%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV116+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 : n002.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 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 172 ( 10 unt; 11 def)
% Number of atoms : 628 ( 63 equ)
% Maximal formula atoms : 42 ( 3 avg)
% Number of connectives : 651 ( 195 ~; 325 |; 100 &)
% ( 11 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 74 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [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(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X8] :
( ( leq(n0,X8)
& leq(X8,minus(n6,n1)) )
=> ! [X9] :
( ( leq(n0,X9)
& leq(X9,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) ) )
=> ( ! [X10,X11] :
( ( leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X10,X11) = a_select3(q_ds1_filter,X11,X10) )
& ! [X12,X13] :
( ( leq(n0,X12)
& leq(n0,X13)
& leq(X12,minus(n3,n1))
& leq(X13,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X12,X13) = a_select3(r_ds1_filter,X13,X12) )
& ! [X14,X15] :
( ( leq(n0,X14)
& leq(n0,X15)
& leq(X14,minus(n6,n1))
& leq(X15,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X14,X15) = a_select3(pminus_ds1_filter,X15,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0009) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [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(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6) )
& ! [X8] :
( ( leq(n0,X8)
& leq(X8,minus(n6,n1)) )
=> ! [X9] :
( ( leq(n0,X9)
& leq(X9,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) ) )
=> ( ! [X10,X11] :
( ( leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X10,X11) = a_select3(q_ds1_filter,X11,X10) )
& ! [X12,X13] :
( ( leq(n0,X12)
& leq(n0,X13)
& leq(X12,minus(n3,n1))
& leq(X13,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X12,X13) = a_select3(r_ds1_filter,X13,X12) )
& ! [X14,X15] :
( ( leq(n0,X14)
& leq(n0,X15)
& leq(X14,minus(n6,n1))
& leq(X15,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X14,X15) = a_select3(pminus_ds1_filter,X15,X14) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f153,plain,
( ( ? [X10,X11] :
( a_select3(q_ds1_filter,X10,X11) != a_select3(q_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ? [X12,X13] :
( a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12)
& leq(n0,X12)
& leq(n0,X13)
& leq(X12,minus(n3,n1))
& leq(X13,minus(n3,n1)) )
| ? [X14,X15] :
( a_select3(pminus_ds1_filter,X14,X15) != a_select3(pminus_ds1_filter,X15,X14)
& leq(n0,X14)
& leq(n0,X15)
& leq(X14,minus(n6,n1))
& leq(X15,minus(n6,n1)) ) )
& leq(n0,pv5)
& leq(pv5,minus(n999,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)) )
& ! [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)) )
& ! [X8] :
( ! [X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ leq(n0,X9)
| ~ leq(X9,minus(n6,n1)) )
| ~ leq(n0,X8)
| ~ leq(X8,minus(n6,n1)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f154,plain,
( ( ? [X10,X11] :
( a_select3(q_ds1_filter,X10,X11) != a_select3(q_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ? [X12,X13] :
( a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12)
& leq(n0,X12)
& leq(n0,X13)
& leq(X12,minus(n3,n1))
& leq(X13,minus(n3,n1)) )
| ? [X14,X15] :
( a_select3(pminus_ds1_filter,X14,X15) != a_select3(pminus_ds1_filter,X15,X14)
& leq(n0,X14)
& leq(n0,X15)
& leq(X14,minus(n6,n1))
& leq(X15,minus(n6,n1)) ) )
& leq(n0,pv5)
& leq(pv5,minus(n999,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)) )
& ! [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)) )
& ! [X8] :
( ! [X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ leq(n0,X9)
| ~ leq(X9,minus(n6,n1)) )
| ~ leq(n0,X8)
| ~ leq(X8,minus(n6,n1)) ) ),
inference(flattening,[],[f153]) ).
fof(f327,plain,
! [X10,X11] :
( ~ sP37(X11,X10)
| leq(X11,minus(n6,n1)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f328,plain,
! [X10,X11] :
( ~ sP37(X11,X10)
| leq(X10,minus(n6,n1)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f329,plain,
! [X10,X11] :
( ~ sP37(X11,X10)
| leq(n0,X11) ),
inference(cnf_transformation,[],[f154]) ).
fof(f330,plain,
! [X10,X11] :
( ~ sP37(X11,X10)
| leq(n0,X10) ),
inference(cnf_transformation,[],[f154]) ).
fof(f331,plain,
! [X10,X11] :
( ~ sP37(X11,X10)
| a_select3(q_ds1_filter,X10,X11) != a_select3(q_ds1_filter,X11,X10) ),
inference(cnf_transformation,[],[f154]) ).
fof(f333,plain,
( a_select3(pminus_ds1_filter,sK31,sK32) != a_select3(pminus_ds1_filter,sK32,sK31)
| leq(sK34,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f334,plain,
( a_select3(pminus_ds1_filter,sK31,sK32) != a_select3(pminus_ds1_filter,sK32,sK31)
| leq(sK33,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f335,plain,
( a_select3(pminus_ds1_filter,sK31,sK32) != a_select3(pminus_ds1_filter,sK32,sK31)
| leq(n0,sK34)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f336,plain,
( a_select3(pminus_ds1_filter,sK31,sK32) != a_select3(pminus_ds1_filter,sK32,sK31)
| leq(n0,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f337,plain,
( a_select3(pminus_ds1_filter,sK31,sK32) != a_select3(pminus_ds1_filter,sK32,sK31)
| a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f338,plain,
( leq(n0,sK31)
| leq(sK34,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f339,plain,
( leq(n0,sK31)
| leq(sK33,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f340,plain,
( leq(n0,sK31)
| leq(n0,sK34)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f341,plain,
( leq(n0,sK31)
| leq(n0,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f342,plain,
( leq(n0,sK31)
| a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f343,plain,
( leq(n0,sK32)
| leq(sK34,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f344,plain,
( leq(n0,sK32)
| leq(sK33,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f345,plain,
( leq(n0,sK32)
| leq(n0,sK34)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f346,plain,
( leq(n0,sK32)
| leq(n0,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f347,plain,
( leq(n0,sK32)
| a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f348,plain,
( leq(sK31,minus(n6,n1))
| leq(sK34,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f349,plain,
( leq(sK31,minus(n6,n1))
| leq(sK33,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f350,plain,
( leq(sK31,minus(n6,n1))
| leq(n0,sK34)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f351,plain,
( leq(sK31,minus(n6,n1))
| leq(n0,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f352,plain,
( leq(sK31,minus(n6,n1))
| a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f353,plain,
( leq(sK32,minus(n6,n1))
| leq(sK34,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f354,plain,
( leq(sK32,minus(n6,n1))
| leq(sK33,minus(n3,n1))
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f355,plain,
( leq(sK32,minus(n6,n1))
| leq(n0,sK34)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f356,plain,
( leq(sK32,minus(n6,n1))
| leq(n0,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f357,plain,
( leq(sK32,minus(n6,n1))
| a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| sP37(sK36,sK35) ),
inference(cnf_transformation,[],[f154]) ).
fof(f358,plain,
! [X0,X1] :
( ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f359,plain,
! [X2,X3] :
( ~ leq(X3,minus(n3,n1))
| ~ leq(X2,minus(n3,n1))
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) ),
inference(cnf_transformation,[],[f154]) ).
fof(f360,plain,
! [X4,X5] :
( ~ leq(X5,minus(n6,n1))
| ~ leq(X4,minus(n6,n1))
| ~ leq(n0,X5)
| ~ leq(n0,X4)
| a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) ),
inference(cnf_transformation,[],[f154]) ).
fof(f447,definition,
( spl38_1
<=> sP37(sK36,sK35) ),
introduced(definition,[new_symbols(definition,[spl38_1])],[avatar_definition]) ).
fof(f449,plain,
( sP37(sK36,sK35)
| ~ spl38_1 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f451,definition,
( spl38_2
<=> leq(sK34,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_2])],[avatar_definition]) ).
fof(f453,plain,
( leq(sK34,minus(n3,n1))
| ~ spl38_2 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f455,definition,
( spl38_3
<=> a_select3(pminus_ds1_filter,sK31,sK32) = a_select3(pminus_ds1_filter,sK32,sK31) ),
introduced(definition,[new_symbols(definition,[spl38_3])],[avatar_definition]) ).
fof(f457,plain,
( a_select3(pminus_ds1_filter,sK31,sK32) != a_select3(pminus_ds1_filter,sK32,sK31)
| spl38_3 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f458,plain,
( spl38_1
| spl38_2
| ~ spl38_3 ),
inference(avatar_split_clause,[],[f333,f455,f451,f447]) ).
fof(f460,definition,
( spl38_4
<=> leq(sK33,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_4])],[avatar_definition]) ).
fof(f462,plain,
( leq(sK33,minus(n3,n1))
| ~ spl38_4 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f463,plain,
( spl38_1
| spl38_4
| ~ spl38_3 ),
inference(avatar_split_clause,[],[f334,f455,f460,f447]) ).
fof(f465,definition,
( spl38_5
<=> leq(n0,sK34) ),
introduced(definition,[new_symbols(definition,[spl38_5])],[avatar_definition]) ).
fof(f467,plain,
( leq(n0,sK34)
| ~ spl38_5 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f468,plain,
( spl38_1
| spl38_5
| ~ spl38_3 ),
inference(avatar_split_clause,[],[f335,f455,f465,f447]) ).
fof(f470,definition,
( spl38_6
<=> leq(n0,sK33) ),
introduced(definition,[new_symbols(definition,[spl38_6])],[avatar_definition]) ).
fof(f472,plain,
( leq(n0,sK33)
| ~ spl38_6 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f473,plain,
( spl38_1
| spl38_6
| ~ spl38_3 ),
inference(avatar_split_clause,[],[f336,f455,f470,f447]) ).
fof(f475,definition,
( spl38_7
<=> a_select3(r_ds1_filter,sK33,sK34) = a_select3(r_ds1_filter,sK34,sK33) ),
introduced(definition,[new_symbols(definition,[spl38_7])],[avatar_definition]) ).
fof(f477,plain,
( a_select3(r_ds1_filter,sK33,sK34) != a_select3(r_ds1_filter,sK34,sK33)
| spl38_7 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f478,plain,
( spl38_1
| ~ spl38_7
| ~ spl38_3 ),
inference(avatar_split_clause,[],[f337,f455,f475,f447]) ).
fof(f480,definition,
( spl38_8
<=> leq(n0,sK31) ),
introduced(definition,[new_symbols(definition,[spl38_8])],[avatar_definition]) ).
fof(f482,plain,
( leq(n0,sK31)
| ~ spl38_8 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f483,plain,
( spl38_1
| spl38_2
| spl38_8 ),
inference(avatar_split_clause,[],[f338,f480,f451,f447]) ).
fof(f484,plain,
( spl38_1
| spl38_4
| spl38_8 ),
inference(avatar_split_clause,[],[f339,f480,f460,f447]) ).
fof(f485,plain,
( spl38_1
| spl38_5
| spl38_8 ),
inference(avatar_split_clause,[],[f340,f480,f465,f447]) ).
fof(f486,plain,
( spl38_1
| spl38_6
| spl38_8 ),
inference(avatar_split_clause,[],[f341,f480,f470,f447]) ).
fof(f487,plain,
( spl38_1
| ~ spl38_7
| spl38_8 ),
inference(avatar_split_clause,[],[f342,f480,f475,f447]) ).
fof(f489,definition,
( spl38_9
<=> leq(n0,sK32) ),
introduced(definition,[new_symbols(definition,[spl38_9])],[avatar_definition]) ).
fof(f491,plain,
( leq(n0,sK32)
| ~ spl38_9 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f492,plain,
( spl38_1
| spl38_2
| spl38_9 ),
inference(avatar_split_clause,[],[f343,f489,f451,f447]) ).
fof(f493,plain,
( spl38_1
| spl38_4
| spl38_9 ),
inference(avatar_split_clause,[],[f344,f489,f460,f447]) ).
fof(f494,plain,
( spl38_1
| spl38_5
| spl38_9 ),
inference(avatar_split_clause,[],[f345,f489,f465,f447]) ).
fof(f495,plain,
( spl38_1
| spl38_6
| spl38_9 ),
inference(avatar_split_clause,[],[f346,f489,f470,f447]) ).
fof(f496,plain,
( spl38_1
| ~ spl38_7
| spl38_9 ),
inference(avatar_split_clause,[],[f347,f489,f475,f447]) ).
fof(f498,definition,
( spl38_10
<=> leq(sK31,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_10])],[avatar_definition]) ).
fof(f500,plain,
( leq(sK31,minus(n6,n1))
| ~ spl38_10 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f501,plain,
( spl38_1
| spl38_2
| spl38_10 ),
inference(avatar_split_clause,[],[f348,f498,f451,f447]) ).
fof(f502,plain,
( spl38_1
| spl38_4
| spl38_10 ),
inference(avatar_split_clause,[],[f349,f498,f460,f447]) ).
fof(f503,plain,
( spl38_1
| spl38_5
| spl38_10 ),
inference(avatar_split_clause,[],[f350,f498,f465,f447]) ).
fof(f504,plain,
( spl38_1
| spl38_6
| spl38_10 ),
inference(avatar_split_clause,[],[f351,f498,f470,f447]) ).
fof(f505,plain,
( spl38_1
| ~ spl38_7
| spl38_10 ),
inference(avatar_split_clause,[],[f352,f498,f475,f447]) ).
fof(f507,definition,
( spl38_11
<=> leq(sK32,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_11])],[avatar_definition]) ).
fof(f509,plain,
( leq(sK32,minus(n6,n1))
| ~ spl38_11 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f510,plain,
( spl38_1
| spl38_2
| spl38_11 ),
inference(avatar_split_clause,[],[f353,f507,f451,f447]) ).
fof(f511,plain,
( spl38_1
| spl38_4
| spl38_11 ),
inference(avatar_split_clause,[],[f354,f507,f460,f447]) ).
fof(f512,plain,
( spl38_1
| spl38_5
| spl38_11 ),
inference(avatar_split_clause,[],[f355,f507,f465,f447]) ).
fof(f513,plain,
( spl38_1
| spl38_6
| spl38_11 ),
inference(avatar_split_clause,[],[f356,f507,f470,f447]) ).
fof(f514,plain,
( spl38_1
| ~ spl38_7
| spl38_11 ),
inference(avatar_split_clause,[],[f357,f507,f475,f447]) ).
fof(f522,plain,
( ! [X0] :
( ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK34)
| a_select3(r_ds1_filter,X0,sK34) = a_select3(r_ds1_filter,sK34,X0) )
| ~ spl38_2 ),
inference(resolution,[],[f359,f453]) ).
fof(f523,plain,
( ! [X0] :
( ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X0)
| a_select3(r_ds1_filter,X0,sK34) = a_select3(r_ds1_filter,sK34,X0) )
| ~ spl38_2
| ~ spl38_5 ),
inference(forward_subsumption_resolution,[],[f522,f467]) ).
fof(f527,plain,
( ~ leq(n0,sK33)
| a_select3(r_ds1_filter,sK33,sK34) = a_select3(r_ds1_filter,sK34,sK33)
| ~ spl38_2
| ~ spl38_4
| ~ spl38_5 ),
inference(resolution,[],[f523,f462]) ).
fof(f529,plain,
( a_select3(r_ds1_filter,sK33,sK34) = a_select3(r_ds1_filter,sK34,sK33)
| ~ spl38_2
| ~ spl38_4
| ~ spl38_5
| ~ spl38_6 ),
inference(forward_subsumption_resolution,[],[f527,f472]) ).
fof(f530,plain,
( $false
| ~ spl38_2
| ~ spl38_4
| ~ spl38_5
| ~ spl38_6
| spl38_7 ),
inference(forward_subsumption_resolution,[],[f529,f477]) ).
fof(f531,plain,
( ~ spl38_2
| ~ spl38_4
| ~ spl38_5
| ~ spl38_6
| spl38_7 ),
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f533,plain,
( ! [X0] :
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,sK31)
| ~ leq(n0,X0)
| a_select3(pminus_ds1_filter,sK31,X0) = a_select3(pminus_ds1_filter,X0,sK31) )
| ~ spl38_10 ),
inference(resolution,[],[f500,f360]) ).
fof(f542,plain,
( ! [X0] :
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| a_select3(pminus_ds1_filter,sK31,X0) = a_select3(pminus_ds1_filter,X0,sK31) )
| ~ spl38_8
| ~ spl38_10 ),
inference(forward_subsumption_resolution,[],[f533,f482]) ).
fof(f603,plain,
( ~ leq(n0,sK32)
| a_select3(pminus_ds1_filter,sK31,sK32) = a_select3(pminus_ds1_filter,sK32,sK31)
| ~ spl38_8
| ~ spl38_10
| ~ spl38_11 ),
inference(resolution,[],[f542,f509]) ).
fof(f604,plain,
( a_select3(pminus_ds1_filter,sK31,sK32) = a_select3(pminus_ds1_filter,sK32,sK31)
| ~ spl38_8
| ~ spl38_9
| ~ spl38_10
| ~ spl38_11 ),
inference(forward_subsumption_resolution,[],[f603,f491]) ).
fof(f605,plain,
( $false
| spl38_3
| ~ spl38_8
| ~ spl38_9
| ~ spl38_10
| ~ spl38_11 ),
inference(forward_subsumption_resolution,[],[f604,f457]) ).
fof(f606,plain,
( spl38_3
| ~ spl38_8
| ~ spl38_9
| ~ spl38_10
| ~ spl38_11 ),
inference(avatar_contradiction_clause,[],[f605]) ).
fof(f607,plain,
( a_select3(q_ds1_filter,sK35,sK36) != a_select3(q_ds1_filter,sK36,sK35)
| ~ spl38_1 ),
inference(resolution,[],[f449,f331]) ).
fof(f608,plain,
( leq(sK35,minus(n6,n1))
| ~ spl38_1 ),
inference(resolution,[],[f449,f328]) ).
fof(f609,plain,
( leq(sK36,minus(n6,n1))
| ~ spl38_1 ),
inference(resolution,[],[f449,f327]) ).
fof(f610,plain,
( leq(n0,sK35)
| ~ spl38_1 ),
inference(resolution,[],[f449,f330]) ).
fof(f611,plain,
( leq(n0,sK36)
| ~ spl38_1 ),
inference(resolution,[],[f449,f329]) ).
fof(f615,plain,
( ! [X0] :
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| ~ leq(n0,sK35)
| a_select3(q_ds1_filter,X0,sK35) = a_select3(q_ds1_filter,sK35,X0) )
| ~ spl38_1 ),
inference(resolution,[],[f608,f358]) ).
fof(f620,plain,
( ! [X0] :
( ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0)
| a_select3(q_ds1_filter,X0,sK35) = a_select3(q_ds1_filter,sK35,X0) )
| ~ spl38_1 ),
inference(forward_subsumption_resolution,[],[f615,f610]) ).
fof(f662,plain,
( ~ leq(n0,sK36)
| a_select3(q_ds1_filter,sK35,sK36) = a_select3(q_ds1_filter,sK36,sK35)
| ~ spl38_1 ),
inference(resolution,[],[f620,f609]) ).
fof(f663,plain,
( a_select3(q_ds1_filter,sK35,sK36) = a_select3(q_ds1_filter,sK36,sK35)
| ~ spl38_1 ),
inference(forward_subsumption_resolution,[],[f662,f611]) ).
fof(f664,plain,
( $false
| ~ spl38_1 ),
inference(forward_subsumption_resolution,[],[f663,f607]) ).
fof(f665,plain,
~ spl38_1,
inference(avatar_contradiction_clause,[],[f664]) ).
cnf(s1,plain,
( spl38_1
| spl38_2
| ~ spl38_3 ),
inference(sat_conversion,[],[f458]) ).
cnf(s2,plain,
( spl38_1
| ~ spl38_3
| spl38_4 ),
inference(sat_conversion,[],[f463]) ).
cnf(s3,plain,
( spl38_1
| ~ spl38_3
| spl38_5 ),
inference(sat_conversion,[],[f468]) ).
cnf(s4,plain,
( spl38_1
| ~ spl38_3
| spl38_6 ),
inference(sat_conversion,[],[f473]) ).
cnf(s5,plain,
( spl38_1
| ~ spl38_3
| ~ spl38_7 ),
inference(sat_conversion,[],[f478]) ).
cnf(s6,plain,
( spl38_1
| spl38_2
| spl38_8 ),
inference(sat_conversion,[],[f483]) ).
cnf(s7,plain,
( spl38_1
| spl38_4
| spl38_8 ),
inference(sat_conversion,[],[f484]) ).
cnf(s8,plain,
( spl38_1
| spl38_5
| spl38_8 ),
inference(sat_conversion,[],[f485]) ).
cnf(s9,plain,
( spl38_1
| spl38_6
| spl38_8 ),
inference(sat_conversion,[],[f486]) ).
cnf(s10,plain,
( spl38_1
| ~ spl38_7
| spl38_8 ),
inference(sat_conversion,[],[f487]) ).
cnf(s11,plain,
( spl38_1
| spl38_2
| spl38_9 ),
inference(sat_conversion,[],[f492]) ).
cnf(s12,plain,
( spl38_1
| spl38_4
| spl38_9 ),
inference(sat_conversion,[],[f493]) ).
cnf(s13,plain,
( spl38_1
| spl38_5
| spl38_9 ),
inference(sat_conversion,[],[f494]) ).
cnf(s14,plain,
( spl38_1
| spl38_6
| spl38_9 ),
inference(sat_conversion,[],[f495]) ).
cnf(s15,plain,
( spl38_1
| ~ spl38_7
| spl38_9 ),
inference(sat_conversion,[],[f496]) ).
cnf(s16,plain,
( spl38_1
| spl38_2
| spl38_10 ),
inference(sat_conversion,[],[f501]) ).
cnf(s17,plain,
( spl38_1
| spl38_4
| spl38_10 ),
inference(sat_conversion,[],[f502]) ).
cnf(s18,plain,
( spl38_1
| spl38_5
| spl38_10 ),
inference(sat_conversion,[],[f503]) ).
cnf(s19,plain,
( spl38_1
| spl38_6
| spl38_10 ),
inference(sat_conversion,[],[f504]) ).
cnf(s20,plain,
( spl38_1
| ~ spl38_7
| spl38_10 ),
inference(sat_conversion,[],[f505]) ).
cnf(s21,plain,
( spl38_1
| spl38_2
| spl38_11 ),
inference(sat_conversion,[],[f510]) ).
cnf(s22,plain,
( spl38_1
| spl38_4
| spl38_11 ),
inference(sat_conversion,[],[f511]) ).
cnf(s23,plain,
( spl38_1
| spl38_5
| spl38_11 ),
inference(sat_conversion,[],[f512]) ).
cnf(s24,plain,
( spl38_1
| spl38_6
| spl38_11 ),
inference(sat_conversion,[],[f513]) ).
cnf(s25,plain,
( spl38_1
| ~ spl38_7
| spl38_11 ),
inference(sat_conversion,[],[f514]) ).
cnf(s26,plain,
( ~ spl38_2
| ~ spl38_4
| ~ spl38_5
| ~ spl38_6
| spl38_7 ),
inference(sat_conversion,[],[f531]) ).
cnf(s29,plain,
( spl38_3
| ~ spl38_8
| ~ spl38_9
| ~ spl38_10
| ~ spl38_11 ),
inference(sat_conversion,[],[f606]) ).
cnf(s30,plain,
~ spl38_1,
inference(sat_conversion,[],[f665]) ).
cnf(s31,plain,
( ~ spl38_7
| spl38_11 ),
inference(rat,[],[s25,s30]) ).
cnf(s32,plain,
( spl38_6
| spl38_11 ),
inference(rat,[],[s24,s30]) ).
cnf(s33,plain,
( spl38_5
| spl38_11 ),
inference(rat,[],[s23,s30]) ).
cnf(s34,plain,
( spl38_4
| spl38_11 ),
inference(rat,[],[s22,s30]) ).
cnf(s35,plain,
( spl38_2
| spl38_11 ),
inference(rat,[],[s21,s30]) ).
cnf(s36,plain,
( ~ spl38_7
| spl38_10 ),
inference(rat,[],[s20,s30]) ).
cnf(s37,plain,
( spl38_6
| spl38_10 ),
inference(rat,[],[s19,s30]) ).
cnf(s38,plain,
( spl38_5
| spl38_10 ),
inference(rat,[],[s18,s30]) ).
cnf(s39,plain,
( spl38_4
| spl38_10 ),
inference(rat,[],[s17,s30]) ).
cnf(s40,plain,
( spl38_2
| spl38_10 ),
inference(rat,[],[s16,s30]) ).
cnf(s41,plain,
( ~ spl38_7
| spl38_9 ),
inference(rat,[],[s15,s30]) ).
cnf(s42,plain,
( spl38_6
| spl38_9 ),
inference(rat,[],[s14,s30]) ).
cnf(s43,plain,
( spl38_5
| spl38_9 ),
inference(rat,[],[s13,s30]) ).
cnf(s44,plain,
( spl38_4
| spl38_9 ),
inference(rat,[],[s12,s30]) ).
cnf(s45,plain,
( spl38_2
| spl38_9 ),
inference(rat,[],[s11,s30]) ).
cnf(s46,plain,
( ~ spl38_7
| spl38_8 ),
inference(rat,[],[s10,s30]) ).
cnf(s47,plain,
( spl38_6
| spl38_8 ),
inference(rat,[],[s9,s30]) ).
cnf(s48,plain,
( spl38_5
| spl38_8 ),
inference(rat,[],[s8,s30]) ).
cnf(s49,plain,
( spl38_4
| spl38_8 ),
inference(rat,[],[s7,s30]) ).
cnf(s50,plain,
( spl38_2
| spl38_8 ),
inference(rat,[],[s6,s30]) ).
cnf(s51,plain,
( ~ spl38_3
| ~ spl38_7 ),
inference(rat,[],[s5,s30]) ).
cnf(s52,plain,
( ~ spl38_3
| spl38_6 ),
inference(rat,[],[s4,s30]) ).
cnf(s53,plain,
( ~ spl38_3
| spl38_5 ),
inference(rat,[],[s3,s30]) ).
cnf(s54,plain,
( ~ spl38_3
| spl38_4 ),
inference(rat,[],[s2,s30]) ).
cnf(s55,plain,
( spl38_2
| ~ spl38_3 ),
inference(rat,[],[s1,s30]) ).
cnf(s56,plain,
spl38_2,
inference(rat,[],[s29,s55,s50,s45,s40,s35]) ).
cnf(s57,plain,
( spl38_4
| spl38_3 ),
inference(rat,[],[s29,s49,s44,s39,s34]) ).
cnf(s58,plain,
( spl38_11
| ~ spl38_4 ),
inference(rat,[],[s26,s33,s32,s31,s56]) ).
cnf(s59,plain,
( spl38_10
| ~ spl38_4 ),
inference(rat,[],[s26,s38,s37,s36,s56]) ).
cnf(s60,plain,
( spl38_9
| ~ spl38_4 ),
inference(rat,[],[s26,s43,s42,s41,s56]) ).
cnf(s61,plain,
spl38_3,
inference(rat,[],[s26,s48,s47,s46,s29,s60,s59,s58,s57,s56]) ).
cnf(s62,plain,
~ spl38_7,
inference(rat,[],[s51,s61]) ).
cnf(s63,plain,
spl38_6,
inference(rat,[],[s52,s61]) ).
cnf(s64,plain,
spl38_5,
inference(rat,[],[s53,s61]) ).
cnf(s65,plain,
spl38_4,
inference(rat,[],[s54,s61]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s26,s62,s65,s56,s63,s64]) ).
fof(f666,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV116+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:59:12 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.27 % (246982)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (246991)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2564470350:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (246988)% WARNING: option uhcvi not known.
% 0.19/0.27 % (246987)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3388527538_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (246988)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1587531144:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (246989)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=848798372:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (246990)dis+10_1_sil=32000:sp=arity:random_seed=2285275855:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (246992)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=326399909:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (246993)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3850782475:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (246991) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-246982-246991"...
% 0.19/0.27 % (246991)...printing done.
% 0.19/0.27 % (246991)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (246991)------------------------------
% 0.19/0.27 % (246991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (246991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (246991)CaDiCaL version: 2.1.3
% 0.19/0.27 % (246991)Termination reason: Refutation
% 0.19/0.27 % (246991)Time elapsed: 0.011 s
% 0.19/0.27 % (246991)Peak memory usage: 13 MB
% 0.19/0.27 % (246991)Instructions burned: 37 (million)
% 0.19/0.27 % (246982)Success in time 0.04 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------