%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET894+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:42:15 PM UTC 2026
% Result : Theorem 6.92s 1.98s
% Output : Refutation 8.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 114 ( 38 unt; 10 def)
% Number of atoms : 318 ( 125 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 338 ( 134 ~; 153 |; 39 &)
% ( 10 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 152 ( 0 sgn 134 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f11,conjecture,
! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f15,plain,
? [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) != singleton(ordered_pair(X0,X1)),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( in(X6,X0)
& in(X7,X1)
& ordered_pair(X6,X7) = X3 )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( in(X11,X0)
& in(X12,X1)
& ordered_pair(X11,X12) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK1(X0,X1,X2) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1)
& sK1(X0,X1,X2) = ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK4(X0,X1,X8),X0)
& in(sK5(X0,X1,X8),X1)
& ordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK1(X0,X1,X2)),skolemize(X6,sK2(X0,X1,X2)),skolemize(X7,sK3(X0,X1,X2)),skolemize(X11,sK4(X0,X1,X8)),skolemize(X12,sK5(X0,X1,X8))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK8(X0,X1),X1)
| ~ in(sK8(X0,X1),X0) )
& ( in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f26]) ).
fof(f28,plain,
cartesian_product2(singleton(sK9),singleton(sK10)) != singleton(ordered_pair(sK9,sK10)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f15]) ).
fof(f30,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X2,X0,X1,X8] :
( in(sK5(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X2,X0,X1,X8] :
( in(sK4(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f43,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f50,plain,
! [X0,X1] :
( in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(sK8(X0,X1),X1)
| X0 = X1
| ~ in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
cartesian_product2(singleton(sK9),singleton(sK10)) != singleton(ordered_pair(sK9,sK10)),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)),singleton(sK4(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f35,f43]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f47,f43]) ).
fof(f61,plain,
cartesian_product2(singleton(sK9),singleton(sK10)) != singleton(unordered_pair(unordered_pair(sK9,sK10),singleton(sK9))),
inference(definition_unfolding,[],[f52,f43]) ).
fof(f62,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f32]) ).
fof(f63,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f62]) ).
fof(f64,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f31]) ).
fof(f67,plain,
! [X0,X1,X8] :
( in(sK4(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f37]) ).
fof(f68,plain,
! [X0,X1,X8] :
( in(sK5(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f36]) ).
fof(f69,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)),singleton(sK4(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f56]) ).
fof(f70,definition,
sF11 = singleton(sK9),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f71,plain,
singleton(sK9) = sF11,
inference(reorient_equations,[],[f70]) ).
fof(f72,definition,
sF12 = singleton(sK10),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f73,plain,
singleton(sK10) = sF12,
inference(reorient_equations,[],[f72]) ).
fof(f74,definition,
sF13 = cartesian_product2(sF11,sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f75,plain,
cartesian_product2(sF11,sF12) = sF13,
inference(reorient_equations,[],[f74]) ).
fof(f76,definition,
sF14 = unordered_pair(sK9,sK10),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f77,plain,
unordered_pair(sK9,sK10) = sF14,
inference(reorient_equations,[],[f76]) ).
fof(f78,definition,
sF15 = unordered_pair(sF14,sF11),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f79,plain,
unordered_pair(sF14,sF11) = sF15,
inference(reorient_equations,[],[f78]) ).
fof(f80,definition,
sF16 = singleton(sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f81,plain,
singleton(sF15) = sF16,
inference(reorient_equations,[],[f80]) ).
fof(f82,plain,
sF13 != sF16,
inference(definition_folding,[],[f61,f81,f79,f71,f77,f75,f73,f71]) ).
fof(f97,plain,
! [X0] :
( ~ in(X0,sF11)
| sK9 = X0 ),
inference(superposition,[],[f64,f71]) ).
fof(f98,plain,
! [X0] :
( ~ in(X0,sF12)
| sK10 = X0 ),
inference(superposition,[],[f64,f73]) ).
fof(f99,plain,
! [X0] :
( ~ in(X0,sF13)
| unordered_pair(unordered_pair(sK4(sF11,sF12,X0),sK5(sF11,sF12,X0)),singleton(sK4(sF11,sF12,X0))) = X0 ),
inference(superposition,[],[f69,f75]) ).
fof(f100,plain,
! [X0] :
( ~ in(X0,sF16)
| sF15 = X0 ),
inference(superposition,[],[f64,f81]) ).
fof(f104,plain,
in(sK9,sF11),
inference(superposition,[],[f63,f71]) ).
fof(f105,plain,
in(sK10,sF12),
inference(superposition,[],[f63,f73]) ).
fof(f106,plain,
in(sF15,sF16),
inference(superposition,[],[f63,f81]) ).
fof(f115,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF13)
| ~ in(X0,sF11)
| ~ in(X1,sF12) ),
inference(superposition,[],[f58,f75]) ).
fof(f125,plain,
( in(unordered_pair(sF14,singleton(sK9)),sF13)
| ~ in(sK9,sF11)
| ~ in(sK10,sF12) ),
inference(superposition,[],[f115,f77]) ).
fof(f160,plain,
( in(unordered_pair(sF14,singleton(sK9)),sF13)
| ~ in(sK10,sF12) ),
inference(forward_subsumption_resolution,[],[f125,f104]) ).
fof(f161,plain,
in(unordered_pair(sF14,singleton(sK9)),sF13),
inference(forward_subsumption_resolution,[],[f160,f105]) ).
fof(f162,plain,
in(unordered_pair(sF14,sF11),sF13),
inference(forward_demodulation,[],[f161,f71]) ).
fof(f163,plain,
in(sF15,sF13),
inference(forward_demodulation,[],[f162,f79]) ).
fof(f184,plain,
sF15 = unordered_pair(sF11,sF14),
inference(superposition,[],[f79,f30]) ).
fof(f185,plain,
! [X0,X1] :
( ~ in(X1,cartesian_product2(sF11,X0))
| sK9 = sK4(sF11,X0,X1) ),
inference(resolution,[],[f97,f67]) ).
fof(f206,plain,
! [X0,X1] :
( ~ in(X1,cartesian_product2(X0,sF12))
| sK10 = sK5(X0,sF12,X1) ),
inference(resolution,[],[f98,f68]) ).
fof(f214,plain,
! [X0] :
( ~ in(X0,sF13)
| sK9 = sK4(sF11,sF12,X0) ),
inference(superposition,[],[f185,f75]) ).
fof(f225,plain,
! [X0] :
( ~ in(X0,sF13)
| sK10 = sK5(sF11,sF12,X0) ),
inference(superposition,[],[f206,f75]) ).
fof(f260,plain,
! [X0] :
( in(sK8(X0,sF16),X0)
| sF16 = X0
| sF15 = sK8(X0,sF16) ),
inference(resolution,[],[f50,f100]) ).
fof(f316,plain,
( sF13 = sF16
| sF15 = sK8(sF13,sF16)
| sK10 = sK5(sF11,sF12,sK8(sF13,sF16)) ),
inference(resolution,[],[f260,f225]) ).
fof(f317,plain,
( sF13 = sF16
| sF15 = sK8(sF13,sF16)
| sK9 = sK4(sF11,sF12,sK8(sF13,sF16)) ),
inference(resolution,[],[f260,f214]) ).
fof(f318,plain,
( sF13 = sF16
| sF15 = sK8(sF13,sF16)
| sK8(sF13,sF16) = unordered_pair(unordered_pair(sK4(sF11,sF12,sK8(sF13,sF16)),sK5(sF11,sF12,sK8(sF13,sF16))),singleton(sK4(sF11,sF12,sK8(sF13,sF16)))) ),
inference(resolution,[],[f260,f99]) ).
fof(f322,plain,
( sF15 = sK8(sF13,sF16)
| sK8(sF13,sF16) = unordered_pair(unordered_pair(sK4(sF11,sF12,sK8(sF13,sF16)),sK5(sF11,sF12,sK8(sF13,sF16))),singleton(sK4(sF11,sF12,sK8(sF13,sF16)))) ),
inference(forward_subsumption_resolution,[],[f318,f82]) ).
fof(f323,plain,
( sF15 = sK8(sF13,sF16)
| sK9 = sK4(sF11,sF12,sK8(sF13,sF16)) ),
inference(forward_subsumption_resolution,[],[f317,f82]) ).
fof(f324,plain,
( sF15 = sK8(sF13,sF16)
| sK10 = sK5(sF11,sF12,sK8(sF13,sF16)) ),
inference(forward_subsumption_resolution,[],[f316,f82]) ).
fof(f352,definition,
( spl17_17
<=> sK8(sF13,sF16) = unordered_pair(unordered_pair(sK4(sF11,sF12,sK8(sF13,sF16)),sK5(sF11,sF12,sK8(sF13,sF16))),singleton(sK4(sF11,sF12,sK8(sF13,sF16)))) ),
introduced(definition,[new_symbols(definition,[spl17_17])],[avatar_definition]) ).
fof(f354,plain,
( sK8(sF13,sF16) = unordered_pair(unordered_pair(sK4(sF11,sF12,sK8(sF13,sF16)),sK5(sF11,sF12,sK8(sF13,sF16))),singleton(sK4(sF11,sF12,sK8(sF13,sF16))))
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f356,definition,
( spl17_18
<=> sF15 = sK8(sF13,sF16) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
fof(f357,plain,
( sF15 != sK8(sF13,sF16)
| spl17_18 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f358,plain,
( sF15 = sK8(sF13,sF16)
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f359,plain,
( spl17_17
| spl17_18 ),
inference(avatar_split_clause,[],[f322,f356,f352]) ).
fof(f361,definition,
( spl17_19
<=> sK9 = sK4(sF11,sF12,sK8(sF13,sF16)) ),
introduced(definition,[new_symbols(definition,[spl17_19])],[avatar_definition]) ).
fof(f363,plain,
( sK9 = sK4(sF11,sF12,sK8(sF13,sF16))
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f364,plain,
( spl17_19
| spl17_18 ),
inference(avatar_split_clause,[],[f323,f356,f361]) ).
fof(f366,definition,
( spl17_20
<=> sK10 = sK5(sF11,sF12,sK8(sF13,sF16)) ),
introduced(definition,[new_symbols(definition,[spl17_20])],[avatar_definition]) ).
fof(f368,plain,
( sK10 = sK5(sF11,sF12,sK8(sF13,sF16))
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f369,plain,
( spl17_20
| spl17_18 ),
inference(avatar_split_clause,[],[f324,f356,f366]) ).
fof(f372,plain,
( ~ in(sF15,sF16)
| sF13 = sF16
| ~ in(sF15,sF13)
| ~ spl17_18 ),
inference(superposition,[],[f51,f358]) ).
fof(f373,plain,
( sF13 = sF16
| ~ in(sF15,sF13)
| ~ spl17_18 ),
inference(forward_subsumption_resolution,[],[f372,f106]) ).
fof(f374,plain,
( ~ in(sF15,sF13)
| ~ spl17_18 ),
inference(forward_subsumption_resolution,[],[f373,f82]) ).
fof(f375,plain,
( $false
| ~ spl17_18 ),
inference(forward_subsumption_resolution,[],[f374,f163]) ).
fof(f376,plain,
~ spl17_18,
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f377,plain,
( sK8(sF13,sF16) = unordered_pair(singleton(sK4(sF11,sF12,sK8(sF13,sF16))),unordered_pair(sK4(sF11,sF12,sK8(sF13,sF16)),sK5(sF11,sF12,sK8(sF13,sF16))))
| ~ spl17_17 ),
inference(superposition,[],[f354,f30]) ).
fof(f404,plain,
( sK8(sF13,sF16) = unordered_pair(singleton(sK4(sF11,sF12,sK8(sF13,sF16))),unordered_pair(sK4(sF11,sF12,sK8(sF13,sF16)),sK10))
| ~ spl17_17
| ~ spl17_20 ),
inference(forward_demodulation,[],[f377,f368]) ).
fof(f416,plain,
( sK8(sF13,sF16) = unordered_pair(singleton(sK9),unordered_pair(sK9,sK10))
| ~ spl17_17
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_demodulation,[],[f404,f363]) ).
fof(f427,plain,
( sK8(sF13,sF16) = unordered_pair(singleton(sK9),sF14)
| ~ spl17_17
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_demodulation,[],[f416,f77]) ).
fof(f438,plain,
( unordered_pair(sF11,sF14) = sK8(sF13,sF16)
| ~ spl17_17
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_demodulation,[],[f427,f71]) ).
fof(f447,plain,
( sF15 = sK8(sF13,sF16)
| ~ spl17_17
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_demodulation,[],[f438,f184]) ).
fof(f457,plain,
( $false
| ~ spl17_17
| spl17_18
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_subsumption_resolution,[],[f447,f357]) ).
fof(f458,plain,
( ~ spl17_17
| spl17_18
| ~ spl17_19
| ~ spl17_20 ),
inference(avatar_contradiction_clause,[],[f457]) ).
cnf(s7,plain,
( spl17_17
| spl17_18 ),
inference(sat_conversion,[],[f359]) ).
cnf(s8,plain,
( spl17_18
| spl17_19 ),
inference(sat_conversion,[],[f364]) ).
cnf(s9,plain,
( spl17_18
| spl17_20 ),
inference(sat_conversion,[],[f369]) ).
cnf(s10,plain,
~ spl17_18,
inference(sat_conversion,[],[f376]) ).
cnf(s14,plain,
( ~ spl17_17
| spl17_18
| ~ spl17_19
| ~ spl17_20 ),
inference(sat_conversion,[],[f458]) ).
cnf(s15,plain,
spl17_20,
inference(rat,[],[s9,s10]) ).
cnf(s16,plain,
spl17_19,
inference(rat,[],[s8,s10]) ).
cnf(s17,plain,
~ spl17_17,
inference(rat,[],[s14,s15,s10,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s7,s10,s17]) ).
fof(f461,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET894+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:07:39 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.92/1.98 % (1829258)Detected formulas, will run a generic FOF schedule.
% 6.92/1.98 % (1829269)dis-21_1_sil=8000:lcm=predicate:random_seed=3098507242: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)
% 6.92/1.98 % (1829269)Instruction limit reached!
% 6.92/1.98 % (1829269)------------------------------
% 6.92/1.98 % (1829269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829269)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829269)Termination reason: Instruction limit
% 6.92/1.98 % (1829269)Termination phase: Saturation
% 6.92/1.98 % (1829269)Time elapsed: 0.037 s
% 6.92/1.98 % (1829269)Peak memory usage: 89 MB
% 6.92/1.98 % (1829269)Instructions burned: 132 (million)
% 6.92/1.98 % (1829265)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=1121405589:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.92/1.98 % (1829264)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=3512237175:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.92/1.98 % (1829266)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=237580850:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.92/1.98 % (1829263)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=1918169907:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.92/1.98 % (1829267)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1431904473:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.92/1.98 % (1829268)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3061805646:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.92/1.98 % (1829266)Refutation not found, incomplete strategy
% 6.92/1.98 % (1829266)------------------------------
% 6.92/1.98 % (1829266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829266)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829266)Termination reason: Refutation not found, incomplete strategy
% 6.92/1.98 % (1829266)Time elapsed: 0.002 s
% 6.92/1.98 % (1829266)Peak memory usage: 88 MB
% 6.92/1.98 % (1829266)Instructions burned: 1 (million)
% 6.92/1.98 % (1829267)Instruction limit reached!
% 6.92/1.98 % (1829267)------------------------------
% 6.92/1.98 % (1829267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829267)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829267)Termination reason: Instruction limit
% 6.92/1.98 % (1829267)Termination phase: Saturation
% 6.92/1.98 % (1829267)Time elapsed: 0.068 s
% 6.92/1.98 % (1829267)Peak memory usage: 88 MB
% 6.92/1.98 % (1829267)Instructions burned: 120 (million)
% 6.92/1.98 % (1829268)Instruction limit reached!
% 6.92/1.98 % (1829268)------------------------------
% 6.92/1.98 % (1829268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829268)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829268)Termination reason: Instruction limit
% 6.92/1.98 % (1829268)Termination phase: Saturation
% 6.92/1.98 % (1829268)Time elapsed: 0.087 s
% 6.92/1.98 % (1829268)Peak memory usage: 89 MB
% 6.92/1.98 % (1829268)Instructions burned: 140 (million)
% 6.92/1.98 % (1829276)lrs+10_1_sil=8000:sp=occurrence:random_seed=3294060383:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.92/1.98 % (1829278)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3476084548:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.92/1.98 % (1829276)Instruction limit reached!
% 6.92/1.98 % (1829276)------------------------------
% 6.92/1.98 % (1829276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829276)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829276)Termination reason: Instruction limit
% 6.92/1.98 % (1829276)Termination phase: Saturation
% 6.92/1.98 % (1829276)Time elapsed: 0.084 s
% 6.92/1.98 % (1829276)Peak memory usage: 91 MB
% 6.92/1.98 % (1829276)Instructions burned: 286 (million)
% 6.92/1.98 % (1829279)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3111423654:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.92/1.98 % (1829266)------------------------------
% 6.92/1.98 % (1829266)------------------------------
% 6.92/1.98 % (1829278)Instruction limit reached!
% 6.92/1.98 % (1829278)------------------------------
% 6.92/1.98 % (1829278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829278)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829278)Termination reason: Instruction limit
% 6.92/1.98 % (1829278)Termination phase: Saturation
% 6.92/1.98 % (1829278)Time elapsed: 0.089 s
% 6.92/1.98 % (1829278)Peak memory usage: 89 MB
% 6.92/1.98 % (1829278)Instructions burned: 158 (million)
% 6.92/1.98 % (1829282)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=265192157:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.92/1.98 % (1829282)Instruction limit reached!
% 6.92/1.98 % (1829282)------------------------------
% 6.92/1.98 % (1829282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829282)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829282)Termination reason: Instruction limit
% 6.92/1.98 % (1829282)Termination phase: Saturation
% 6.92/1.98 % (1829282)Time elapsed: 0.076 s
% 6.92/1.98 % (1829282)Peak memory usage: 90 MB
% 6.92/1.98 % (1829282)Instructions burned: 252 (million)
% 6.92/1.98 % (1829284)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1405206579:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.92/1.98 % (1829284)Refutation not found, incomplete strategy
% 6.92/1.98 % (1829284)------------------------------
% 6.92/1.98 % (1829284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829284)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829284)Termination reason: Refutation not found, incomplete strategy
% 6.92/1.98 % (1829284)Time elapsed: 0.002 s
% 6.92/1.98 % (1829284)Peak memory usage: 88 MB
% 6.92/1.98 % (1829284)Instructions burned: 1 (million)
% 6.92/1.98 % (1829279)Instruction limit reached!
% 6.92/1.98 % (1829279)------------------------------
% 6.92/1.98 % (1829279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829279)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829279)Termination reason: Instruction limit
% 6.92/1.98 % (1829279)Termination phase: Saturation
% 6.92/1.98 % (1829279)Time elapsed: 0.210 s
% 6.92/1.98 % (1829279)Peak memory usage: 91 MB
% 6.92/1.98 % (1829279)Instructions burned: 325 (million)
% 6.92/1.98 % (1829285)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=755705182:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.92/1.98 % (1829287)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1800780478:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.92/1.98 % (1829287)Instruction limit reached!
% 6.92/1.98 % (1829287)------------------------------
% 6.92/1.98 % (1829287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829287)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829287)Termination reason: Instruction limit
% 6.92/1.98 % (1829287)Termination phase: Saturation
% 6.92/1.98 % (1829287)Time elapsed: 0.041 s
% 6.92/1.98 % (1829287)Peak memory usage: 89 MB
% 6.92/1.98 % (1829287)Instructions burned: 115 (million)
% 6.92/1.98 % (1829289)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2392491233:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.92/1.98 % (1829289)Refutation not found, incomplete strategy
% 6.92/1.98 % (1829289)------------------------------
% 6.92/1.98 % (1829289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829289)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829289)Termination reason: Refutation not found, incomplete strategy
% 6.92/1.98 % (1829289)Time elapsed: 0.002 s
% 6.92/1.98 % (1829289)Peak memory usage: 88 MB
% 6.92/1.98 % (1829289)Instructions burned: 1 (million)
% 6.92/1.98 % (1829263)First to succeed.
% 6.92/1.98 % (1829284)------------------------------
% 6.92/1.98 % (1829284)------------------------------
% 6.92/1.98 % (1829263)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1829258"
% 6.92/1.98 % (1829292)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=145047312:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.92/1.98 % (1829292)Instruction limit reached!
% 6.92/1.98 % (1829292)------------------------------
% 6.92/1.98 % (1829292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829292)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829292)Termination reason: Instruction limit
% 6.92/1.98 % (1829292)Termination phase: Saturation
% 6.92/1.98 % (1829292)Time elapsed: 0.035 s
% 6.92/1.98 % (1829292)Peak memory usage: 89 MB
% 6.92/1.98 % (1829292)Instructions burned: 115 (million)
% 6.92/1.98 % (1829265)Also succeeded, but the first one will report.
% 6.92/1.98 % (1829294)lrs+10_1_sil=8000:sp=occurrence:random_seed=740166430:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.92/1.98 % (1829289)------------------------------
% 6.92/1.98 % (1829289)------------------------------
% 6.92/1.98 % (1829296)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2295442558:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.92/1.98 % (1829296)Refutation not found, incomplete strategy
% 6.92/1.98 % (1829296)------------------------------
% 6.92/1.98 % (1829296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.92/1.98 % (1829296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.92/1.98 % (1829296)CaDiCaL version: 2.1.3
% 6.92/1.98 % (1829296)Termination reason: Refutation not found, incomplete strategy
% 6.92/1.98 % (1829296)Time elapsed: 0.001 s
% 6.92/1.98 % (1829296)Peak memory usage: 88 MB
% 6.92/1.98 % (1829296)Instructions burned: 1 (million)
% 6.92/1.98 % (1829263)Refutation found. Thanks to Tanya!
% 6.92/1.98 % SZS status Theorem for theBenchmark
% 6.92/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 8.49/2.18 % (1829263)------------------------------
% 8.49/2.18 % (1829263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.49/2.18 % (1829263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.49/2.18 % (1829263)CaDiCaL version: 2.1.3
% 8.49/2.18 % (1829263)Termination reason: Refutation
% 8.49/2.18 % (1829263)Time elapsed: 0.671 s
% 8.49/2.18 % (1829263)Peak memory usage: 128 MB
% 8.49/2.18 % (1829263)Instructions burned: 998 (million)
% 8.49/2.18 % (1829263)------------------------------
% 8.49/2.18 % (1829263)------------------------------
% 8.49/2.18 % (1829258)Success in time 1.115 s
% 8.49/2.18 % Vampire exiting
%------------------------------------------------------------------------------