%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 11:41:27 AM UTC 2026
% Result : Unsatisfiable 2.82s 1.32s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 16
% Syntax : Number of formulae : 77 ( 14 unt; 3 def)
% Number of atoms : 483 ( 0 equ)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 820 ( 414 ~; 403 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 129 ( 0 sgn 129 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f2,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
! [X0] :
( d(X0)
| c(X0)
| ~ a(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f6,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ e(X2)
| ~ r(X2,X0)
| ~ r(X2,X1)
| ~ c(X0)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
! [X0] :
( ~ e(X0)
| r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f8,axiom,
! [X0,X1] :
( a(X0)
| ~ e(X1)
| ~ r(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f19,axiom,
! [X0] :
( ~ equalish(u2r2(X0),u2r1(X0))
| ~ r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
fof(f20,axiom,
! [X0] :
( ~ equalish(u2r3(X0),u2r1(X0))
| ~ r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
fof(f21,axiom,
! [X0] :
( ~ equalish(u2r3(X0),u2r2(X0))
| ~ r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
fof(f22,axiom,
! [X0] :
( ~ r3least(X0)
| r(X0,u2r1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
fof(f23,axiom,
! [X0] :
( ~ r3least(X0)
| r(X0,u2r2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
fof(f24,axiom,
! [X0] :
( ~ r3least(X0)
| r(X0,u2r3(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
fof(f31,axiom,
! [X2,X0,X1] :
( equalish(X1,X2)
| f(X0)
| ~ r(X0,X1)
| ~ r(X0,X2)
| ~ d(X1)
| ~ d(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
fof(f32,plain,
r3least(exist),
inference(resolution,[],[f7,f1]) ).
fof(f36,plain,
r(exist,u2r1(exist)),
inference(resolution,[],[f22,f32]) ).
fof(f37,plain,
r(exist,u2r2(exist)),
inference(resolution,[],[f23,f32]) ).
fof(f38,plain,
r(exist,u2r3(exist)),
inference(resolution,[],[f24,f32]) ).
fof(f48,plain,
! [X0,X1] :
( ~ c(u2r1(X1))
| ~ r(X0,u2r2(X1))
| ~ r(X0,u2r1(X1))
| ~ c(u2r2(X1))
| ~ e(X0)
| ~ r3least(X1) ),
inference(resolution,[],[f6,f19]) ).
fof(f49,plain,
! [X0,X1] :
( ~ c(u2r3(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r1(X1))
| ~ e(X0)
| ~ c(u2r1(X1))
| ~ r3least(X1) ),
inference(resolution,[],[f6,f20]) ).
fof(f50,plain,
! [X0,X1] :
( ~ c(u2r3(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r2(X1))
| ~ e(X0)
| ~ c(u2r2(X1))
| ~ r3least(X1) ),
inference(resolution,[],[f6,f21]) ).
fof(f52,plain,
! [X0,X1] :
( ~ d(u2r1(X1))
| ~ r(X0,u2r2(X1))
| ~ r(X0,u2r1(X1))
| ~ d(u2r2(X1))
| f(X0)
| ~ r3least(X1) ),
inference(resolution,[],[f31,f19]) ).
fof(f53,plain,
! [X0,X1] :
( ~ d(u2r3(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r1(X1))
| f(X0)
| ~ d(u2r1(X1))
| ~ r3least(X1) ),
inference(resolution,[],[f31,f20]) ).
fof(f54,plain,
! [X0,X1] :
( ~ d(u2r3(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r2(X1))
| f(X0)
| ~ d(u2r2(X1))
| ~ r3least(X1) ),
inference(resolution,[],[f31,f21]) ).
fof(f63,plain,
! [X0,X1] :
( ~ d(u2r2(X1))
| ~ r(X0,u2r1(X1))
| ~ r(X0,u2r2(X1))
| f(X0)
| ~ r3least(X1)
| c(u2r1(X1))
| ~ a(u2r1(X1)) ),
inference(resolution,[],[f52,f3]) ).
fof(f64,plain,
! [X0,X1] :
( ~ d(u2r1(X1))
| ~ r(X0,u2r1(X1))
| f(X0)
| ~ r(X0,u2r3(X1))
| ~ r3least(X1)
| c(u2r3(X1))
| ~ a(u2r3(X1)) ),
inference(resolution,[],[f53,f3]) ).
fof(f65,plain,
! [X0,X1] :
( ~ d(u2r2(X1))
| ~ r(X0,u2r2(X1))
| f(X0)
| ~ r(X0,u2r3(X1))
| ~ r3least(X1)
| c(u2r3(X1))
| ~ a(u2r3(X1)) ),
inference(resolution,[],[f54,f3]) ).
fof(f66,plain,
! [X0,X1] :
( f(X0)
| ~ r(X0,u2r2(X1))
| ~ r(X0,u2r1(X1))
| ~ r3least(X1)
| c(u2r1(X1))
| ~ a(u2r1(X1))
| c(u2r2(X1))
| ~ a(u2r2(X1)) ),
inference(resolution,[],[f63,f3]) ).
fof(f71,plain,
! [X0,X1] :
( f(X0)
| ~ r(X0,u2r1(X1))
| ~ r(X0,u2r3(X1))
| ~ r3least(X1)
| c(u2r3(X1))
| ~ a(u2r3(X1))
| c(u2r1(X1))
| ~ a(u2r1(X1)) ),
inference(resolution,[],[f64,f3]) ).
fof(f72,plain,
! [X0,X1] :
( f(X0)
| ~ r(X0,u2r2(X1))
| ~ r(X0,u2r3(X1))
| ~ r3least(X1)
| c(u2r3(X1))
| ~ a(u2r3(X1))
| c(u2r2(X1))
| ~ a(u2r2(X1)) ),
inference(resolution,[],[f65,f3]) ).
fof(f106,plain,
! [X0] :
( c(u2r1(X0))
| ~ r(exist,u2r1(X0))
| ~ r3least(X0)
| ~ r(exist,u2r2(X0))
| ~ a(u2r1(X0))
| c(u2r2(X0))
| ~ a(u2r2(X0)) ),
inference(resolution,[],[f66,f2]) ).
fof(f115,plain,
! [X0] :
( c(u2r3(X0))
| ~ r(exist,u2r3(X0))
| ~ r3least(X0)
| ~ r(exist,u2r1(X0))
| ~ a(u2r3(X0))
| c(u2r1(X0))
| ~ a(u2r1(X0)) ),
inference(resolution,[],[f71,f2]) ).
fof(f121,plain,
! [X0,X1] :
( ~ r(exist,u2r3(X0))
| ~ r3least(X0)
| ~ r(exist,u2r1(X0))
| ~ a(u2r3(X0))
| c(u2r1(X0))
| ~ a(u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ c(u2r2(X0))
| ~ r3least(X0) ),
inference(resolution,[],[f115,f50]) ).
fof(f125,plain,
! [X0,X1] :
( c(u2r1(X0))
| ~ r3least(X0)
| ~ r(exist,u2r1(X0))
| ~ a(u2r3(X0))
| ~ r(exist,u2r3(X0))
| ~ a(u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ c(u2r2(X0)) ),
inference(duplicate_literal_removal,[],[f121]) ).
fof(f126,plain,
! [X0] :
( c(u2r3(X0))
| ~ r(exist,u2r3(X0))
| ~ r3least(X0)
| ~ r(exist,u2r2(X0))
| ~ a(u2r3(X0))
| c(u2r2(X0))
| ~ a(u2r2(X0)) ),
inference(resolution,[],[f72,f2]) ).
fof(f133,plain,
! [X0,X1] :
( ~ r(exist,u2r3(X0))
| ~ r3least(X0)
| ~ r(exist,u2r2(X0))
| ~ a(u2r3(X0))
| c(u2r2(X0))
| ~ a(u2r2(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r1(X0))
| ~ e(X1)
| ~ c(u2r1(X0))
| ~ r3least(X0) ),
inference(resolution,[],[f126,f49]) ).
fof(f135,plain,
! [X0,X1] :
( ~ c(u2r1(X0))
| ~ r3least(X0)
| ~ r(exist,u2r2(X0))
| ~ a(u2r3(X0))
| c(u2r2(X0))
| ~ a(u2r2(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r1(X0))
| ~ e(X1)
| ~ r(exist,u2r3(X0)) ),
inference(duplicate_literal_removal,[],[f133]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ r3least(X0)
| ~ r(exist,u2r1(X0))
| ~ a(u2r3(X0))
| ~ r(exist,u2r3(X0))
| ~ a(u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ c(u2r2(X0))
| ~ r(X2,u2r2(X0))
| ~ r(X2,u2r1(X0))
| ~ c(u2r2(X0))
| ~ e(X2)
| ~ r3least(X0) ),
inference(resolution,[],[f125,f48]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ c(u2r2(X0))
| ~ r(exist,u2r1(X0))
| ~ a(u2r3(X0))
| ~ r(exist,u2r3(X0))
| ~ a(u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ r3least(X0)
| ~ r(X2,u2r2(X0))
| ~ r(X2,u2r1(X0))
| ~ e(X2) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f146,plain,
! [X0,X1] :
( ~ r3least(X0)
| ~ r(exist,u2r2(X0))
| ~ a(u2r3(X0))
| c(u2r2(X0))
| ~ a(u2r2(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r1(X0))
| ~ e(X1)
| ~ r(exist,u2r3(X0))
| ~ r(exist,u2r1(X0))
| ~ r3least(X0)
| ~ r(exist,u2r2(X0))
| ~ a(u2r1(X0))
| c(u2r2(X0))
| ~ a(u2r2(X0)) ),
inference(resolution,[],[f135,f106]) ).
fof(f147,plain,
! [X0,X1] :
( c(u2r2(X0))
| ~ r(exist,u2r2(X0))
| ~ a(u2r3(X0))
| ~ r3least(X0)
| ~ a(u2r2(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r1(X0))
| ~ e(X1)
| ~ r(exist,u2r3(X0))
| ~ r(exist,u2r1(X0))
| ~ a(u2r1(X0)) ),
inference(duplicate_literal_removal,[],[f146]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( ~ r(exist,u2r1(X0))
| ~ a(u2r3(X0))
| ~ r(exist,u2r3(X0))
| ~ a(u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ r3least(X0)
| ~ r(X2,u2r2(X0))
| ~ r(X2,u2r1(X0))
| ~ e(X2)
| ~ r(exist,u2r2(X0))
| ~ a(u2r3(X0))
| ~ r3least(X0)
| ~ a(u2r2(X0))
| ~ r(X3,u2r3(X0))
| ~ r(X3,u2r1(X0))
| ~ e(X3)
| ~ r(exist,u2r3(X0))
| ~ r(exist,u2r1(X0))
| ~ a(u2r1(X0)) ),
inference(resolution,[],[f143,f147]) ).
fof(f152,plain,
! [X2,X3,X0,X1] :
( ~ a(u2r3(X0))
| ~ r(exist,u2r1(X0))
| ~ r(exist,u2r3(X0))
| ~ a(u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ r3least(X0)
| ~ r(X2,u2r2(X0))
| ~ r(X2,u2r1(X0))
| ~ e(X2)
| ~ r(exist,u2r2(X0))
| ~ a(u2r2(X0))
| ~ r(X3,u2r3(X0))
| ~ r(X3,u2r1(X0))
| ~ e(X3) ),
inference(duplicate_literal_removal,[],[f151]) ).
fof(f174,plain,
! [X2,X3,X0,X1,X4] :
( ~ a(u2r1(X0))
| ~ r(exist,u2r3(X0))
| ~ r(exist,u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ r3least(X0)
| ~ r(X2,u2r2(X0))
| ~ r(X2,u2r1(X0))
| ~ e(X2)
| ~ r(exist,u2r2(X0))
| ~ a(u2r2(X0))
| ~ r(X3,u2r3(X0))
| ~ r(X3,u2r1(X0))
| ~ e(X3)
| ~ e(X4)
| ~ r(X4,u2r3(X0)) ),
inference(resolution,[],[f152,f8]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ a(u2r2(X0))
| ~ r(exist,u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(X1,u2r2(X0))
| ~ e(X1)
| ~ r3least(X0)
| ~ r(X2,u2r2(X0))
| ~ r(X2,u2r1(X0))
| ~ e(X2)
| ~ r(exist,u2r2(X0))
| ~ r(exist,u2r3(X0))
| ~ r(X3,u2r3(X0))
| ~ r(X3,u2r1(X0))
| ~ e(X3)
| ~ e(X4)
| ~ r(X4,u2r3(X0))
| ~ e(X5)
| ~ r(X5,u2r1(X0)) ),
inference(resolution,[],[f174,f8]) ).
fof(f186,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ e(X1)
| ~ e(X2)
| ~ e(X3)
| ~ e(X4)
| ~ e(X5)
| ~ e(X6)
| ~ r(X2,u2r1(X0))
| ~ r(X1,u2r3(X0))
| ~ r(exist,u2r2(X0))
| ~ r(exist,u2r3(X0))
| ~ r(X3,u2r3(X0))
| ~ r(X3,u2r1(X0))
| ~ r(X1,u2r2(X0))
| ~ r(exist,u2r1(X0))
| ~ r(X4,u2r3(X0))
| ~ r3least(X0)
| ~ r(X5,u2r1(X0))
| ~ r(X2,u2r2(X0))
| ~ r(X6,u2r2(X0)) ),
inference(resolution,[],[f180,f8]) ).
fof(f198,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ e(X0)
| ~ e(X1)
| ~ e(X2)
| ~ e(X3)
| ~ e(X4)
| ~ r(X1,u2r1(X5))
| ~ r(X0,u2r3(X5))
| ~ r(exist,u2r2(X5))
| ~ r(exist,u2r3(X5))
| ~ r(exist,u2r3(X5))
| ~ r(exist,u2r1(X5))
| ~ r(X0,u2r2(X5))
| ~ r(exist,u2r1(X5))
| ~ r(X2,u2r3(X5))
| ~ r3least(X5)
| ~ r(X3,u2r1(X5))
| ~ r(X1,u2r2(X5))
| ~ r(X4,u2r2(X5)) ),
inference(resolution,[],[f186,f1]) ).
fof(f237,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ e(X0)
| ~ e(X1)
| ~ e(X2)
| ~ e(X3)
| ~ e(X4)
| ~ r(X1,u2r1(X5))
| ~ r(X0,u2r3(X5))
| ~ r(exist,u2r2(X5))
| ~ r(exist,u2r3(X5))
| ~ r(exist,u2r1(X5))
| ~ r(X0,u2r2(X5))
| ~ r(X2,u2r3(X5))
| ~ r3least(X5)
| ~ r(X3,u2r1(X5))
| ~ r(X1,u2r2(X5))
| ~ r(X4,u2r2(X5)) ),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f264,plain,
! [X2,X3,X0,X1,X4] :
( ~ e(X0)
| ~ e(X1)
| ~ e(X2)
| ~ e(X3)
| ~ r(exist,u2r1(X4))
| ~ r(X0,u2r3(X4))
| ~ r(exist,u2r2(X4))
| ~ r(exist,u2r3(X4))
| ~ r(exist,u2r1(X4))
| ~ r(X0,u2r2(X4))
| ~ r(X1,u2r3(X4))
| ~ r3least(X4)
| ~ r(X2,u2r1(X4))
| ~ r(exist,u2r2(X4))
| ~ r(X3,u2r2(X4)) ),
inference(resolution,[],[f237,f1]) ).
fof(f294,plain,
! [X2,X3,X0,X1,X4] :
( ~ e(X0)
| ~ e(X1)
| ~ e(X2)
| ~ e(X3)
| ~ r(exist,u2r1(X4))
| ~ r(X0,u2r3(X4))
| ~ r(exist,u2r2(X4))
| ~ r(exist,u2r3(X4))
| ~ r(X0,u2r2(X4))
| ~ r(X1,u2r3(X4))
| ~ r3least(X4)
| ~ r(X2,u2r1(X4))
| ~ r(X3,u2r2(X4)) ),
inference(duplicate_literal_removal,[],[f264]) ).
fof(f301,plain,
! [X2,X3,X0,X1] :
( ~ e(X0)
| ~ e(X1)
| ~ e(X2)
| ~ r(exist,u2r1(X3))
| ~ r(exist,u2r3(X3))
| ~ r(exist,u2r2(X3))
| ~ r(exist,u2r3(X3))
| ~ r(exist,u2r2(X3))
| ~ r(X0,u2r3(X3))
| ~ r3least(X3)
| ~ r(X1,u2r1(X3))
| ~ r(X2,u2r2(X3)) ),
inference(resolution,[],[f294,f1]) ).
fof(f324,plain,
! [X2,X3,X0,X1] :
( ~ e(X0)
| ~ e(X1)
| ~ e(X2)
| ~ r(exist,u2r1(X3))
| ~ r(exist,u2r3(X3))
| ~ r(exist,u2r2(X3))
| ~ r(X0,u2r3(X3))
| ~ r3least(X3)
| ~ r(X1,u2r1(X3))
| ~ r(X2,u2r2(X3)) ),
inference(duplicate_literal_removal,[],[f301]) ).
fof(f336,plain,
! [X2,X0,X1] :
( ~ e(X0)
| ~ e(X1)
| ~ r(exist,u2r1(X2))
| ~ r(exist,u2r3(X2))
| ~ r(exist,u2r2(X2))
| ~ r(X0,u2r3(X2))
| ~ r3least(X2)
| ~ r(X1,u2r1(X2))
| ~ r(exist,u2r2(X2)) ),
inference(resolution,[],[f324,f1]) ).
fof(f342,plain,
! [X2,X0,X1] :
( ~ e(X0)
| ~ e(X1)
| ~ r(exist,u2r1(X2))
| ~ r(exist,u2r3(X2))
| ~ r(exist,u2r2(X2))
| ~ r(X0,u2r3(X2))
| ~ r3least(X2)
| ~ r(X1,u2r1(X2)) ),
inference(duplicate_literal_removal,[],[f336]) ).
fof(f353,plain,
! [X0,X1] :
( ~ e(X0)
| ~ r(exist,u2r1(X1))
| ~ r(exist,u2r3(X1))
| ~ r(exist,u2r2(X1))
| ~ r(X0,u2r3(X1))
| ~ r3least(X1)
| ~ r(exist,u2r1(X1)) ),
inference(resolution,[],[f342,f1]) ).
fof(f357,plain,
! [X0,X1] :
( ~ e(X0)
| ~ r(exist,u2r1(X1))
| ~ r(exist,u2r3(X1))
| ~ r(exist,u2r2(X1))
| ~ r(X0,u2r3(X1))
| ~ r3least(X1) ),
inference(duplicate_literal_removal,[],[f353]) ).
fof(f364,plain,
! [X0] :
( ~ r(exist,u2r1(X0))
| ~ r(exist,u2r3(X0))
| ~ r(exist,u2r2(X0))
| ~ r(exist,u2r3(X0))
| ~ r3least(X0) ),
inference(resolution,[],[f357,f1]) ).
fof(f367,plain,
! [X0] :
( ~ r3least(X0)
| ~ r(exist,u2r3(X0))
| ~ r(exist,u2r2(X0))
| ~ r(exist,u2r1(X0)) ),
inference(duplicate_literal_removal,[],[f364]) ).
fof(f373,plain,
( ~ r(exist,u2r3(exist))
| ~ r(exist,u2r2(exist))
| ~ r(exist,u2r1(exist)) ),
inference(resolution,[],[f367,f32]) ).
fof(f376,definition,
( spl0_1
<=> r(exist,u2r1(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f377,plain,
( ~ r(exist,u2r1(exist))
| spl0_1 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f379,definition,
( spl0_2
<=> r(exist,u2r2(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f380,plain,
( ~ r(exist,u2r2(exist))
| spl0_2 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f382,definition,
( spl0_3
<=> r(exist,u2r3(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f383,plain,
( ~ r(exist,u2r3(exist))
| spl0_3 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f384,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f373,f382,f379,f376]) ).
fof(f390,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f377,f36]) ).
fof(f392,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f390]) ).
fof(f393,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f380,f37]) ).
fof(f395,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f396,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f383,f38]) ).
fof(f398,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f396]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f384]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f392]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f395]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f398]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f399,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:13:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.82/1.32 % (1409345)Input is clausal, will run a generic CNF schedule.
% 2.82/1.32 % (1409353)lrs+10_1_sil=8000:sp=occurrence:random_seed=4245320601:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.82/1.32 % (1409353)Refutation not found, incomplete strategy
% 2.82/1.32 % (1409353)------------------------------
% 2.82/1.32 % (1409353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.32 % (1409353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.32 % (1409353)CaDiCaL version: 2.1.3
% 2.82/1.32 % (1409353)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.32 % (1409353)Time elapsed: 0.001 s
% 2.82/1.32 % (1409353)Peak memory usage: 87 MB
% 2.82/1.32 % (1409353)Instructions burned: 2 (million)
% 2.82/1.32 % (1409356)dis-21_1_sil=8000:lcm=predicate:random_seed=479893743:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.82/1.32 % (1409355)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3397623992:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.82/1.32 % (1409352)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3629079056:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.82/1.32 % (1409354)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2563200951:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.82/1.32 % (1409350)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=2083617538:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.82/1.32 % (1409351)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3770514293:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.82/1.32 % (1409354)Refutation not found, incomplete strategy
% 2.82/1.32 % (1409354)------------------------------
% 2.82/1.32 % (1409354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.32 % (1409354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.32 % (1409354)CaDiCaL version: 2.1.3
% 2.82/1.32 % (1409354)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.32 % (1409354)Time elapsed: 0.003 s
% 2.82/1.32 % (1409354)Peak memory usage: 87 MB
% 2.82/1.32 % (1409354)Instructions burned: 4 (million)
% 2.82/1.32 % (1409356)First to succeed.
% 2.82/1.32 % (1409356)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1409345"
% 2.82/1.32 % (1409355)Instruction limit reached!
% 2.82/1.32 % (1409355)------------------------------
% 2.82/1.32 % (1409355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.32 % (1409355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.32 % (1409355)CaDiCaL version: 2.1.3
% 2.82/1.32 % (1409355)Termination reason: Instruction limit
% 2.82/1.32 % (1409355)Termination phase: Saturation
% 2.82/1.32 % (1409355)Time elapsed: 0.081 s
% 2.82/1.32 % (1409355)Peak memory usage: 88 MB
% 2.82/1.32 % (1409355)Instructions burned: 180 (million)
% 2.82/1.32 % (1409353)------------------------------
% 2.82/1.32 % (1409353)------------------------------
% 2.82/1.32 % (1409365)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2232597040:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.82/1.32 % (1409365)Refutation not found, incomplete strategy
% 2.82/1.32 % (1409365)------------------------------
% 2.82/1.32 % (1409365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.32 % (1409365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.32 % (1409365)CaDiCaL version: 2.1.3
% 2.82/1.32 % (1409365)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.32 % (1409365)Time elapsed: 0.002 s
% 2.82/1.32 % (1409365)Peak memory usage: 87 MB
% 2.82/1.32 % (1409365)Instructions burned: 4 (million)
% 2.82/1.32 % (1409364)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3244947974:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.82/1.32 % (1409364)Refutation not found, incomplete strategy
% 2.82/1.32 % (1409364)------------------------------
% 2.82/1.32 % (1409364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.32 % (1409364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.32 % (1409364)CaDiCaL version: 2.1.3
% 2.82/1.32 % (1409364)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.32 % (1409364)Time elapsed: 0.001 s
% 2.82/1.32 % (1409364)Peak memory usage: 87 MB
% 2.82/1.32 % (1409364)Instructions burned: 1 (million)
% 2.82/1.32 % (1409354)------------------------------
% 2.82/1.32 % (1409354)------------------------------
% 2.82/1.32 % (1409356)Refutation found. Thanks to Tanya!
% 2.82/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.82/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.52 % (1409356)------------------------------
% 3.88/1.52 % (1409356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.52 % (1409356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.52 % (1409356)CaDiCaL version: 2.1.3
% 3.88/1.52 % (1409356)Termination reason: Refutation
% 3.88/1.52 % (1409356)Time elapsed: 0.016 s
% 3.88/1.52 % (1409356)Peak memory usage: 89 MB
% 3.88/1.52 % (1409356)Instructions burned: 28 (million)
% 3.88/1.52 % (1409356)------------------------------
% 3.88/1.52 % (1409356)------------------------------
% 3.88/1.52 % (1409345)Success in time 0.456 s
% 3.88/1.52 % Vampire exiting
%------------------------------------------------------------------------------