%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV122+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 01:20:16 PM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 138 ( 10 unt; 22 def)
% Number of atoms : 553 ( 71 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 625 ( 210 ~; 254 |; 127 &)
% ( 20 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 23 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn 75 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,minus(n6,n1))
& leq(X1,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,minus(n3,n1))
& leq(X3,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,minus(n6,n1))
& leq(X5,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) ) )
=> ( ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X6,X7) = a_select3(q_ds1_filter,X7,X6) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X8,X9) = a_select3(r_ds1_filter,X9,X8) )
& ! [X10,X11] :
( ( leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X10,X11) = a_select3(pminus_ds1_filter,X11,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0015) ).
fof(f54,negated_conjecture,
~ ( ( ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,minus(n6,n1))
& leq(X1,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,minus(n3,n1))
& leq(X3,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,minus(n6,n1))
& leq(X5,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) ) )
=> ( ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X6,X7) = a_select3(q_ds1_filter,X7,X6) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X8,X9) = a_select3(r_ds1_filter,X9,X8) )
& ! [X10,X11] :
( ( leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X10,X11) = a_select3(pminus_ds1_filter,X11,X10) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f145,plain,
( ( ? [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) != a_select3(q_ds1_filter,X7,X6)
& leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
| ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) ) )
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,minus(n6,n1))
| ~ leq(X1,minus(n6,n1)) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,minus(n3,n1))
| ~ leq(X3,minus(n3,n1)) )
& ! [X4,X5] :
( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,minus(n6,n1))
| ~ leq(X5,minus(n6,n1)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f146,plain,
( ( ? [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) != a_select3(q_ds1_filter,X7,X6)
& leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
| ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) ) )
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,minus(n6,n1))
| ~ leq(X1,minus(n6,n1)) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,minus(n3,n1))
| ~ leq(X3,minus(n3,n1)) )
& ! [X4,X5] :
( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,minus(n6,n1))
| ~ leq(X5,minus(n6,n1)) ) ),
inference(flattening,[],[f145]) ).
fof(f168,definition,
( ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f169,definition,
( ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ~ sP5 ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f170,plain,
( ( ? [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) != a_select3(q_ds1_filter,X7,X6)
& leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
| sP5
| sP4 )
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,minus(n6,n1))
| ~ leq(X1,minus(n6,n1)) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,minus(n3,n1))
| ~ leq(X3,minus(n3,n1)) )
& ! [X4,X5] :
( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,minus(n6,n1))
| ~ leq(X5,minus(n6,n1)) ) ),
inference(definition_folding,[],[f146,f169,f168]) ).
fof(f204,plain,
( ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ~ sP5 ),
inference(nnf_transformation,[],[f169]) ).
fof(f205,plain,
( ? [X0,X1] :
( a_select3(r_ds1_filter,X0,X1) != a_select3(r_ds1_filter,X1,X0)
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,minus(n3,n1))
& leq(X1,minus(n3,n1)) )
| ~ sP5 ),
inference(rectify,[],[f204]) ).
fof(f206,plain,
( ( a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
& leq(n0,sK33)
& leq(n0,sK34)
& leq(sK33,minus(n3,n1))
& leq(sK34,minus(n3,n1)) )
| ~ sP5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33,sK34]),skolemize(X0,sK33),skolemize(X1,sK34)],[f205]) ).
fof(f207,plain,
( ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ~ sP4 ),
inference(nnf_transformation,[],[f168]) ).
fof(f208,plain,
( ? [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) != a_select3(pminus_ds1_filter,X1,X0)
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,minus(n6,n1))
& leq(X1,minus(n6,n1)) )
| ~ sP4 ),
inference(rectify,[],[f207]) ).
fof(f209,plain,
( ( a_select3(pminus_ds1_filter,sK35,sK36) != a_select3(pminus_ds1_filter,sK36,sK35)
& leq(n0,sK35)
& leq(n0,sK36)
& leq(sK35,minus(n6,n1))
& leq(sK36,minus(n6,n1)) )
| ~ sP4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35,sK36]),skolemize(X0,sK35),skolemize(X1,sK36)],[f208]) ).
fof(f210,plain,
( ( ? [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) != a_select3(q_ds1_filter,X1,X0)
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,minus(n6,n1))
& leq(X1,minus(n6,n1)) )
| sP5
| sP4 )
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,minus(n6,n1))
| ~ leq(X3,minus(n6,n1)) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,minus(n3,n1))
| ~ leq(X5,minus(n3,n1)) )
& ! [X6,X7] :
( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,minus(n6,n1))
| ~ leq(X7,minus(n6,n1)) ) ),
inference(rectify,[],[f170]) ).
fof(f211,plain,
( ( ( a_select3(q_ds1_filter,sK37,sK38) != a_select3(q_ds1_filter,sK38,sK37)
& leq(n0,sK37)
& leq(n0,sK38)
& leq(sK37,minus(n6,n1))
& leq(sK38,minus(n6,n1)) )
| sP5
| sP4 )
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,minus(n6,n1))
| ~ leq(X3,minus(n6,n1)) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,minus(n3,n1))
| ~ leq(X5,minus(n3,n1)) )
& ! [X6,X7] :
( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,minus(n6,n1))
| ~ leq(X7,minus(n6,n1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38]),skolemize(X0,sK37),skolemize(X1,sK38)],[f210]) ).
fof(f322,plain,
( leq(sK34,minus(n3,n1))
| ~ sP5 ),
inference(cnf_transformation,[],[f206]) ).
fof(f323,plain,
( leq(sK33,minus(n3,n1))
| ~ sP5 ),
inference(cnf_transformation,[],[f206]) ).
fof(f324,plain,
( leq(n0,sK34)
| ~ sP5 ),
inference(cnf_transformation,[],[f206]) ).
fof(f325,plain,
( leq(n0,sK33)
| ~ sP5 ),
inference(cnf_transformation,[],[f206]) ).
fof(f326,plain,
( a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| ~ sP5 ),
inference(cnf_transformation,[],[f206]) ).
fof(f327,plain,
( leq(sK36,minus(n6,n1))
| ~ sP4 ),
inference(cnf_transformation,[],[f209]) ).
fof(f328,plain,
( leq(sK35,minus(n6,n1))
| ~ sP4 ),
inference(cnf_transformation,[],[f209]) ).
fof(f329,plain,
( leq(n0,sK36)
| ~ sP4 ),
inference(cnf_transformation,[],[f209]) ).
fof(f330,plain,
( leq(n0,sK35)
| ~ sP4 ),
inference(cnf_transformation,[],[f209]) ).
fof(f331,plain,
( a_select3(pminus_ds1_filter,sK35,sK36) != a_select3(pminus_ds1_filter,sK36,sK35)
| ~ sP4 ),
inference(cnf_transformation,[],[f209]) ).
fof(f332,plain,
! [X6,X7] :
( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,minus(n6,n1))
| ~ leq(X7,minus(n6,n1)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f333,plain,
! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,minus(n3,n1))
| ~ leq(X5,minus(n3,n1)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f334,plain,
! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,minus(n6,n1))
| ~ leq(X3,minus(n6,n1)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f335,plain,
( leq(sK38,minus(n6,n1))
| sP5
| sP4 ),
inference(cnf_transformation,[],[f211]) ).
fof(f336,plain,
( leq(sK37,minus(n6,n1))
| sP5
| sP4 ),
inference(cnf_transformation,[],[f211]) ).
fof(f337,plain,
( leq(n0,sK38)
| sP5
| sP4 ),
inference(cnf_transformation,[],[f211]) ).
fof(f338,plain,
( leq(n0,sK37)
| sP5
| sP4 ),
inference(cnf_transformation,[],[f211]) ).
fof(f339,plain,
( a_select3(q_ds1_filter,sK37,sK38) != a_select3(q_ds1_filter,sK38,sK37)
| sP5
| sP4 ),
inference(cnf_transformation,[],[f211]) ).
fof(f498,plain,
( a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| sP5 ),
inference(consistent_polarity_flipping,[],[f326]) ).
fof(f499,plain,
( ~ leq(n0,sK33)
| sP5 ),
inference(consistent_polarity_flipping,[],[f325]) ).
fof(f500,plain,
( ~ leq(n0,sK34)
| sP5 ),
inference(consistent_polarity_flipping,[],[f324]) ).
fof(f501,plain,
( ~ leq(sK33,minus(n3,n1))
| sP5 ),
inference(consistent_polarity_flipping,[],[f323]) ).
fof(f502,plain,
( ~ leq(sK34,minus(n3,n1))
| sP5 ),
inference(consistent_polarity_flipping,[],[f322]) ).
fof(f503,plain,
( a_select3(pminus_ds1_filter,sK35,sK36) != a_select3(pminus_ds1_filter,sK36,sK35)
| sP4 ),
inference(consistent_polarity_flipping,[],[f331]) ).
fof(f504,plain,
( ~ leq(n0,sK35)
| sP4 ),
inference(consistent_polarity_flipping,[],[f330]) ).
fof(f505,plain,
( ~ leq(n0,sK36)
| sP4 ),
inference(consistent_polarity_flipping,[],[f329]) ).
fof(f506,plain,
( ~ leq(sK35,minus(n6,n1))
| sP4 ),
inference(consistent_polarity_flipping,[],[f328]) ).
fof(f507,plain,
( ~ leq(sK36,minus(n6,n1))
| sP4 ),
inference(consistent_polarity_flipping,[],[f327]) ).
fof(f508,plain,
( a_select3(q_ds1_filter,sK37,sK38) != a_select3(q_ds1_filter,sK38,sK37)
| ~ sP5
| ~ sP4 ),
inference(consistent_polarity_flipping,[],[f339]) ).
fof(f509,plain,
( ~ leq(n0,sK37)
| ~ sP5
| ~ sP4 ),
inference(consistent_polarity_flipping,[],[f338]) ).
fof(f510,plain,
( ~ leq(n0,sK38)
| ~ sP5
| ~ sP4 ),
inference(consistent_polarity_flipping,[],[f337]) ).
fof(f511,plain,
( ~ leq(sK37,minus(n6,n1))
| ~ sP5
| ~ sP4 ),
inference(consistent_polarity_flipping,[],[f336]) ).
fof(f512,plain,
( ~ leq(sK38,minus(n6,n1))
| ~ sP5
| ~ sP4 ),
inference(consistent_polarity_flipping,[],[f335]) ).
fof(f513,plain,
! [X2,X3] :
( leq(n0,X3)
| leq(n0,X2)
| a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| leq(X2,minus(n6,n1))
| leq(X3,minus(n6,n1)) ),
inference(consistent_polarity_flipping,[],[f334]) ).
fof(f514,plain,
! [X4,X5] :
( leq(n0,X5)
| leq(n0,X4)
| a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| leq(X4,minus(n3,n1))
| leq(X5,minus(n3,n1)) ),
inference(consistent_polarity_flipping,[],[f333]) ).
fof(f515,plain,
! [X6,X7] :
( leq(n0,X7)
| leq(n0,X6)
| a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| leq(X6,minus(n6,n1))
| leq(X7,minus(n6,n1)) ),
inference(consistent_polarity_flipping,[],[f332]) ).
fof(f552,definition,
( spl39_1
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl39_1])],[avatar_definition]) ).
fof(f556,definition,
( spl39_2
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl39_2])],[avatar_definition]) ).
fof(f560,definition,
( spl39_3
<=> leq(sK38,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl39_3])],[avatar_definition]) ).
fof(f563,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(avatar_split_clause,[],[f512,f560,f556,f552]) ).
fof(f565,definition,
( spl39_4
<=> leq(sK37,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl39_4])],[avatar_definition]) ).
fof(f568,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_4 ),
inference(avatar_split_clause,[],[f511,f565,f556,f552]) ).
fof(f570,definition,
( spl39_5
<=> leq(n0,sK38) ),
introduced(definition,[new_symbols(definition,[spl39_5])],[avatar_definition]) ).
fof(f572,plain,
( ~ leq(n0,sK38)
| spl39_5 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f573,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_5 ),
inference(avatar_split_clause,[],[f510,f570,f556,f552]) ).
fof(f575,definition,
( spl39_6
<=> leq(n0,sK37) ),
introduced(definition,[new_symbols(definition,[spl39_6])],[avatar_definition]) ).
fof(f577,plain,
( ~ leq(n0,sK37)
| spl39_6 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f578,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_6 ),
inference(avatar_split_clause,[],[f509,f575,f556,f552]) ).
fof(f580,definition,
( spl39_7
<=> a_select3(q_ds1_filter,sK37,sK38) = a_select3(q_ds1_filter,sK38,sK37) ),
introduced(definition,[new_symbols(definition,[spl39_7])],[avatar_definition]) ).
fof(f583,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_7 ),
inference(avatar_split_clause,[],[f508,f580,f556,f552]) ).
fof(f585,definition,
( spl39_8
<=> leq(sK36,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl39_8])],[avatar_definition]) ).
fof(f588,plain,
( spl39_1
| ~ spl39_8 ),
inference(avatar_split_clause,[],[f507,f585,f552]) ).
fof(f590,definition,
( spl39_9
<=> leq(sK35,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl39_9])],[avatar_definition]) ).
fof(f593,plain,
( spl39_1
| ~ spl39_9 ),
inference(avatar_split_clause,[],[f506,f590,f552]) ).
fof(f595,definition,
( spl39_10
<=> leq(n0,sK36) ),
introduced(definition,[new_symbols(definition,[spl39_10])],[avatar_definition]) ).
fof(f597,plain,
( ~ leq(n0,sK36)
| spl39_10 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f598,plain,
( spl39_1
| ~ spl39_10 ),
inference(avatar_split_clause,[],[f505,f595,f552]) ).
fof(f600,definition,
( spl39_11
<=> leq(n0,sK35) ),
introduced(definition,[new_symbols(definition,[spl39_11])],[avatar_definition]) ).
fof(f602,plain,
( ~ leq(n0,sK35)
| spl39_11 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f603,plain,
( spl39_1
| ~ spl39_11 ),
inference(avatar_split_clause,[],[f504,f600,f552]) ).
fof(f605,definition,
( spl39_12
<=> a_select3(pminus_ds1_filter,sK35,sK36) = a_select3(pminus_ds1_filter,sK36,sK35) ),
introduced(definition,[new_symbols(definition,[spl39_12])],[avatar_definition]) ).
fof(f608,plain,
( spl39_1
| ~ spl39_12 ),
inference(avatar_split_clause,[],[f503,f605,f552]) ).
fof(f610,definition,
( spl39_13
<=> leq(sK34,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl39_13])],[avatar_definition]) ).
fof(f613,plain,
( spl39_2
| ~ spl39_13 ),
inference(avatar_split_clause,[],[f502,f610,f556]) ).
fof(f615,definition,
( spl39_14
<=> leq(sK33,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl39_14])],[avatar_definition]) ).
fof(f618,plain,
( spl39_2
| ~ spl39_14 ),
inference(avatar_split_clause,[],[f501,f615,f556]) ).
fof(f620,definition,
( spl39_15
<=> leq(n0,sK34) ),
introduced(definition,[new_symbols(definition,[spl39_15])],[avatar_definition]) ).
fof(f622,plain,
( ~ leq(n0,sK34)
| spl39_15 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f623,plain,
( spl39_2
| ~ spl39_15 ),
inference(avatar_split_clause,[],[f500,f620,f556]) ).
fof(f625,definition,
( spl39_16
<=> leq(n0,sK33) ),
introduced(definition,[new_symbols(definition,[spl39_16])],[avatar_definition]) ).
fof(f627,plain,
( ~ leq(n0,sK33)
| spl39_16 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f628,plain,
( spl39_2
| ~ spl39_16 ),
inference(avatar_split_clause,[],[f499,f625,f556]) ).
fof(f630,definition,
( spl39_17
<=> a_select3(r_ds1_filter,sK33,sK34) = a_select3(r_ds1_filter,sK34,sK33) ),
introduced(definition,[new_symbols(definition,[spl39_17])],[avatar_definition]) ).
fof(f633,plain,
( spl39_2
| ~ spl39_17 ),
inference(avatar_split_clause,[],[f498,f630,f556]) ).
fof(f634,plain,
( ! [X0] :
( leq(n0,X0)
| a_select3(q_ds1_filter,X0,sK38) = a_select3(q_ds1_filter,sK38,X0)
| leq(X0,minus(n6,n1))
| leq(sK38,minus(n6,n1)) )
| spl39_5 ),
inference(resolution,[],[f513,f572]) ).
fof(f641,definition,
( spl39_19
<=> ! [X0] :
( leq(n0,X0)
| leq(X0,minus(n6,n1))
| a_select3(q_ds1_filter,X0,sK38) = a_select3(q_ds1_filter,sK38,X0) ) ),
introduced(definition,[new_symbols(definition,[spl39_19])],[avatar_definition]) ).
fof(f642,plain,
( ! [X0] :
( leq(n0,X0)
| leq(X0,minus(n6,n1))
| a_select3(q_ds1_filter,X0,sK38) = a_select3(q_ds1_filter,sK38,X0) )
| ~ spl39_19 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f643,plain,
( spl39_3
| spl39_19
| spl39_5 ),
inference(avatar_split_clause,[],[f634,f570,f641,f560]) ).
fof(f704,plain,
( ! [X0] :
( leq(n0,X0)
| a_select3(pminus_ds1_filter,X0,sK35) = a_select3(pminus_ds1_filter,sK35,X0)
| leq(X0,minus(n6,n1))
| leq(sK35,minus(n6,n1)) )
| spl39_11 ),
inference(resolution,[],[f602,f515]) ).
fof(f720,definition,
( spl39_36
<=> ! [X0] :
( leq(n0,X0)
| leq(X0,minus(n6,n1))
| a_select3(pminus_ds1_filter,X0,sK35) = a_select3(pminus_ds1_filter,sK35,X0) ) ),
introduced(definition,[new_symbols(definition,[spl39_36])],[avatar_definition]) ).
fof(f721,plain,
( ! [X0] :
( leq(n0,X0)
| leq(X0,minus(n6,n1))
| a_select3(pminus_ds1_filter,X0,sK35) = a_select3(pminus_ds1_filter,sK35,X0) )
| ~ spl39_36 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f722,plain,
( spl39_9
| spl39_36
| spl39_11 ),
inference(avatar_split_clause,[],[f704,f600,f720,f590]) ).
fof(f724,plain,
( ! [X0] :
( leq(n0,X0)
| a_select3(r_ds1_filter,X0,sK34) = a_select3(r_ds1_filter,sK34,X0)
| leq(X0,minus(n3,n1))
| leq(sK34,minus(n3,n1)) )
| spl39_15 ),
inference(resolution,[],[f622,f514]) ).
fof(f735,definition,
( spl39_39
<=> ! [X0] :
( leq(n0,X0)
| leq(X0,minus(n3,n1))
| a_select3(r_ds1_filter,X0,sK34) = a_select3(r_ds1_filter,sK34,X0) ) ),
introduced(definition,[new_symbols(definition,[spl39_39])],[avatar_definition]) ).
fof(f736,plain,
( ! [X0] :
( leq(n0,X0)
| leq(X0,minus(n3,n1))
| a_select3(r_ds1_filter,X0,sK34) = a_select3(r_ds1_filter,sK34,X0) )
| ~ spl39_39 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f737,plain,
( spl39_13
| spl39_39
| spl39_15 ),
inference(avatar_split_clause,[],[f724,f620,f735,f610]) ).
fof(f770,plain,
( leq(sK37,minus(n6,n1))
| a_select3(q_ds1_filter,sK37,sK38) = a_select3(q_ds1_filter,sK38,sK37)
| spl39_6
| ~ spl39_19 ),
inference(resolution,[],[f642,f577]) ).
fof(f772,plain,
( spl39_7
| spl39_4
| spl39_6
| ~ spl39_19 ),
inference(avatar_split_clause,[],[f770,f641,f575,f565,f580]) ).
fof(f796,plain,
( leq(sK36,minus(n6,n1))
| a_select3(pminus_ds1_filter,sK35,sK36) = a_select3(pminus_ds1_filter,sK36,sK35)
| spl39_10
| ~ spl39_36 ),
inference(resolution,[],[f721,f597]) ).
fof(f799,plain,
( spl39_12
| spl39_8
| spl39_10
| ~ spl39_36 ),
inference(avatar_split_clause,[],[f796,f720,f595,f585,f605]) ).
fof(f831,plain,
( leq(sK33,minus(n3,n1))
| a_select3(r_ds1_filter,sK33,sK34) = a_select3(r_ds1_filter,sK34,sK33)
| spl39_16
| ~ spl39_39 ),
inference(resolution,[],[f627,f736]) ).
fof(f842,plain,
( spl39_17
| spl39_14
| spl39_16
| ~ spl39_39 ),
inference(avatar_split_clause,[],[f831,f735,f625,f615,f630]) ).
cnf(s1,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(sat_conversion,[],[f563]) ).
cnf(s2,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_4 ),
inference(sat_conversion,[],[f568]) ).
cnf(s3,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_5 ),
inference(sat_conversion,[],[f573]) ).
cnf(s4,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_6 ),
inference(sat_conversion,[],[f578]) ).
cnf(s5,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_7 ),
inference(sat_conversion,[],[f583]) ).
cnf(s6,plain,
( spl39_1
| ~ spl39_8 ),
inference(sat_conversion,[],[f588]) ).
cnf(s7,plain,
( spl39_1
| ~ spl39_9 ),
inference(sat_conversion,[],[f593]) ).
cnf(s8,plain,
( spl39_1
| ~ spl39_10 ),
inference(sat_conversion,[],[f598]) ).
cnf(s9,plain,
( spl39_1
| ~ spl39_11 ),
inference(sat_conversion,[],[f603]) ).
cnf(s10,plain,
( spl39_1
| ~ spl39_12 ),
inference(sat_conversion,[],[f608]) ).
cnf(s11,plain,
( spl39_2
| ~ spl39_13 ),
inference(sat_conversion,[],[f613]) ).
cnf(s12,plain,
( spl39_2
| ~ spl39_14 ),
inference(sat_conversion,[],[f618]) ).
cnf(s13,plain,
( spl39_2
| ~ spl39_15 ),
inference(sat_conversion,[],[f623]) ).
cnf(s14,plain,
( spl39_2
| ~ spl39_16 ),
inference(sat_conversion,[],[f628]) ).
cnf(s15,plain,
( spl39_2
| ~ spl39_17 ),
inference(sat_conversion,[],[f633]) ).
cnf(s17,plain,
( spl39_3
| spl39_5
| spl39_19 ),
inference(sat_conversion,[],[f643]) ).
cnf(s28,plain,
( spl39_9
| spl39_11
| spl39_36 ),
inference(sat_conversion,[],[f722]) ).
cnf(s30,plain,
( spl39_13
| spl39_15
| spl39_39 ),
inference(sat_conversion,[],[f737]) ).
cnf(s35,plain,
( spl39_4
| spl39_6
| spl39_7
| ~ spl39_19 ),
inference(sat_conversion,[],[f772]) ).
cnf(s38,plain,
( spl39_8
| spl39_10
| spl39_12
| ~ spl39_36 ),
inference(sat_conversion,[],[f799]) ).
cnf(s41,plain,
( spl39_14
| spl39_16
| spl39_17
| ~ spl39_39 ),
inference(sat_conversion,[],[f842]) ).
cnf(s50,plain,
spl39_1,
inference(rat,[],[s38,s28,s6,s7,s8,s9,s10]) ).
cnf(s51,plain,
spl39_2,
inference(rat,[],[s30,s41,s11,s12,s13,s14,s15]) ).
cnf(s52,plain,
~ spl39_7,
inference(rat,[],[s5,s50,s51]) ).
cnf(s53,plain,
~ spl39_6,
inference(rat,[],[s4,s50,s51]) ).
cnf(s54,plain,
~ spl39_5,
inference(rat,[],[s3,s50,s51]) ).
cnf(s55,plain,
~ spl39_4,
inference(rat,[],[s2,s50,s51]) ).
cnf(s56,plain,
~ spl39_3,
inference(rat,[],[s1,s50,s51]) ).
cnf(s57,plain,
~ spl39_19,
inference(rat,[],[s35,s53,s52,s55]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s17,s54,s57,s56]) ).
fof(f880,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV122+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n005.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 09:57:17 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.29 % (682421)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (682432)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1322213866:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (682427)% WARNING: option uhcvi not known.
% 0.19/0.29 % (682426)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2237940137_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (682432) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-682421-682432"...
% 0.19/0.29 % (682431)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3912796344:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (682427)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=518022722:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (682429)dis+10_1_sil=32000:sp=arity:random_seed=2388497902:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (682428)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3368009295:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (682430)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2131753384:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (682432)...printing done.
% 0.19/0.29 % (682432)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (682432)------------------------------
% 0.19/0.29 % (682432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (682432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (682432)CaDiCaL version: 2.1.3
% 0.19/0.29 % (682432)Termination reason: Refutation
% 0.19/0.29 % (682432)Time elapsed: 0.008 s
% 0.19/0.29 % (682432)Peak memory usage: 13 MB
% 0.19/0.29 % (682432)Instructions burned: 25 (million)
% 0.19/0.29 % (682421)Success in time 0.037 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------