%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV115+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:08:10 PM UTC 2026
% Result : Theorem 3.07s 1.07s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 37
% Syntax : Number of formulae : 190 ( 17 unt; 36 def)
% Number of atoms : 909 ( 84 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 1095 ( 376 ~; 430 |; 231 &)
% ( 32 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 36 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 20 con; 0-3 aty)
% Number of variables : 156 ( 0 sgn 108 !; 48 ?)
% 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) ) ) )
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [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) )
& ! [X16,X17] :
( ( leq(n0,X16)
& leq(n0,X17)
& leq(X16,minus(n6,n1))
& leq(X17,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X16,X17) = a_select3(pminus_ds1_filter,X17,X16) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,minus(n6,n1)) )
=> ! [X19] :
( ( leq(n0,X19)
& leq(X19,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X18,X19) = a_select3(id_ds1_filter,X19,X18) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0008) ).
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) ) ) )
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [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) )
& ! [X16,X17] :
( ( leq(n0,X16)
& leq(n0,X17)
& leq(X16,minus(n6,n1))
& leq(X17,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X16,X17) = a_select3(pminus_ds1_filter,X17,X16) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,minus(n6,n1)) )
=> ! [X19] :
( ( leq(n0,X19)
& leq(X19,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X18,X19) = a_select3(id_ds1_filter,X19,X18) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f110,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ? [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)) )
| ? [X16,X17] :
( a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16)
& leq(n0,X16)
& leq(n0,X17)
& leq(X16,minus(n6,n1))
& leq(X17,minus(n6,n1)) )
| ? [X18] :
( ? [X19] :
( a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18)
& leq(n0,X19)
& leq(X19,minus(n6,n1)) )
& leq(n0,X18)
& leq(X18,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(f111,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ? [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)) )
| ? [X16,X17] :
( a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16)
& leq(n0,X16)
& leq(n0,X17)
& leq(X16,minus(n6,n1))
& leq(X17,minus(n6,n1)) )
| ? [X18] :
( ? [X19] :
( a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18)
& leq(n0,X19)
& leq(X19,minus(n6,n1)) )
& leq(n0,X18)
& leq(X18,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,[],[f110]) ).
fof(f152,definition,
( ? [X18] :
( ? [X19] :
( a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18)
& leq(n0,X19)
& leq(X19,minus(n6,n1)) )
& leq(n0,X18)
& leq(X18,minus(n6,n1)) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f153,definition,
( ? [X16,X17] :
( a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16)
& leq(n0,X16)
& leq(n0,X17)
& leq(X16,minus(n6,n1))
& leq(X17,minus(n6,n1)) )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f154,definition,
( ? [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)) )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f155,definition,
( ? [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)) )
| ~ sP3 ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f156,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ? [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)) )
| sP3
| sP2
| sP1
| sP0 )
& 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(definition_folding,[],[f111,f155,f154,f153,f152]) ).
fof(f162,plain,
( ? [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)) )
| ~ sP3 ),
inference(nnf_transformation,[],[f155]) ).
fof(f163,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)) )
| ~ sP3 ),
inference(rectify,[],[f162]) ).
fof(f164,plain,
( ( a_select3(r_ds1_filter,sK7,sK8) != a_select3(r_ds1_filter,sK8,sK7)
& leq(n0,sK7)
& leq(n0,sK8)
& leq(sK7,minus(n3,n1))
& leq(sK8,minus(n3,n1)) )
| ~ sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f163]) ).
fof(f165,plain,
( ? [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)) )
| ~ sP2 ),
inference(nnf_transformation,[],[f154]) ).
fof(f166,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)) )
| ~ sP2 ),
inference(rectify,[],[f165]) ).
fof(f167,plain,
( ( a_select3(pminus_ds1_filter,sK9,sK10) != a_select3(pminus_ds1_filter,sK10,sK9)
& leq(n0,sK9)
& leq(n0,sK10)
& leq(sK9,minus(n6,n1))
& leq(sK10,minus(n6,n1)) )
| ~ sP2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f166]) ).
fof(f168,plain,
( ? [X16,X17] :
( a_select3(pminus_ds1_filter,X16,X17) != a_select3(pminus_ds1_filter,X17,X16)
& leq(n0,X16)
& leq(n0,X17)
& leq(X16,minus(n6,n1))
& leq(X17,minus(n6,n1)) )
| ~ sP1 ),
inference(nnf_transformation,[],[f153]) ).
fof(f169,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)) )
| ~ sP1 ),
inference(rectify,[],[f168]) ).
fof(f170,plain,
( ( a_select3(pminus_ds1_filter,sK11,sK12) != a_select3(pminus_ds1_filter,sK12,sK11)
& leq(n0,sK11)
& leq(n0,sK12)
& leq(sK11,minus(n6,n1))
& leq(sK12,minus(n6,n1)) )
| ~ sP1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f169]) ).
fof(f171,plain,
( ? [X18] :
( ? [X19] :
( a_select3(id_ds1_filter,X18,X19) != a_select3(id_ds1_filter,X19,X18)
& leq(n0,X19)
& leq(X19,minus(n6,n1)) )
& leq(n0,X18)
& leq(X18,minus(n6,n1)) )
| ~ sP0 ),
inference(nnf_transformation,[],[f152]) ).
fof(f172,plain,
( ? [X0] :
( ? [X1] :
( a_select3(id_ds1_filter,X0,X1) != a_select3(id_ds1_filter,X1,X0)
& leq(n0,X1)
& leq(X1,minus(n6,n1)) )
& leq(n0,X0)
& leq(X0,minus(n6,n1)) )
| ~ sP0 ),
inference(rectify,[],[f171]) ).
fof(f173,plain,
( ( a_select3(id_ds1_filter,sK13,sK14) != a_select3(id_ds1_filter,sK14,sK13)
& leq(n0,sK14)
& leq(sK14,minus(n6,n1))
& leq(n0,sK13)
& leq(sK13,minus(n6,n1)) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f172]) ).
fof(f174,plain,
( ( ~ 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)) )
| sP3
| sP2
| sP1
| sP0 )
& leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [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)) )
& ! [X8,X9] :
( a_select3(pminus_ds1_filter,X8,X9) = a_select3(pminus_ds1_filter,X9,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,minus(n6,n1))
| ~ leq(X9,minus(n6,n1)) )
& ! [X10] :
( ! [X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(n0,X11)
| ~ leq(X11,minus(n6,n1)) )
| ~ leq(n0,X10)
| ~ leq(X10,minus(n6,n1)) ) ),
inference(rectify,[],[f156]) ).
fof(f175,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ( a_select3(q_ds1_filter,sK15,sK16) != a_select3(q_ds1_filter,sK16,sK15)
& leq(n0,sK15)
& leq(n0,sK16)
& leq(sK15,minus(n6,n1))
& leq(sK16,minus(n6,n1)) )
| sP3
| sP2
| sP1
| sP0 )
& leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [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)) )
& ! [X8,X9] :
( a_select3(pminus_ds1_filter,X8,X9) = a_select3(pminus_ds1_filter,X9,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,minus(n6,n1))
| ~ leq(X9,minus(n6,n1)) )
& ! [X10] :
( ! [X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(n0,X11)
| ~ leq(X11,minus(n6,n1)) )
| ~ leq(n0,X10)
| ~ leq(X10,minus(n6,n1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f174]) ).
fof(f201,plain,
( leq(sK8,minus(n3,n1))
| ~ sP3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f202,plain,
( leq(sK7,minus(n3,n1))
| ~ sP3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f203,plain,
( leq(n0,sK8)
| ~ sP3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f204,plain,
( leq(n0,sK7)
| ~ sP3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f205,plain,
( a_select3(r_ds1_filter,sK7,sK8) != a_select3(r_ds1_filter,sK8,sK7)
| ~ sP3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f206,plain,
( leq(sK10,minus(n6,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f167]) ).
fof(f207,plain,
( leq(sK9,minus(n6,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f167]) ).
fof(f208,plain,
( leq(n0,sK10)
| ~ sP2 ),
inference(cnf_transformation,[],[f167]) ).
fof(f209,plain,
( leq(n0,sK9)
| ~ sP2 ),
inference(cnf_transformation,[],[f167]) ).
fof(f210,plain,
( a_select3(pminus_ds1_filter,sK9,sK10) != a_select3(pminus_ds1_filter,sK10,sK9)
| ~ sP2 ),
inference(cnf_transformation,[],[f167]) ).
fof(f211,plain,
( leq(sK12,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f170]) ).
fof(f212,plain,
( leq(sK11,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f170]) ).
fof(f213,plain,
( leq(n0,sK12)
| ~ sP1 ),
inference(cnf_transformation,[],[f170]) ).
fof(f214,plain,
( leq(n0,sK11)
| ~ sP1 ),
inference(cnf_transformation,[],[f170]) ).
fof(f215,plain,
( a_select3(pminus_ds1_filter,sK11,sK12) != a_select3(pminus_ds1_filter,sK12,sK11)
| ~ sP1 ),
inference(cnf_transformation,[],[f170]) ).
fof(f216,plain,
( leq(sK13,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f173]) ).
fof(f217,plain,
( leq(n0,sK13)
| ~ sP0 ),
inference(cnf_transformation,[],[f173]) ).
fof(f218,plain,
( leq(sK14,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f173]) ).
fof(f219,plain,
( leq(n0,sK14)
| ~ sP0 ),
inference(cnf_transformation,[],[f173]) ).
fof(f220,plain,
( a_select3(id_ds1_filter,sK13,sK14) != a_select3(id_ds1_filter,sK14,sK13)
| ~ sP0 ),
inference(cnf_transformation,[],[f173]) ).
fof(f221,plain,
! [X10,X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(n0,X11)
| ~ leq(X11,minus(n6,n1))
| ~ leq(n0,X10)
| ~ leq(X10,minus(n6,n1)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f223,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,[],[f175]) ).
fof(f224,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,[],[f175]) ).
fof(f225,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,[],[f175]) ).
fof(f226,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f175]) ).
fof(f227,plain,
leq(n0,pv5),
inference(cnf_transformation,[],[f175]) ).
fof(f228,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(sK16,minus(n6,n1))
| sP3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f229,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(sK15,minus(n6,n1))
| sP3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f230,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(n0,sK16)
| sP3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f231,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(n0,sK15)
| sP3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f232,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| a_select3(q_ds1_filter,sK15,sK16) != a_select3(q_ds1_filter,sK16,sK15)
| sP3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f394,definition,
! [X0,X1] :
( sQ37_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ37_eqProxy])],[equality_proxy_definition]) ).
fof(f395,plain,
( ~ sQ37_eqProxy(a_select3(r_ds1_filter,sK7,sK8),a_select3(r_ds1_filter,sK8,sK7))
| ~ sP3 ),
inference(equality_proxy_replacement,[],[f205,f394]) ).
fof(f396,plain,
( ~ sQ37_eqProxy(a_select3(pminus_ds1_filter,sK9,sK10),a_select3(pminus_ds1_filter,sK10,sK9))
| ~ sP2 ),
inference(equality_proxy_replacement,[],[f210,f394]) ).
fof(f397,plain,
( ~ sQ37_eqProxy(a_select3(pminus_ds1_filter,sK11,sK12),a_select3(pminus_ds1_filter,sK12,sK11))
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f215,f394]) ).
fof(f398,plain,
( ~ sQ37_eqProxy(a_select3(id_ds1_filter,sK13,sK14),a_select3(id_ds1_filter,sK14,sK13))
| ~ sP0 ),
inference(equality_proxy_replacement,[],[f220,f394]) ).
fof(f399,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ~ sQ37_eqProxy(a_select3(q_ds1_filter,sK15,sK16),a_select3(q_ds1_filter,sK16,sK15))
| sP3
| sP2
| sP1
| sP0 ),
inference(equality_proxy_replacement,[],[f232,f394]) ).
fof(f400,plain,
! [X2,X3] :
( sQ37_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,[],[f225,f394]) ).
fof(f401,plain,
! [X4,X5] :
( sQ37_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,[],[f224,f394]) ).
fof(f402,plain,
! [X6,X7] :
( sQ37_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,[],[f223,f394]) ).
fof(f404,plain,
! [X10,X11] :
( sQ37_eqProxy(a_select3(id_ds1_filter,X10,X11),a_select3(id_ds1_filter,X11,X10))
| ~ leq(n0,X11)
| ~ leq(X11,minus(n6,n1))
| ~ leq(n0,X10)
| ~ leq(X10,minus(n6,n1)) ),
inference(equality_proxy_replacement,[],[f221,f394]) ).
fof(f475,definition,
( spl38_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl38_1])],[avatar_definition]) ).
fof(f478,definition,
( spl38_2
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl38_2])],[avatar_definition]) ).
fof(f481,definition,
( spl38_3
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl38_3])],[avatar_definition]) ).
fof(f484,definition,
( spl38_4
<=> sP3 ),
introduced(definition,[new_symbols(definition,[spl38_4])],[avatar_definition]) ).
fof(f487,definition,
( spl38_5
<=> leq(sK16,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_5])],[avatar_definition]) ).
fof(f490,definition,
( spl38_6
<=> leq(pv5,minus(n999,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_6])],[avatar_definition]) ).
fof(f491,plain,
( ~ leq(pv5,minus(n999,n1))
| spl38_6 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f493,definition,
( spl38_7
<=> leq(n0,pv5) ),
introduced(definition,[new_symbols(definition,[spl38_7])],[avatar_definition]) ).
fof(f494,plain,
( ~ leq(n0,pv5)
| spl38_7 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f495,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_5
| ~ spl38_6
| ~ spl38_7 ),
inference(avatar_split_clause,[],[f228,f493,f490,f487,f484,f481,f478,f475]) ).
fof(f497,definition,
( spl38_8
<=> leq(sK15,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_8])],[avatar_definition]) ).
fof(f499,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_8
| ~ spl38_6
| ~ spl38_7 ),
inference(avatar_split_clause,[],[f229,f493,f490,f497,f484,f481,f478,f475]) ).
fof(f501,definition,
( spl38_9
<=> leq(n0,sK16) ),
introduced(definition,[new_symbols(definition,[spl38_9])],[avatar_definition]) ).
fof(f503,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_9
| ~ spl38_6
| ~ spl38_7 ),
inference(avatar_split_clause,[],[f230,f493,f490,f501,f484,f481,f478,f475]) ).
fof(f505,definition,
( spl38_10
<=> leq(n0,sK15) ),
introduced(definition,[new_symbols(definition,[spl38_10])],[avatar_definition]) ).
fof(f507,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_10
| ~ spl38_6
| ~ spl38_7 ),
inference(avatar_split_clause,[],[f231,f493,f490,f505,f484,f481,f478,f475]) ).
fof(f509,definition,
( spl38_11
<=> sQ37_eqProxy(a_select3(q_ds1_filter,sK15,sK16),a_select3(q_ds1_filter,sK16,sK15)) ),
introduced(definition,[new_symbols(definition,[spl38_11])],[avatar_definition]) ).
fof(f510,plain,
( ~ sQ37_eqProxy(a_select3(q_ds1_filter,sK15,sK16),a_select3(q_ds1_filter,sK16,sK15))
| spl38_11 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f511,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| ~ spl38_11
| ~ spl38_6
| ~ spl38_7 ),
inference(avatar_split_clause,[],[f399,f493,f490,f509,f484,f481,f478,f475]) ).
fof(f514,definition,
( spl38_12
<=> leq(sK13,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_12])],[avatar_definition]) ).
fof(f516,plain,
( ~ spl38_1
| spl38_12 ),
inference(avatar_split_clause,[],[f216,f514,f475]) ).
fof(f518,definition,
( spl38_13
<=> leq(n0,sK13) ),
introduced(definition,[new_symbols(definition,[spl38_13])],[avatar_definition]) ).
fof(f520,plain,
( ~ spl38_1
| spl38_13 ),
inference(avatar_split_clause,[],[f217,f518,f475]) ).
fof(f522,definition,
( spl38_14
<=> leq(sK14,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_14])],[avatar_definition]) ).
fof(f524,plain,
( ~ spl38_1
| spl38_14 ),
inference(avatar_split_clause,[],[f218,f522,f475]) ).
fof(f526,definition,
( spl38_15
<=> leq(n0,sK14) ),
introduced(definition,[new_symbols(definition,[spl38_15])],[avatar_definition]) ).
fof(f528,plain,
( ~ spl38_1
| spl38_15 ),
inference(avatar_split_clause,[],[f219,f526,f475]) ).
fof(f530,definition,
( spl38_16
<=> sQ37_eqProxy(a_select3(id_ds1_filter,sK13,sK14),a_select3(id_ds1_filter,sK14,sK13)) ),
introduced(definition,[new_symbols(definition,[spl38_16])],[avatar_definition]) ).
fof(f531,plain,
( ~ sQ37_eqProxy(a_select3(id_ds1_filter,sK13,sK14),a_select3(id_ds1_filter,sK14,sK13))
| spl38_16 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f532,plain,
( ~ spl38_1
| ~ spl38_16 ),
inference(avatar_split_clause,[],[f398,f530,f475]) ).
fof(f535,definition,
( spl38_17
<=> leq(sK12,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_17])],[avatar_definition]) ).
fof(f537,plain,
( ~ spl38_2
| spl38_17 ),
inference(avatar_split_clause,[],[f211,f535,f478]) ).
fof(f539,definition,
( spl38_18
<=> leq(sK11,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_18])],[avatar_definition]) ).
fof(f541,plain,
( ~ spl38_2
| spl38_18 ),
inference(avatar_split_clause,[],[f212,f539,f478]) ).
fof(f543,definition,
( spl38_19
<=> leq(n0,sK12) ),
introduced(definition,[new_symbols(definition,[spl38_19])],[avatar_definition]) ).
fof(f545,plain,
( ~ spl38_2
| spl38_19 ),
inference(avatar_split_clause,[],[f213,f543,f478]) ).
fof(f547,definition,
( spl38_20
<=> leq(n0,sK11) ),
introduced(definition,[new_symbols(definition,[spl38_20])],[avatar_definition]) ).
fof(f549,plain,
( ~ spl38_2
| spl38_20 ),
inference(avatar_split_clause,[],[f214,f547,f478]) ).
fof(f551,definition,
( spl38_21
<=> sQ37_eqProxy(a_select3(pminus_ds1_filter,sK11,sK12),a_select3(pminus_ds1_filter,sK12,sK11)) ),
introduced(definition,[new_symbols(definition,[spl38_21])],[avatar_definition]) ).
fof(f552,plain,
( ~ sQ37_eqProxy(a_select3(pminus_ds1_filter,sK11,sK12),a_select3(pminus_ds1_filter,sK12,sK11))
| spl38_21 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f553,plain,
( ~ spl38_2
| ~ spl38_21 ),
inference(avatar_split_clause,[],[f397,f551,f478]) ).
fof(f556,definition,
( spl38_22
<=> leq(sK10,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_22])],[avatar_definition]) ).
fof(f558,plain,
( ~ spl38_3
| spl38_22 ),
inference(avatar_split_clause,[],[f206,f556,f481]) ).
fof(f560,definition,
( spl38_23
<=> leq(sK9,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_23])],[avatar_definition]) ).
fof(f562,plain,
( ~ spl38_3
| spl38_23 ),
inference(avatar_split_clause,[],[f207,f560,f481]) ).
fof(f564,definition,
( spl38_24
<=> leq(n0,sK10) ),
introduced(definition,[new_symbols(definition,[spl38_24])],[avatar_definition]) ).
fof(f566,plain,
( ~ spl38_3
| spl38_24 ),
inference(avatar_split_clause,[],[f208,f564,f481]) ).
fof(f568,definition,
( spl38_25
<=> leq(n0,sK9) ),
introduced(definition,[new_symbols(definition,[spl38_25])],[avatar_definition]) ).
fof(f570,plain,
( ~ spl38_3
| spl38_25 ),
inference(avatar_split_clause,[],[f209,f568,f481]) ).
fof(f572,definition,
( spl38_26
<=> sQ37_eqProxy(a_select3(pminus_ds1_filter,sK9,sK10),a_select3(pminus_ds1_filter,sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl38_26])],[avatar_definition]) ).
fof(f573,plain,
( ~ sQ37_eqProxy(a_select3(pminus_ds1_filter,sK9,sK10),a_select3(pminus_ds1_filter,sK10,sK9))
| spl38_26 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f574,plain,
( ~ spl38_3
| ~ spl38_26 ),
inference(avatar_split_clause,[],[f396,f572,f481]) ).
fof(f577,definition,
( spl38_27
<=> leq(sK8,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_27])],[avatar_definition]) ).
fof(f579,plain,
( ~ spl38_4
| spl38_27 ),
inference(avatar_split_clause,[],[f201,f577,f484]) ).
fof(f581,definition,
( spl38_28
<=> leq(sK7,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[spl38_28])],[avatar_definition]) ).
fof(f583,plain,
( ~ spl38_4
| spl38_28 ),
inference(avatar_split_clause,[],[f202,f581,f484]) ).
fof(f585,definition,
( spl38_29
<=> leq(n0,sK8) ),
introduced(definition,[new_symbols(definition,[spl38_29])],[avatar_definition]) ).
fof(f587,plain,
( ~ spl38_4
| spl38_29 ),
inference(avatar_split_clause,[],[f203,f585,f484]) ).
fof(f589,definition,
( spl38_30
<=> leq(n0,sK7) ),
introduced(definition,[new_symbols(definition,[spl38_30])],[avatar_definition]) ).
fof(f591,plain,
( ~ spl38_4
| spl38_30 ),
inference(avatar_split_clause,[],[f204,f589,f484]) ).
fof(f593,definition,
( spl38_31
<=> sQ37_eqProxy(a_select3(r_ds1_filter,sK7,sK8),a_select3(r_ds1_filter,sK8,sK7)) ),
introduced(definition,[new_symbols(definition,[spl38_31])],[avatar_definition]) ).
fof(f594,plain,
( ~ sQ37_eqProxy(a_select3(r_ds1_filter,sK7,sK8),a_select3(r_ds1_filter,sK8,sK7))
| spl38_31 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f595,plain,
( ~ spl38_4
| ~ spl38_31 ),
inference(avatar_split_clause,[],[f395,f593,f484]) ).
fof(f596,plain,
( $false
| spl38_6 ),
inference(resolution,[],[f226,f491]) ).
fof(f597,plain,
spl38_6,
inference(avatar_contradiction_clause,[],[f596]) ).
fof(f598,plain,
( $false
| spl38_7 ),
inference(resolution,[],[f494,f227]) ).
fof(f599,plain,
spl38_7,
inference(avatar_contradiction_clause,[],[f598]) ).
fof(f600,plain,
( ~ leq(n0,sK11)
| ~ leq(n0,sK12)
| ~ leq(sK11,minus(n6,n1))
| ~ leq(sK12,minus(n6,n1))
| spl38_21 ),
inference(resolution,[],[f402,f552]) ).
fof(f605,plain,
( ~ spl38_17
| ~ spl38_18
| ~ spl38_19
| ~ spl38_20
| spl38_21 ),
inference(avatar_split_clause,[],[f600,f551,f547,f543,f539,f535]) ).
fof(f606,plain,
( ~ leq(n0,sK15)
| ~ leq(n0,sK16)
| ~ leq(sK15,minus(n6,n1))
| ~ leq(sK16,minus(n6,n1))
| spl38_11 ),
inference(resolution,[],[f510,f400]) ).
fof(f611,plain,
( ~ spl38_5
| ~ spl38_8
| ~ spl38_9
| ~ spl38_10
| spl38_11 ),
inference(avatar_split_clause,[],[f606,f509,f505,f501,f497,f487]) ).
fof(f612,plain,
( ~ leq(n0,sK14)
| ~ leq(sK14,minus(n6,n1))
| ~ leq(n0,sK13)
| ~ leq(sK13,minus(n6,n1))
| spl38_16 ),
inference(resolution,[],[f404,f531]) ).
fof(f617,plain,
( ~ spl38_12
| ~ spl38_13
| ~ spl38_14
| ~ spl38_15
| spl38_16 ),
inference(avatar_split_clause,[],[f612,f530,f526,f522,f518,f514]) ).
fof(f618,plain,
( ~ leq(n0,sK7)
| ~ leq(n0,sK8)
| ~ leq(sK7,minus(n3,n1))
| ~ leq(sK8,minus(n3,n1))
| spl38_31 ),
inference(resolution,[],[f594,f401]) ).
fof(f623,plain,
( ~ spl38_27
| ~ spl38_28
| ~ spl38_29
| ~ spl38_30
| spl38_31 ),
inference(avatar_split_clause,[],[f618,f593,f589,f585,f581,f577]) ).
fof(f624,plain,
( ~ leq(n0,sK9)
| ~ leq(n0,sK10)
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1))
| spl38_26 ),
inference(resolution,[],[f573,f402]) ).
fof(f629,plain,
( ~ spl38_22
| ~ spl38_23
| ~ spl38_24
| ~ spl38_25
| spl38_26 ),
inference(avatar_split_clause,[],[f624,f572,f568,f564,f560,f556]) ).
cnf(s1,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_5
| ~ spl38_6
| ~ spl38_7 ),
inference(sat_conversion,[],[f495]) ).
cnf(s2,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| ~ spl38_6
| ~ spl38_7
| spl38_8 ),
inference(sat_conversion,[],[f499]) ).
cnf(s3,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| ~ spl38_6
| ~ spl38_7
| spl38_9 ),
inference(sat_conversion,[],[f503]) ).
cnf(s4,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| ~ spl38_6
| ~ spl38_7
| spl38_10 ),
inference(sat_conversion,[],[f507]) ).
cnf(s5,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| ~ spl38_6
| ~ spl38_7
| ~ spl38_11 ),
inference(sat_conversion,[],[f511]) ).
cnf(s6,plain,
( ~ spl38_1
| spl38_12 ),
inference(sat_conversion,[],[f516]) ).
cnf(s7,plain,
( ~ spl38_1
| spl38_13 ),
inference(sat_conversion,[],[f520]) ).
cnf(s8,plain,
( ~ spl38_1
| spl38_14 ),
inference(sat_conversion,[],[f524]) ).
cnf(s9,plain,
( ~ spl38_1
| spl38_15 ),
inference(sat_conversion,[],[f528]) ).
cnf(s10,plain,
( ~ spl38_1
| ~ spl38_16 ),
inference(sat_conversion,[],[f532]) ).
cnf(s11,plain,
( ~ spl38_2
| spl38_17 ),
inference(sat_conversion,[],[f537]) ).
cnf(s12,plain,
( ~ spl38_2
| spl38_18 ),
inference(sat_conversion,[],[f541]) ).
cnf(s13,plain,
( ~ spl38_2
| spl38_19 ),
inference(sat_conversion,[],[f545]) ).
cnf(s14,plain,
( ~ spl38_2
| spl38_20 ),
inference(sat_conversion,[],[f549]) ).
cnf(s15,plain,
( ~ spl38_2
| ~ spl38_21 ),
inference(sat_conversion,[],[f553]) ).
cnf(s16,plain,
( ~ spl38_3
| spl38_22 ),
inference(sat_conversion,[],[f558]) ).
cnf(s17,plain,
( ~ spl38_3
| spl38_23 ),
inference(sat_conversion,[],[f562]) ).
cnf(s18,plain,
( ~ spl38_3
| spl38_24 ),
inference(sat_conversion,[],[f566]) ).
cnf(s19,plain,
( ~ spl38_3
| spl38_25 ),
inference(sat_conversion,[],[f570]) ).
cnf(s20,plain,
( ~ spl38_3
| ~ spl38_26 ),
inference(sat_conversion,[],[f574]) ).
cnf(s21,plain,
( ~ spl38_4
| spl38_27 ),
inference(sat_conversion,[],[f579]) ).
cnf(s22,plain,
( ~ spl38_4
| spl38_28 ),
inference(sat_conversion,[],[f583]) ).
cnf(s23,plain,
( ~ spl38_4
| spl38_29 ),
inference(sat_conversion,[],[f587]) ).
cnf(s24,plain,
( ~ spl38_4
| spl38_30 ),
inference(sat_conversion,[],[f591]) ).
cnf(s25,plain,
( ~ spl38_4
| ~ spl38_31 ),
inference(sat_conversion,[],[f595]) ).
cnf(s26,plain,
spl38_6,
inference(sat_conversion,[],[f597]) ).
cnf(s27,plain,
spl38_7,
inference(sat_conversion,[],[f599]) ).
cnf(s28,plain,
( ~ spl38_17
| ~ spl38_18
| ~ spl38_19
| ~ spl38_20
| spl38_21 ),
inference(sat_conversion,[],[f605]) ).
cnf(s29,plain,
( ~ spl38_5
| ~ spl38_8
| ~ spl38_9
| ~ spl38_10
| spl38_11 ),
inference(sat_conversion,[],[f611]) ).
cnf(s30,plain,
( ~ spl38_12
| ~ spl38_13
| ~ spl38_14
| ~ spl38_15
| spl38_16 ),
inference(sat_conversion,[],[f617]) ).
cnf(s31,plain,
( ~ spl38_27
| ~ spl38_28
| ~ spl38_29
| ~ spl38_30
| spl38_31 ),
inference(sat_conversion,[],[f623]) ).
cnf(s32,plain,
( ~ spl38_22
| ~ spl38_23
| ~ spl38_24
| ~ spl38_25
| spl38_26 ),
inference(sat_conversion,[],[f629]) ).
cnf(s33,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| ~ spl38_11 ),
inference(rat,[],[s5,s27,s26]) ).
cnf(s34,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_10 ),
inference(rat,[],[s4,s27,s26]) ).
cnf(s35,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_9 ),
inference(rat,[],[s3,s27,s26]) ).
cnf(s36,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_8 ),
inference(rat,[],[s2,s27,s26]) ).
cnf(s37,plain,
( spl38_1
| spl38_2
| spl38_3
| spl38_4
| spl38_5 ),
inference(rat,[],[s1,s27,s26]) ).
cnf(s38,plain,
( spl38_4
| spl38_3
| spl38_2
| spl38_1 ),
inference(rat,[],[s29,s37,s36,s35,s34,s33]) ).
cnf(s39,plain,
~ spl38_4,
inference(rat,[],[s31,s21,s22,s23,s24,s25]) ).
cnf(s40,plain,
~ spl38_3,
inference(rat,[],[s32,s16,s17,s18,s19,s20]) ).
cnf(s41,plain,
~ spl38_2,
inference(rat,[],[s28,s11,s12,s13,s14,s15]) ).
cnf(s42,plain,
spl38_1,
inference(rat,[],[s38,s40,s39,s41]) ).
cnf(s43,plain,
~ spl38_16,
inference(rat,[],[s10,s42]) ).
cnf(s44,plain,
spl38_15,
inference(rat,[],[s9,s42]) ).
cnf(s45,plain,
spl38_14,
inference(rat,[],[s8,s42]) ).
cnf(s46,plain,
spl38_13,
inference(rat,[],[s7,s42]) ).
cnf(s47,plain,
spl38_12,
inference(rat,[],[s6,s42]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s30,s43,s44,s45,s46,s47]) ).
fof(f630,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV115+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:58:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.07/1.07 % (2144687)Detected formulas, will run a generic FOF schedule.
% 3.07/1.07 % (2144695)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2797175072:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.07/1.07 % (2144695)Instruction limit reached!
% 3.07/1.07 % (2144695)------------------------------
% 3.07/1.07 % (2144695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.07 % (2144695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.07 % (2144695)CaDiCaL version: 2.1.3
% 3.07/1.07 % (2144695)Termination reason: Instruction limit
% 3.07/1.07 % (2144695)Termination phase: Saturation
% 3.07/1.07 % (2144695)Time elapsed: 0.026 s
% 3.07/1.07 % (2144695)Peak memory usage: 88 MB
% 3.07/1.07 % (2144695)Instructions burned: 110 (million)
% 3.07/1.07 % (2144697)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=809389118:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.07/1.07 % (2144694)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=3642337246:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.07/1.07 % (2144692)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=4225302470:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.07/1.07 % (2144696)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4234099654:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.07/1.07 % (2144693)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=3588262593:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.07/1.07 % (2144698)dis-21_1_sil=8000:lcm=predicate:random_seed=1784555504: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)
% 3.07/1.07 % (2144698)First to succeed.
% 3.07/1.07 % (2144696)Also succeeded, but the first one will report.
% 3.07/1.07 % (2144698)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2144687"
% 3.07/1.07 % (2144700)lrs+10_1_sil=8000:sp=occurrence:random_seed=1742223014:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.07/1.07 % (2144697)Instruction limit reached!
% 3.07/1.07 % (2144697)------------------------------
% 3.07/1.07 % (2144697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.07 % (2144697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.07 % (2144697)CaDiCaL version: 2.1.3
% 3.07/1.07 % (2144697)Termination reason: Instruction limit
% 3.07/1.07 % (2144697)Termination phase: Saturation
% 3.07/1.07 % (2144697)Time elapsed: 0.087 s
% 3.07/1.07 % (2144697)Peak memory usage: 89 MB
% 3.07/1.07 % (2144697)Instructions burned: 139 (million)
% 3.07/1.07 % (2144700)Instruction limit reached!
% 3.07/1.07 % (2144700)------------------------------
% 3.07/1.07 % (2144700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.07 % (2144700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.07 % (2144700)CaDiCaL version: 2.1.3
% 3.07/1.07 % (2144700)Termination reason: Instruction limit
% 3.07/1.07 % (2144700)Termination phase: Saturation
% 3.07/1.07 % (2144700)Time elapsed: 0.098 s
% 3.07/1.07 % (2144700)Peak memory usage: 91 MB
% 3.07/1.07 % (2144700)Instructions burned: 286 (million)
% 3.07/1.07 % (2144708)lrs+10_1_sil=32000:urr=on:br=off:random_seed=806840066:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.07/1.07 % (2144708)Also succeeded, but the first one will report.
% 3.07/1.07 % (2144709)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4286760106:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.07/1.07 % (2144698)Refutation found. Thanks to Tanya!
% 3.07/1.07 % SZS status Theorem for theBenchmark
% 3.07/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.26 % (2144698)------------------------------
% 3.53/1.26 % (2144698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.26 % (2144698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.26 % (2144698)CaDiCaL version: 2.1.3
% 3.53/1.26 % (2144698)Termination reason: Refutation
% 3.53/1.26 % (2144698)Time elapsed: 0.010 s
% 3.53/1.26 % (2144698)Peak memory usage: 89 MB
% 3.53/1.26 % (2144698)Instructions burned: 17 (million)
% 3.53/1.26 % (2144698)------------------------------
% 3.53/1.26 % (2144698)------------------------------
% 3.53/1.26 % (2144687)Success in time 0.416 s
% 3.53/1.26 % Vampire exiting
%------------------------------------------------------------------------------