%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV122+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:08:11 PM UTC 2026
% Result : Theorem 1.98s 0.78s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 109 ( 9 unt; 20 def)
% Number of atoms : 474 ( 51 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 560 ( 195 ~; 206 |; 127 &)
% ( 18 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 20 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 68 !; 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/sandbox/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(f102,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(f103,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,[],[f102]) ).
fof(f144,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)) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f145,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)) )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
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)) )
| sP1
| sP0 )
& ! [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,[],[f103,f145,f144]) ).
fof(f152,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)) )
| ~ sP1 ),
inference(nnf_transformation,[],[f145]) ).
fof(f153,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)) )
| ~ sP1 ),
inference(rectify,[],[f152]) ).
fof(f154,plain,
( ( a_select3(r_ds1_filter,sK5,sK6) != a_select3(r_ds1_filter,sK6,sK5)
& leq(n0,sK5)
& leq(n0,sK6)
& leq(sK5,minus(n3,n1))
& leq(sK6,minus(n3,n1)) )
| ~ sP1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f153]) ).
fof(f155,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)) )
| ~ sP0 ),
inference(nnf_transformation,[],[f144]) ).
fof(f156,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)) )
| ~ sP0 ),
inference(rectify,[],[f155]) ).
fof(f157,plain,
( ( a_select3(pminus_ds1_filter,sK7,sK8) != a_select3(pminus_ds1_filter,sK8,sK7)
& leq(n0,sK7)
& leq(n0,sK8)
& leq(sK7,minus(n6,n1))
& leq(sK8,minus(n6,n1)) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f156]) ).
fof(f158,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)) )
| sP1
| sP0 )
& ! [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,[],[f146]) ).
fof(f159,plain,
( ( ( a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9)
& leq(n0,sK9)
& leq(n0,sK10)
& leq(sK9,minus(n6,n1))
& leq(sK10,minus(n6,n1)) )
| sP1
| sP0 )
& ! [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,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f158]) ).
fof(f185,plain,
( leq(sK6,minus(n3,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f186,plain,
( leq(sK5,minus(n3,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f187,plain,
( leq(n0,sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f188,plain,
( leq(n0,sK5)
| ~ sP1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f189,plain,
( a_select3(r_ds1_filter,sK5,sK6) != a_select3(r_ds1_filter,sK6,sK5)
| ~ sP1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f190,plain,
( leq(sK8,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f157]) ).
fof(f191,plain,
( leq(sK7,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f157]) ).
fof(f192,plain,
( leq(n0,sK8)
| ~ sP0 ),
inference(cnf_transformation,[],[f157]) ).
fof(f193,plain,
( leq(n0,sK7)
| ~ sP0 ),
inference(cnf_transformation,[],[f157]) ).
fof(f194,plain,
( a_select3(pminus_ds1_filter,sK7,sK8) != a_select3(pminus_ds1_filter,sK8,sK7)
| ~ sP0 ),
inference(cnf_transformation,[],[f157]) ).
fof(f195,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,[],[f159]) ).
fof(f196,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,[],[f159]) ).
fof(f197,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,[],[f159]) ).
fof(f198,plain,
( leq(sK10,minus(n6,n1))
| sP1
| sP0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f199,plain,
( leq(sK9,minus(n6,n1))
| sP1
| sP0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f200,plain,
( leq(n0,sK10)
| sP1
| sP0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f201,plain,
( leq(n0,sK9)
| sP1
| sP0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f202,plain,
( a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9)
| sP1
| sP0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f358,definition,
! [X0,X1] :
( sQ31_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ31_eqProxy])],[equality_proxy_definition]) ).
fof(f359,plain,
( ~ sQ31_eqProxy(a_select3(r_ds1_filter,sK5,sK6),a_select3(r_ds1_filter,sK6,sK5))
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f189,f358]) ).
fof(f360,plain,
( ~ sQ31_eqProxy(a_select3(pminus_ds1_filter,sK7,sK8),a_select3(pminus_ds1_filter,sK8,sK7))
| ~ sP0 ),
inference(equality_proxy_replacement,[],[f194,f358]) ).
fof(f361,plain,
( ~ sQ31_eqProxy(a_select3(q_ds1_filter,sK9,sK10),a_select3(q_ds1_filter,sK10,sK9))
| sP1
| sP0 ),
inference(equality_proxy_replacement,[],[f202,f358]) ).
fof(f362,plain,
! [X2,X3] :
( sQ31_eqProxy(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(equality_proxy_replacement,[],[f197,f358]) ).
fof(f363,plain,
! [X4,X5] :
( sQ31_eqProxy(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(equality_proxy_replacement,[],[f196,f358]) ).
fof(f364,plain,
! [X6,X7] :
( sQ31_eqProxy(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(equality_proxy_replacement,[],[f195,f358]) ).
fof(f437,definition,
( spl32_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
fof(f440,definition,
( spl32_2
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl32_2])],[avatar_definition]) ).
fof(f443,definition,
( spl32_3
<=> leq(sK10,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl32_3])],[avatar_definition]) ).
fof(f445,plain,
( spl32_1
| spl32_2
| spl32_3 ),
inference(avatar_split_clause,[],[f198,f443,f440,f437]) ).
fof(f447,definition,
( spl32_4
<=> leq(sK9,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl32_4])],[avatar_definition]) ).
fof(f449,plain,
( spl32_1
| spl32_2
| spl32_4 ),
inference(avatar_split_clause,[],[f199,f447,f440,f437]) ).
fof(f451,definition,
( spl32_5
<=> leq(n0,sK10) ),
introduced(definition,[new_symbols(definition,[spl32_5])],[avatar_definition]) ).
fof(f453,plain,
( spl32_1
| spl32_2
| spl32_5 ),
inference(avatar_split_clause,[],[f200,f451,f440,f437]) ).
fof(f455,definition,
( spl32_6
<=> leq(n0,sK9) ),
introduced(definition,[new_symbols(definition,[spl32_6])],[avatar_definition]) ).
fof(f457,plain,
( spl32_1
| spl32_2
| spl32_6 ),
inference(avatar_split_clause,[],[f201,f455,f440,f437]) ).
fof(f459,definition,
( spl32_7
<=> sQ31_eqProxy(a_select3(q_ds1_filter,sK9,sK10),a_select3(q_ds1_filter,sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl32_7])],[avatar_definition]) ).
fof(f460,plain,
( ~ sQ31_eqProxy(a_select3(q_ds1_filter,sK9,sK10),a_select3(q_ds1_filter,sK10,sK9))
| spl32_7 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f461,plain,
( spl32_1
| spl32_2
| ~ spl32_7 ),
inference(avatar_split_clause,[],[f361,f459,f440,f437]) ).
fof(f464,definition,
( spl32_8
<=> leq(sK8,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl32_8])],[avatar_definition]) ).
fof(f466,plain,
( ~ spl32_1
| spl32_8 ),
inference(avatar_split_clause,[],[f190,f464,f437]) ).
fof(f468,definition,
( spl32_9
<=> leq(sK7,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl32_9])],[avatar_definition]) ).
fof(f470,plain,
( ~ spl32_1
| spl32_9 ),
inference(avatar_split_clause,[],[f191,f468,f437]) ).
fof(f472,definition,
( spl32_10
<=> leq(n0,sK8) ),
introduced(definition,[new_symbols(definition,[spl32_10])],[avatar_definition]) ).
fof(f474,plain,
( ~ spl32_1
| spl32_10 ),
inference(avatar_split_clause,[],[f192,f472,f437]) ).
fof(f476,definition,
( spl32_11
<=> leq(n0,sK7) ),
introduced(definition,[new_symbols(definition,[spl32_11])],[avatar_definition]) ).
fof(f478,plain,
( ~ spl32_1
| spl32_11 ),
inference(avatar_split_clause,[],[f193,f476,f437]) ).
fof(f480,definition,
( spl32_12
<=> sQ31_eqProxy(a_select3(pminus_ds1_filter,sK7,sK8),a_select3(pminus_ds1_filter,sK8,sK7)) ),
introduced(definition,[new_symbols(definition,[spl32_12])],[avatar_definition]) ).
fof(f481,plain,
( ~ sQ31_eqProxy(a_select3(pminus_ds1_filter,sK7,sK8),a_select3(pminus_ds1_filter,sK8,sK7))
| spl32_12 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f482,plain,
( ~ spl32_1
| ~ spl32_12 ),
inference(avatar_split_clause,[],[f360,f480,f437]) ).
fof(f485,definition,
( spl32_13
<=> leq(sK6,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl32_13])],[avatar_definition]) ).
fof(f487,plain,
( ~ spl32_2
| spl32_13 ),
inference(avatar_split_clause,[],[f185,f485,f440]) ).
fof(f489,definition,
( spl32_14
<=> leq(sK5,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl32_14])],[avatar_definition]) ).
fof(f491,plain,
( ~ spl32_2
| spl32_14 ),
inference(avatar_split_clause,[],[f186,f489,f440]) ).
fof(f493,definition,
( spl32_15
<=> leq(n0,sK6) ),
introduced(definition,[new_symbols(definition,[spl32_15])],[avatar_definition]) ).
fof(f495,plain,
( ~ spl32_2
| spl32_15 ),
inference(avatar_split_clause,[],[f187,f493,f440]) ).
fof(f497,definition,
( spl32_16
<=> leq(n0,sK5) ),
introduced(definition,[new_symbols(definition,[spl32_16])],[avatar_definition]) ).
fof(f499,plain,
( ~ spl32_2
| spl32_16 ),
inference(avatar_split_clause,[],[f188,f497,f440]) ).
fof(f501,definition,
( spl32_17
<=> sQ31_eqProxy(a_select3(r_ds1_filter,sK5,sK6),a_select3(r_ds1_filter,sK6,sK5)) ),
introduced(definition,[new_symbols(definition,[spl32_17])],[avatar_definition]) ).
fof(f502,plain,
( ~ sQ31_eqProxy(a_select3(r_ds1_filter,sK5,sK6),a_select3(r_ds1_filter,sK6,sK5))
| spl32_17 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f503,plain,
( ~ spl32_2
| ~ spl32_17 ),
inference(avatar_split_clause,[],[f359,f501,f440]) ).
fof(f504,plain,
( ~ leq(n0,sK9)
| ~ leq(n0,sK10)
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1))
| spl32_7 ),
inference(resolution,[],[f460,f362]) ).
fof(f509,plain,
( ~ spl32_3
| ~ spl32_4
| ~ spl32_5
| ~ spl32_6
| spl32_7 ),
inference(avatar_split_clause,[],[f504,f459,f455,f451,f447,f443]) ).
fof(f510,plain,
( ~ leq(n0,sK5)
| ~ leq(n0,sK6)
| ~ leq(sK5,minus(n3,n1))
| ~ leq(sK6,minus(n3,n1))
| spl32_17 ),
inference(resolution,[],[f363,f502]) ).
fof(f515,plain,
( ~ spl32_13
| ~ spl32_14
| ~ spl32_15
| ~ spl32_16
| spl32_17 ),
inference(avatar_split_clause,[],[f510,f501,f497,f493,f489,f485]) ).
fof(f516,plain,
( ~ leq(n0,sK7)
| ~ leq(n0,sK8)
| ~ leq(sK7,minus(n6,n1))
| ~ leq(sK8,minus(n6,n1))
| spl32_12 ),
inference(resolution,[],[f481,f364]) ).
fof(f521,plain,
( ~ spl32_8
| ~ spl32_9
| ~ spl32_10
| ~ spl32_11
| spl32_12 ),
inference(avatar_split_clause,[],[f516,f480,f476,f472,f468,f464]) ).
cnf(s1,plain,
( spl32_1
| spl32_2
| spl32_3 ),
inference(sat_conversion,[],[f445]) ).
cnf(s2,plain,
( spl32_1
| spl32_2
| spl32_4 ),
inference(sat_conversion,[],[f449]) ).
cnf(s3,plain,
( spl32_1
| spl32_2
| spl32_5 ),
inference(sat_conversion,[],[f453]) ).
cnf(s4,plain,
( spl32_1
| spl32_2
| spl32_6 ),
inference(sat_conversion,[],[f457]) ).
cnf(s5,plain,
( spl32_1
| spl32_2
| ~ spl32_7 ),
inference(sat_conversion,[],[f461]) ).
cnf(s6,plain,
( ~ spl32_1
| spl32_8 ),
inference(sat_conversion,[],[f466]) ).
cnf(s7,plain,
( ~ spl32_1
| spl32_9 ),
inference(sat_conversion,[],[f470]) ).
cnf(s8,plain,
( ~ spl32_1
| spl32_10 ),
inference(sat_conversion,[],[f474]) ).
cnf(s9,plain,
( ~ spl32_1
| spl32_11 ),
inference(sat_conversion,[],[f478]) ).
cnf(s10,plain,
( ~ spl32_1
| ~ spl32_12 ),
inference(sat_conversion,[],[f482]) ).
cnf(s11,plain,
( ~ spl32_2
| spl32_13 ),
inference(sat_conversion,[],[f487]) ).
cnf(s12,plain,
( ~ spl32_2
| spl32_14 ),
inference(sat_conversion,[],[f491]) ).
cnf(s13,plain,
( ~ spl32_2
| spl32_15 ),
inference(sat_conversion,[],[f495]) ).
cnf(s14,plain,
( ~ spl32_2
| spl32_16 ),
inference(sat_conversion,[],[f499]) ).
cnf(s15,plain,
( ~ spl32_2
| ~ spl32_17 ),
inference(sat_conversion,[],[f503]) ).
cnf(s16,plain,
( ~ spl32_3
| ~ spl32_4
| ~ spl32_5
| ~ spl32_6
| spl32_7 ),
inference(sat_conversion,[],[f509]) ).
cnf(s17,plain,
( ~ spl32_13
| ~ spl32_14
| ~ spl32_15
| ~ spl32_16
| spl32_17 ),
inference(sat_conversion,[],[f515]) ).
cnf(s18,plain,
( ~ spl32_8
| ~ spl32_9
| ~ spl32_10
| ~ spl32_11
| spl32_12 ),
inference(sat_conversion,[],[f521]) ).
cnf(s19,plain,
( spl32_2
| spl32_1 ),
inference(rat,[],[s16,s1,s2,s3,s4,s5]) ).
cnf(s20,plain,
~ spl32_2,
inference(rat,[],[s17,s11,s12,s13,s14,s15]) ).
cnf(s21,plain,
spl32_1,
inference(rat,[],[s19,s20]) ).
cnf(s22,plain,
~ spl32_12,
inference(rat,[],[s10,s21]) ).
cnf(s23,plain,
spl32_11,
inference(rat,[],[s9,s21]) ).
cnf(s24,plain,
spl32_10,
inference(rat,[],[s8,s21]) ).
cnf(s25,plain,
spl32_9,
inference(rat,[],[s7,s21]) ).
cnf(s26,plain,
spl32_8,
inference(rat,[],[s6,s21]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s18,s22,s23,s24,s25,s26]) ).
fof(f522,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n019.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Mon Sep 28 09:57:33 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 1.98/0.78 % (3897225)Detected formulas, will run a generic FOF schedule.
% 1.98/0.78 % (3897236)dis-21_1_sil=8000:lcm=predicate:random_seed=344245935: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)
% 1.98/0.78 % (3897235)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3478061812:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.98/0.78 % (3897234)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2217991268:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.98/0.78 % (3897231)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=818607174:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.98/0.78 % (3897230)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=3964142169:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.98/0.78 % (3897233)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2790580213:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.98/0.78 % (3897232)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=545674006:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.98/0.78 % (3897236)First to succeed.
% 1.98/0.78 % (3897236)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3897225"
% 1.98/0.78 % (3897233)Refutation not found, incomplete strategy
% 1.98/0.78 % (3897233)------------------------------
% 1.98/0.78 % (3897233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.78 % (3897233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.78 % (3897233)CaDiCaL version: 2.1.3
% 1.98/0.78 % (3897233)Termination reason: Refutation not found, incomplete strategy
% 1.98/0.78 % (3897233)Time elapsed: 0.004 s
% 1.98/0.78 % (3897233)Peak memory usage: 89 MB
% 1.98/0.78 % (3897233)Instructions burned: 5 (million)
% 1.98/0.78 % (3897234)Also succeeded, but the first one will report.
% 1.98/0.78 % (3897235)Instruction limit reached!
% 1.98/0.78 % (3897235)------------------------------
% 1.98/0.78 % (3897235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.78 % (3897235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.78 % (3897235)CaDiCaL version: 2.1.3
% 1.98/0.78 % (3897235)Termination reason: Instruction limit
% 1.98/0.78 % (3897235)Termination phase: Saturation
% 1.98/0.78 % (3897235)Time elapsed: 0.091 s
% 1.98/0.78 % (3897235)Peak memory usage: 90 MB
% 1.98/0.78 % (3897235)Instructions burned: 141 (million)
% 1.98/0.78 % (3897236)Refutation found. Thanks to Tanya!
% 1.98/0.78 % SZS status Theorem for theBenchmark
% 1.98/0.78 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/0.98 % (3897236)------------------------------
% 2.70/0.98 % (3897236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/0.98 % (3897236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.98 % (3897236)CaDiCaL version: 2.1.3
% 2.70/0.98 % (3897236)Termination reason: Refutation
% 2.70/0.98 % (3897236)Time elapsed: 0.005 s
% 2.70/0.98 % (3897236)Peak memory usage: 89 MB
% 2.70/0.98 % (3897236)Instructions burned: 13 (million)
% 2.70/0.98 % (3897236)------------------------------
% 2.70/0.98 % (3897236)------------------------------
% 2.70/0.98 % (3897225)Success in time 0.328 s
% 2.70/0.98 % Vampire exiting
%------------------------------------------------------------------------------