%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM525+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:15:35 PM UTC 2026
% Result : Theorem 2.28s 1.18s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 109 ( 32 unt; 8 def)
% Number of atoms : 299 ( 69 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 333 ( 143 ~; 141 |; 35 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f40,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(f44,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(f45,axiom,
( aNaturalNumber0(xq)
& xn = sdtasdt0(xp,xq)
& xq = sdtsldt0(xn,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(f46,conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
& doDivides0(xp,xn) ),
inference(rectify,[],[f44]) ).
fof(f49,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(flattening,[],[f47]) ).
fof(f66,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f67,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f71,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f70]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f85,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f84]) ).
fof(f87,plain,
( aNaturalNumber0(sK2)
& sdtasdt0(xn,xn) = sdtasdt0(xp,sK2)
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(sK3)
& xn = sdtasdt0(xp,sK3)
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f48]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f85]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f101,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f103,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f111,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f116,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f87]) ).
fof(f117,plain,
xn = sdtasdt0(xp,sK3),
inference(cnf_transformation,[],[f87]) ).
fof(f118,plain,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f87]) ).
fof(f122,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[],[f45]) ).
fof(f125,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(cnf_transformation,[],[f49]) ).
fof(f139,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f140,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f141,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f160,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f165,definition,
~ sP9(sz00),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
fof(f166,plain,
sP9(xp),
inference(inequality_splitting,[],[f98,f165]) ).
fof(f173,definition,
~ sP13(sdtasdt0(xp,sdtasdt0(xm,xm))),
introduced(definition,[new_symbols(definition,[sP13])],[inequality_splitting_name_introduction]) ).
fof(f174,plain,
sP13(sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq)))),
inference(inequality_splitting,[],[f125,f173]) ).
fof(f188,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f160]) ).
fof(f226,plain,
( xn = sdtasdt0(sK3,xp)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f140,f117]) ).
fof(f231,plain,
( sdtsldt0(xn,xp) = sK3
| ~ aNaturalNumber0(sK3)
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f188,f117]) ).
fof(f232,plain,
( sdtsldt0(xn,xp) = sK3
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f231,f118]) ).
fof(f235,plain,
( xn = sdtasdt0(sK3,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f226,f118]) ).
fof(f244,plain,
( sdtsldt0(xn,xp) = sK3
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f232,f116]) ).
fof(f247,plain,
xn = sdtasdt0(sK3,xp),
inference(forward_subsumption_resolution,[],[f235,f101]) ).
fof(f256,plain,
( sdtsldt0(xn,xp) = sK3
| sz00 = xp
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f244,f101]) ).
fof(f258,definition,
( spl20_4
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
fof(f260,plain,
( sz00 = xp
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f280,plain,
( sdtsldt0(xn,xp) = sK3
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f256,f103]) ).
fof(f282,definition,
( spl20_9
<=> sdtsldt0(xn,xp) = sK3 ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
fof(f284,plain,
( sdtsldt0(xn,xp) = sK3
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,plain,
( spl20_4
| spl20_9 ),
inference(avatar_split_clause,[],[f280,f282,f258]) ).
fof(f290,plain,
( sP9(sz00)
| ~ spl20_4 ),
inference(superposition,[],[f166,f260]) ).
fof(f301,plain,
( $false
| ~ spl20_4 ),
inference(forward_subsumption_resolution,[],[f290,f165]) ).
fof(f302,plain,
~ spl20_4,
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f330,plain,
sP13(sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))))),
inference(superposition,[],[f174,f122]) ).
fof(f425,plain,
( sP13(sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(sK3,sK3))))
| ~ spl20_9 ),
inference(forward_demodulation,[],[f330,f284]) ).
fof(f469,plain,
~ sP13(sdtasdt0(xn,xn)),
inference(superposition,[],[f173,f111]) ).
fof(f539,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sdtasdt0(sK3,sK3),xp)))
| ~ aNaturalNumber0(sdtasdt0(sK3,sK3))
| ~ aNaturalNumber0(xp)
| ~ spl20_9 ),
inference(superposition,[],[f425,f140]) ).
fof(f542,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sdtasdt0(sK3,sK3),xp)))
| ~ aNaturalNumber0(sdtasdt0(sK3,sK3))
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f539,f101]) ).
fof(f544,definition,
( spl20_27
<=> aNaturalNumber0(sdtasdt0(sK3,sK3)) ),
introduced(definition,[new_symbols(definition,[spl20_27])],[avatar_definition]) ).
fof(f546,plain,
( ~ aNaturalNumber0(sdtasdt0(sK3,sK3))
| spl20_27 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f548,definition,
( spl20_28
<=> sP13(sdtasdt0(xp,sdtasdt0(sdtasdt0(sK3,sK3),xp))) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
fof(f550,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sdtasdt0(sK3,sK3),xp)))
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f552,plain,
( ~ spl20_27
| spl20_28
| ~ spl20_9 ),
inference(avatar_split_clause,[],[f542,f282,f548,f544]) ).
fof(f595,plain,
( ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(sK3)
| spl20_27 ),
inference(resolution,[],[f546,f141]) ).
fof(f596,plain,
( ~ aNaturalNumber0(sK3)
| spl20_27 ),
inference(duplicate_literal_removal,[],[f595]) ).
fof(f597,plain,
( $false
| spl20_27 ),
inference(forward_subsumption_resolution,[],[f596,f118]) ).
fof(f598,plain,
spl20_27,
inference(avatar_contradiction_clause,[],[f597]) ).
fof(f713,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sK3,sdtasdt0(sK3,xp))))
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(xp)
| ~ spl20_28 ),
inference(superposition,[],[f550,f139]) ).
fof(f714,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sK3,sdtasdt0(sK3,xp))))
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(xp)
| ~ spl20_28 ),
inference(duplicate_literal_removal,[],[f713]) ).
fof(f715,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sK3,sdtasdt0(sK3,xp))))
| ~ aNaturalNumber0(xp)
| ~ spl20_28 ),
inference(forward_subsumption_resolution,[],[f714,f118]) ).
fof(f716,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sK3,sdtasdt0(sK3,xp))))
| ~ spl20_28 ),
inference(forward_subsumption_resolution,[],[f715,f101]) ).
fof(f717,plain,
( sP13(sdtasdt0(xp,sdtasdt0(sK3,xn)))
| ~ spl20_28 ),
inference(forward_demodulation,[],[f716,f247]) ).
fof(f765,plain,
( sP13(sdtasdt0(sdtasdt0(sK3,xn),xp))
| ~ aNaturalNumber0(sdtasdt0(sK3,xn))
| ~ aNaturalNumber0(xp)
| ~ spl20_28 ),
inference(superposition,[],[f717,f140]) ).
fof(f768,plain,
( sP13(sdtasdt0(sdtasdt0(sK3,xn),xp))
| ~ aNaturalNumber0(sdtasdt0(sK3,xn))
| ~ spl20_28 ),
inference(forward_subsumption_resolution,[],[f765,f101]) ).
fof(f772,definition,
( spl20_40
<=> aNaturalNumber0(sdtasdt0(sK3,xn)) ),
introduced(definition,[new_symbols(definition,[spl20_40])],[avatar_definition]) ).
fof(f774,plain,
( ~ aNaturalNumber0(sdtasdt0(sK3,xn))
| spl20_40 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f776,definition,
( spl20_41
<=> sP13(sdtasdt0(sdtasdt0(sK3,xn),xp)) ),
introduced(definition,[new_symbols(definition,[spl20_41])],[avatar_definition]) ).
fof(f778,plain,
( sP13(sdtasdt0(sdtasdt0(sK3,xn),xp))
| ~ spl20_41 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f780,plain,
( ~ spl20_40
| spl20_41
| ~ spl20_28 ),
inference(avatar_split_clause,[],[f768,f548,f776,f772]) ).
fof(f829,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,sK3))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK3)
| spl20_40 ),
inference(superposition,[],[f774,f140]) ).
fof(f832,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK3)
| spl20_40 ),
inference(forward_subsumption_resolution,[],[f829,f141]) ).
fof(f835,plain,
( ~ aNaturalNumber0(sK3)
| spl20_40 ),
inference(forward_subsumption_resolution,[],[f832,f103]) ).
fof(f840,plain,
( $false
| spl20_40 ),
inference(forward_subsumption_resolution,[],[f835,f118]) ).
fof(f841,plain,
spl20_40,
inference(avatar_contradiction_clause,[],[f840]) ).
fof(f935,plain,
( sP13(sdtasdt0(sdtasdt0(xn,sK3),xp))
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(xn)
| ~ spl20_41 ),
inference(superposition,[],[f778,f140]) ).
fof(f938,plain,
( sP13(sdtasdt0(sdtasdt0(xn,sK3),xp))
| ~ aNaturalNumber0(xn)
| ~ spl20_41 ),
inference(forward_subsumption_resolution,[],[f935,f118]) ).
fof(f941,plain,
( sP13(sdtasdt0(sdtasdt0(xn,sK3),xp))
| ~ spl20_41 ),
inference(forward_subsumption_resolution,[],[f938,f103]) ).
fof(f991,plain,
( sP13(sdtasdt0(xn,sdtasdt0(sK3,xp)))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(xp)
| ~ spl20_41 ),
inference(superposition,[],[f941,f139]) ).
fof(f992,plain,
( sP13(sdtasdt0(xn,sdtasdt0(sK3,xp)))
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(xp)
| ~ spl20_41 ),
inference(forward_subsumption_resolution,[],[f991,f103]) ).
fof(f993,plain,
( sP13(sdtasdt0(xn,sdtasdt0(sK3,xp)))
| ~ aNaturalNumber0(xp)
| ~ spl20_41 ),
inference(forward_subsumption_resolution,[],[f992,f118]) ).
fof(f994,plain,
( sP13(sdtasdt0(xn,sdtasdt0(sK3,xp)))
| ~ spl20_41 ),
inference(forward_subsumption_resolution,[],[f993,f101]) ).
fof(f995,plain,
( sP13(sdtasdt0(xn,xn))
| ~ spl20_41 ),
inference(forward_demodulation,[],[f994,f247]) ).
fof(f996,plain,
( $false
| ~ spl20_41 ),
inference(forward_subsumption_resolution,[],[f995,f469]) ).
fof(f997,plain,
~ spl20_41,
inference(avatar_contradiction_clause,[],[f996]) ).
cnf(s7,plain,
( spl20_4
| spl20_9 ),
inference(sat_conversion,[],[f285]) ).
cnf(s9,plain,
~ spl20_4,
inference(sat_conversion,[],[f302]) ).
cnf(s31,plain,
( ~ spl20_9
| ~ spl20_27
| spl20_28 ),
inference(sat_conversion,[],[f552]) ).
cnf(s34,plain,
spl20_27,
inference(sat_conversion,[],[f598]) ).
cnf(s42,plain,
( ~ spl20_28
| ~ spl20_40
| spl20_41 ),
inference(sat_conversion,[],[f780]) ).
cnf(s45,plain,
spl20_40,
inference(sat_conversion,[],[f841]) ).
cnf(s46,plain,
~ spl20_41,
inference(sat_conversion,[],[f997]) ).
cnf(s47,plain,
~ spl20_28,
inference(rat,[],[s42,s46,s45]) ).
cnf(s48,plain,
~ spl20_9,
inference(rat,[],[s31,s47,s34]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s7,s48,s9]) ).
fof(f998,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM525+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:20:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.28/1.18 % (2734413)Detected formulas, will run a generic FOF schedule.
% 2.28/1.18 % (2734421)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4202216796:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.28/1.18 % (2734421)First to succeed.
% 2.28/1.18 % (2734421)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2734413"
% 2.28/1.18 % (2734423)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1652314036:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.28/1.18 % (2734418)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=3816877840:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.28/1.18 % (2734424)dis-21_1_sil=8000:lcm=predicate:random_seed=2384204295: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)
% 2.28/1.18 % (2734422)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=764462964:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.28/1.18 % (2734420)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=4180779726:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.28/1.18 % (2734419)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=2878942376:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.28/1.18 % (2734422)Also succeeded, but the first one will report.
% 2.28/1.18 % (2734424)Instruction limit reached!
% 2.28/1.18 % (2734424)------------------------------
% 2.28/1.18 % (2734424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.18 % (2734424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.18 % (2734424)CaDiCaL version: 2.1.3
% 2.28/1.18 % (2734424)Termination reason: Instruction limit
% 2.28/1.18 % (2734424)Termination phase: Saturation
% 2.28/1.18 % (2734424)Time elapsed: 0.077 s
% 2.28/1.18 % (2734424)Peak memory usage: 91 MB
% 2.28/1.18 % (2734424)Instructions burned: 130 (million)
% 2.28/1.18 % (2734423)Instruction limit reached!
% 2.28/1.18 % (2734423)------------------------------
% 2.28/1.18 % (2734423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.18 % (2734423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.18 % (2734423)CaDiCaL version: 2.1.3
% 2.28/1.18 % (2734423)Termination reason: Instruction limit
% 2.28/1.18 % (2734423)Termination phase: Saturation
% 2.28/1.18 % (2734423)Time elapsed: 0.089 s
% 2.28/1.18 % (2734423)Peak memory usage: 90 MB
% 2.28/1.18 % (2734423)Instructions burned: 141 (million)
% 2.28/1.18 % (2734421)Refutation found. Thanks to Tanya!
% 2.28/1.18 % SZS status Theorem for theBenchmark
% 2.28/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.38 % (2734421)------------------------------
% 2.80/1.38 % (2734421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.38 % (2734421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.38 % (2734421)CaDiCaL version: 2.1.3
% 2.80/1.38 % (2734421)Termination reason: Refutation
% 2.80/1.38 % (2734421)Time elapsed: 0.018 s
% 2.80/1.38 % (2734421)Peak memory usage: 90 MB
% 2.80/1.38 % (2734421)Instructions burned: 55 (million)
% 2.80/1.38 % (2734421)------------------------------
% 2.80/1.38 % (2734421)------------------------------
% 2.80/1.38 % (2734413)Success in time 0.313 s
% 2.80/1.38 % Vampire exiting
%------------------------------------------------------------------------------