference(rat,[],[s82,s6]) ).
cnf(s85,plain,
spl23_30,
inference(rat,[],[s62,s6]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s64,s84,s85]) ).
fof(f2541,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU418+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 05:18:12 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.65/2.33 % (1236645)Detected formulas, will run a generic FOF schedule.
% 10.65/2.33 % (1236653)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1553660541:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.65/2.33 % (1236653)Refutation not found, incomplete strategy
% 10.65/2.33 % (1236653)------------------------------
% 10.65/2.33 % (1236653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236653)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236653)Termination reason: Refutation not found, incomplete strategy
% 10.65/2.33 % (1236653)Time elapsed: 0.001 s
% 10.65/2.33 % (1236653)Peak memory usage: 88 MB
% 10.65/2.33 % (1236653)Instructions burned: 1 (million)
% 10.65/2.33 % (1236656)dis-21_1_sil=8000:lcm=predicate:random_seed=2726988897:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.65/2.33 % (1236655)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1531957180:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.65/2.33 % (1236650)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3488355681:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.65/2.33 % (1236654)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3723929685:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.65/2.33 % (1236651)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2881811820:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.65/2.33 % (1236652)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1960306049:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.65/2.33 % (1236654)Instruction limit reached!
% 10.65/2.33 % (1236654)------------------------------
% 10.65/2.33 % (1236654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236654)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236654)Termination reason: Instruction limit
% 10.65/2.33 % (1236654)Termination phase: Saturation
% 10.65/2.33 % (1236654)Time elapsed: 0.071 s
% 10.65/2.33 % (1236654)Peak memory usage: 88 MB
% 10.65/2.33 % (1236654)Instructions burned: 120 (million)
% 10.65/2.33 % (1236656)Instruction limit reached!
% 10.65/2.33 % (1236656)------------------------------
% 10.65/2.33 % (1236656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236656)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236656)Termination reason: Instruction limit
% 10.65/2.33 % (1236656)Termination phase: Saturation
% 10.65/2.33 % (1236656)Time elapsed: 0.079 s
% 10.65/2.33 % (1236656)Peak memory usage: 90 MB
% 10.65/2.33 % (1236656)Instructions burned: 129 (million)
% 10.65/2.33 % (1236655)Instruction limit reached!
% 10.65/2.33 % (1236655)------------------------------
% 10.65/2.33 % (1236655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236655)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236655)Termination reason: Instruction limit
% 10.65/2.33 % (1236655)Termination phase: Saturation
% 10.65/2.33 % (1236655)Time elapsed: 0.093 s
% 10.65/2.33 % (1236655)Peak memory usage: 89 MB
% 10.65/2.33 % (1236655)Instructions burned: 139 (million)
% 10.65/2.33 % (1236653)------------------------------
% 10.65/2.33 % (1236653)------------------------------
% 10.65/2.33 % (1236665)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3192487833:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.65/2.33 % (1236664)lrs+10_1_sil=8000:sp=occurrence:random_seed=915456061:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.65/2.33 % (1236667)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3138200228:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.65/2.33 % (1236666)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2979834344:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.65/2.33 % (1236665)Instruction limit reached!
% 10.65/2.33 % (1236665)------------------------------
% 10.65/2.33 % (1236665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236665)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236665)Termination reason: Instruction limit
% 10.65/2.33 % (1236665)Termination phase: Saturation
% 10.65/2.33 % (1236665)Time elapsed: 0.077 s
% 10.65/2.33 % (1236665)Peak memory usage: 91 MB
% 10.65/2.33 % (1236665)Instructions burned: 159 (million)
% 10.65/2.33 % (1236667)Instruction limit reached!
% 10.65/2.33 % (1236667)------------------------------
% 10.65/2.33 % (1236667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236667)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236667)Termination reason: Instruction limit
% 10.65/2.33 % (1236667)Termination phase: Saturation
% 10.65/2.33 % (1236667)Time elapsed: 0.067 s
% 10.65/2.33 % (1236667)Peak memory usage: 95 MB
% 10.65/2.33 % (1236667)Instructions burned: 249 (million)
% 10.65/2.33 % (1236664)Instruction limit reached!
% 10.65/2.33 % (1236664)------------------------------
% 10.65/2.33 % (1236664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236664)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236664)Termination reason: Instruction limit
% 10.65/2.33 % (1236664)Termination phase: Saturation
% 10.65/2.33 % (1236664)Time elapsed: 0.171 s
% 10.65/2.33 % (1236664)Peak memory usage: 91 MB
% 10.65/2.33 % (1236664)Instructions burned: 287 (million)
% 10.65/2.33 % (1236673)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1842094861:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 10.65/2.33 % (1236666)Instruction limit reached!
% 10.65/2.33 % (1236666)------------------------------
% 10.65/2.33 % (1236666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236666)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236666)Termination reason: Instruction limit
% 10.65/2.33 % (1236666)Termination phase: Saturation
% 10.65/2.33 % (1236666)Time elapsed: 0.212 s
% 10.65/2.33 % (1236666)Peak memory usage: 91 MB
% 10.65/2.33 % (1236666)Instructions burned: 325 (million)
% 10.65/2.33 % (1236672)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2297226511:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.65/2.33 % (1236672)Refutation not found, incomplete strategy
% 10.65/2.33 % (1236672)------------------------------
% 10.65/2.33 % (1236672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236672)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236672)Termination reason: Refutation not found, incomplete strategy
% 10.65/2.33 % (1236672)Time elapsed: 0.003 s
% 10.65/2.33 % (1236672)Peak memory usage: 88 MB
% 10.65/2.33 % (1236672)Instructions burned: 3 (million)
% 10.65/2.33 % (1236674)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=404258732:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.65/2.33 % (1236677)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3072865077:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.65/2.33 % (1236674)Instruction limit reached!
% 10.65/2.33 % (1236674)------------------------------
% 10.65/2.33 % (1236674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236674)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236674)Termination reason: Instruction limit
% 10.65/2.33 % (1236674)Termination phase: Saturation
% 10.65/2.33 % (1236674)Time elapsed: 0.073 s
% 10.65/2.33 % (1236674)Peak memory usage: 90 MB
% 10.65/2.33 % (1236674)Instructions burned: 114 (million)
% 10.65/2.33 % (1236677)Instruction limit reached!
% 10.65/2.33 % (1236677)------------------------------
% 10.65/2.33 % (1236677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236677)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236677)Termination reason: Instruction limit
% 10.65/2.33 % (1236677)Termination phase: Saturation
% 10.65/2.33 % (1236677)Time elapsed: 0.065 s
% 10.65/2.33 % (1236677)Peak memory usage: 89 MB
% 10.65/2.33 % (1236677)Instructions burned: 128 (million)
% 10.65/2.33 % (1236672)------------------------------
% 10.65/2.33 % (1236672)------------------------------
% 10.65/2.33 % (1236681)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3550172780:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 10.65/2.33 % (1236683)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3880709718:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 10.65/2.33 % (1236682)lrs+10_1_sil=8000:sp=occurrence:random_seed=1170948604:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 10.65/2.33 % (1236683)Refutation not found, incomplete strategy
% 10.65/2.33 % (1236683)------------------------------
% 10.65/2.33 % (1236683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236683)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236683)Termination reason: Refutation not found, incomplete strategy
% 10.65/2.33 % (1236683)Time elapsed: 0.002 s
% 10.65/2.33 % (1236683)Peak memory usage: 88 MB
% 10.65/2.33 % (1236683)Instructions burned: 3 (million)
% 10.65/2.33 % (1236681)Instruction limit reached!
% 10.65/2.33 % (1236681)------------------------------
% 10.65/2.33 % (1236681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236681)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236681)Termination reason: Instruction limit
% 10.65/2.33 % (1236681)Termination phase: Saturation
% 10.65/2.33 % (1236681)Time elapsed: 0.065 s
% 10.65/2.33 % (1236681)Peak memory usage: 89 MB
% 10.65/2.33 % (1236681)Instructions burned: 116 (million)
% 10.65/2.33 % (1236683)------------------------------
% 10.65/2.33 % (1236683)------------------------------
% 10.65/2.33 % (1236687)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1828547740:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 10.65/2.33 % (1236650)First to succeed.
% 10.65/2.33 % (1236650)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1236645"
% 10.65/2.33 % (1236688)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3624539919:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 10.65/2.33 % (1236688)Instruction limit reached!
% 10.65/2.33 % (1236688)------------------------------
% 10.65/2.33 % (1236688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236688)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236688)Termination reason: Instruction limit
% 10.65/2.33 % (1236688)Termination phase: Saturation
% 10.65/2.33 % (1236688)Time elapsed: 0.038 s
% 10.65/2.33 % (1236688)Peak memory usage: 93 MB
% 10.65/2.33 % (1236688)Instructions burned: 135 (million)
% 10.65/2.33 % (1236691)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3358221440:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 10.65/2.33 % (1236691)Refutation not found, incomplete strategy
% 10.65/2.33 % (1236691)------------------------------
% 10.65/2.33 % (1236691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.33 % (1236691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.33 % (1236691)CaDiCaL version: 2.1.3
% 10.65/2.33 % (1236691)Termination reason: Refutation not found, incomplete strategy
% 10.65/2.33 % (1236691)Time elapsed: 0.001 s
% 10.65/2.33 % (1236691)Peak memory usage: 88 MB
% 10.65/2.33 % (1236691)Instructions burned: 3 (million)
% 10.65/2.33 % (1236651)Also succeeded, but the first one will report.
% 10.65/2.33 % (1236650)Refutation found. Thanks to Tanya!
% 10.65/2.33 % SZS status Theorem for theBenchmark
% 10.65/2.33 % SZS output start Proof for theBenchmark
% See solution above
% 11.20/2.52 % (1236650)------------------------------
% 11.20/2.52 % (1236650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.20/2.52 % (1236650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.20/2.52 % (1236650)CaDiCaL version: 2.1.3
% 11.20/2.52 % (1236650)Termination reason: Refutation
% 11.20/2.52 % (1236650)Time elapsed: 1.057 s
% 11.20/2.52 % (1236650)Peak memory usage: 134 MB
% 11.20/2.52 % (1236650)Instructions burned: 1597 (million)
% 11.20/2.52 % (1236650)------------------------------
% 11.20/2.52 % (1236650)------------------------------
% 11.20/2.52 % (1236645)Success in time 1.495 s
% 11.20/2.52 % Vampire exiting
%------------------------------------------------------------------------------