%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV112+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 : n026.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 1.03s 0.95s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 90 ( 14 unt; 3 def)
% Number of atoms : 629 ( 87 equ)
% Maximal formula atoms : 51 ( 6 avg)
% Number of connectives : 816 ( 277 ~; 302 |; 213 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-3 aty)
% Number of variables : 139 ( 101 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [X0] : plus(n1,X0) = succ(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
fof(f53,conjecture,
( ( leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,minus(n999,n1))
& leq(pv57,minus(n6,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,pv57)
& leq(X7,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) )
& ! [X8] :
( ( leq(n0,X8)
& leq(X8,minus(pv57,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] :
( ( leq(n0,X16)
& leq(X16,minus(plus(n1,pv57),n1)) )
=> ! [X17] :
( ( leq(n0,X17)
& leq(X17,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X16,X17) = a_select3(id_ds1_filter,X17,X16) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0005) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,minus(n999,n1))
& leq(pv57,minus(n6,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,pv57)
& leq(X7,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) )
& ! [X8] :
( ( leq(n0,X8)
& leq(X8,minus(pv57,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] :
( ( leq(n0,X16)
& leq(X16,minus(plus(n1,pv57),n1)) )
=> ! [X17] :
( ( leq(n0,X17)
& leq(X17,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X16,X17) = a_select3(id_ds1_filter,X17,X16) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f104,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(id_ds1_filter,X16,X17) != a_select3(id_ds1_filter,X17,X16)
& leq(n0,X17)
& leq(X17,minus(n6,n1)) )
& leq(n0,X16)
& leq(X16,minus(plus(n1,pv57),n1)) ) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,minus(n999,n1))
& leq(pv57,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)) )
& ! [X6,X7] :
( a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,pv57)
| ~ 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(pv57,n1)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f105,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(id_ds1_filter,X16,X17) != a_select3(id_ds1_filter,X17,X16)
& leq(n0,X17)
& leq(X17,minus(n6,n1)) )
& leq(n0,X16)
& leq(X16,minus(plus(n1,pv57),n1)) ) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,minus(n999,n1))
& leq(pv57,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)) )
& ! [X6,X7] :
( a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,pv57)
| ~ 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(pv57,n1)) ) ),
inference(flattening,[],[f104]) ).
fof(f130,definition,
( ? [X16] :
( ? [X17] :
( a_select3(id_ds1_filter,X16,X17) != a_select3(id_ds1_filter,X17,X16)
& leq(n0,X17)
& leq(X17,minus(n6,n1)) )
& leq(n0,X16)
& leq(X16,minus(plus(n1,pv57),n1)) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f131,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)) )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f132,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)) )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f133,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)) )
| sP2
| sP1
| sP0 )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,minus(n999,n1))
& leq(pv57,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)) )
& ! [X6,X7] :
( a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,pv57)
| ~ 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(pv57,n1)) ) ),
inference(definition_folding,[],[f105,f132,f131,f130]) ).
fof(f134,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)) )
| ~ sP2 ),
inference(nnf_transformation,[],[f132]) ).
fof(f135,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)) )
| ~ sP2 ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
( ( a_select3(r_ds1_filter,sK3,sK4) != a_select3(r_ds1_filter,sK4,sK3)
& leq(n0,sK3)
& leq(n0,sK4)
& leq(sK3,minus(n3,n1))
& leq(sK4,minus(n3,n1)) )
| ~ sP2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f135]) ).
fof(f137,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)) )
| ~ sP1 ),
inference(nnf_transformation,[],[f131]) ).
fof(f138,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,[],[f137]) ).
fof(f139,plain,
( ( a_select3(pminus_ds1_filter,sK5,sK6) != a_select3(pminus_ds1_filter,sK6,sK5)
& leq(n0,sK5)
& leq(n0,sK6)
& leq(sK5,minus(n6,n1))
& leq(sK6,minus(n6,n1)) )
| ~ sP1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f138]) ).
fof(f140,plain,
( ? [X16] :
( ? [X17] :
( a_select3(id_ds1_filter,X16,X17) != a_select3(id_ds1_filter,X17,X16)
& leq(n0,X17)
& leq(X17,minus(n6,n1)) )
& leq(n0,X16)
& leq(X16,minus(plus(n1,pv57),n1)) )
| ~ sP0 ),
inference(nnf_transformation,[],[f130]) ).
fof(f141,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(plus(n1,pv57),n1)) )
| ~ sP0 ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
( ( a_select3(id_ds1_filter,sK7,sK8) != a_select3(id_ds1_filter,sK8,sK7)
& leq(n0,sK8)
& leq(sK8,minus(n6,n1))
& leq(n0,sK7)
& leq(sK7,minus(plus(n1,pv57),n1)) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f141]) ).
fof(f143,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)) )
| sP2
| sP1
| sP0 )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,minus(n999,n1))
& leq(pv57,minus(n6,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(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,pv57)
| ~ 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(pv57,n1)) ) ),
inference(rectify,[],[f133]) ).
fof(f144,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ( 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)) )
| sP2
| sP1
| sP0 )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,minus(n999,n1))
& leq(pv57,minus(n6,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(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,pv57)
| ~ 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(pv57,n1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f143]) ).
fof(f148,plain,
( leq(sK4,minus(n3,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f149,plain,
( leq(sK3,minus(n3,n1))
| ~ sP2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f150,plain,
( leq(n0,sK4)
| ~ sP2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f151,plain,
( leq(n0,sK3)
| ~ sP2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f152,plain,
( a_select3(r_ds1_filter,sK3,sK4) != a_select3(r_ds1_filter,sK4,sK3)
| ~ sP2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f153,plain,
( leq(sK6,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f154,plain,
( leq(sK5,minus(n6,n1))
| ~ sP1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f155,plain,
( leq(n0,sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f156,plain,
( leq(n0,sK5)
| ~ sP1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f157,plain,
( a_select3(pminus_ds1_filter,sK5,sK6) != a_select3(pminus_ds1_filter,sK6,sK5)
| ~ sP1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f158,plain,
( leq(sK7,minus(plus(n1,pv57),n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f159,plain,
( leq(n0,sK7)
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f160,plain,
( leq(sK8,minus(n6,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f161,plain,
( leq(n0,sK8)
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f162,plain,
( a_select3(id_ds1_filter,sK7,sK8) != a_select3(id_ds1_filter,sK8,sK7)
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f164,plain,
! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,pv57)
| ~ leq(X9,minus(n6,n1)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f165,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,[],[f144]) ).
fof(f166,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,[],[f144]) ).
fof(f167,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,[],[f144]) ).
fof(f169,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f144]) ).
fof(f171,plain,
leq(n0,pv5),
inference(cnf_transformation,[],[f144]) ).
fof(f172,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(sK10,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f173,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(sK9,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f174,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(n0,sK10)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f175,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(n0,sK9)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f176,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f193,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f201,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f247,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f280,plain,
! [X0] : minus(plus(n1,X0),n1) = X0,
inference(definition_unfolding,[],[f247,f201,f193]) ).
fof(f284,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(n0,sK10)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f174,f171]) ).
fof(f285,plain,
( leq(n0,sK10)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f284,f169]) ).
fof(f286,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(n0,sK9)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f175,f171]) ).
fof(f287,plain,
( leq(n0,sK9)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f286,f169]) ).
fof(f288,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(sK10,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f172,f171]) ).
fof(f289,plain,
( leq(sK10,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f288,f169]) ).
fof(f290,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(sK9,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f173,f171]) ).
fof(f291,plain,
( leq(sK9,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f290,f169]) ).
fof(f292,plain,
( ~ leq(pv5,minus(n999,n1))
| a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f176,f171]) ).
fof(f293,plain,
( a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f292,f169]) ).
fof(f295,plain,
( a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK9,sK10)
| sP2
| sP1
| sP0
| ~ leq(n0,sK9)
| ~ leq(n0,sK10)
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(superposition,[],[f293,f167]) ).
fof(f296,plain,
( sP2
| sP1
| sP0
| ~ leq(n0,sK9)
| ~ leq(n0,sK10)
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(trivial_inequality_removal,[],[f295]) ).
fof(f298,plain,
( sP2
| sP1
| sP0
| ~ leq(n0,sK10)
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f296,f287]) ).
fof(f300,plain,
( sP2
| sP1
| sP0
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f298,f285]) ).
fof(f302,plain,
( sP2
| sP1
| sP0
| ~ leq(sK10,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f300,f291]) ).
fof(f304,plain,
( sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f302,f289]) ).
fof(f324,plain,
( leq(sK7,pv57)
| ~ sP0 ),
inference(forward_demodulation,[],[f158,f280]) ).
fof(f512,plain,
( a_select3(r_ds1_filter,sK3,sK4) != a_select3(r_ds1_filter,sK3,sK4)
| ~ sP2
| ~ leq(n0,sK4)
| ~ leq(n0,sK3)
| ~ leq(sK4,minus(n3,n1))
| ~ leq(sK3,minus(n3,n1)) ),
inference(superposition,[],[f152,f166]) ).
fof(f513,plain,
( ~ sP2
| ~ leq(n0,sK4)
| ~ leq(n0,sK3)
| ~ leq(sK4,minus(n3,n1))
| ~ leq(sK3,minus(n3,n1)) ),
inference(trivial_inequality_removal,[],[f512]) ).
fof(f515,plain,
( ~ sP2
| ~ leq(n0,sK3)
| ~ leq(sK4,minus(n3,n1))
| ~ leq(sK3,minus(n3,n1)) ),
inference(forward_subsumption_resolution,[],[f513,f150]) ).
fof(f517,plain,
( ~ sP2
| ~ leq(sK4,minus(n3,n1))
| ~ leq(sK3,minus(n3,n1)) ),
inference(forward_subsumption_resolution,[],[f515,f151]) ).
fof(f519,plain,
( ~ sP2
| ~ leq(sK3,minus(n3,n1)) ),
inference(forward_subsumption_resolution,[],[f517,f148]) ).
fof(f521,plain,
~ sP2,
inference(forward_subsumption_resolution,[],[f519,f149]) ).
fof(f523,plain,
( sP1
| sP0 ),
inference(resolution,[],[f521,f304]) ).
fof(f525,plain,
( a_select3(pminus_ds1_filter,sK5,sK6) != a_select3(pminus_ds1_filter,sK5,sK6)
| ~ sP1
| ~ leq(n0,sK6)
| ~ leq(n0,sK5)
| ~ leq(sK6,minus(n6,n1))
| ~ leq(sK5,minus(n6,n1)) ),
inference(superposition,[],[f157,f165]) ).
fof(f526,plain,
( ~ sP1
| ~ leq(n0,sK6)
| ~ leq(n0,sK5)
| ~ leq(sK6,minus(n6,n1))
| ~ leq(sK5,minus(n6,n1)) ),
inference(trivial_inequality_removal,[],[f525]) ).
fof(f528,plain,
( ~ sP1
| ~ leq(n0,sK5)
| ~ leq(sK6,minus(n6,n1))
| ~ leq(sK5,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f526,f155]) ).
fof(f530,plain,
( ~ sP1
| ~ leq(sK6,minus(n6,n1))
| ~ leq(sK5,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f528,f156]) ).
fof(f532,plain,
( ~ sP1
| ~ leq(sK5,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f530,f153]) ).
fof(f534,plain,
~ sP1,
inference(forward_subsumption_resolution,[],[f532,f154]) ).
fof(f538,plain,
( a_select3(id_ds1_filter,sK7,sK8) != a_select3(id_ds1_filter,sK7,sK8)
| ~ sP0
| ~ leq(n0,sK7)
| ~ leq(n0,sK8)
| ~ leq(sK7,pv57)
| ~ leq(sK8,minus(n6,n1)) ),
inference(superposition,[],[f162,f164]) ).
fof(f541,plain,
( ~ sP0
| ~ leq(n0,sK7)
| ~ leq(n0,sK8)
| ~ leq(sK7,pv57)
| ~ leq(sK8,minus(n6,n1)) ),
inference(trivial_inequality_removal,[],[f538]) ).
fof(f545,plain,
( ~ sP0
| ~ leq(n0,sK8)
| ~ leq(sK7,pv57)
| ~ leq(sK8,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f541,f159]) ).
fof(f549,plain,
( ~ sP0
| ~ leq(sK7,pv57)
| ~ leq(sK8,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f545,f161]) ).
fof(f552,plain,
( ~ sP0
| ~ leq(sK8,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f549,f324]) ).
fof(f554,plain,
~ sP0,
inference(forward_subsumption_resolution,[],[f552,f160]) ).
fof(f571,plain,
sP0,
inference(forward_subsumption_resolution,[],[f523,f534]) ).
fof(f572,plain,
$false,
inference(forward_subsumption_resolution,[],[f571,f554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV112+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 09:58:12 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 1.03/0.95 % (3742319)Detected formulas, will run a generic FOF schedule.
% 1.03/0.95 % (3742328)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2255411168:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.03/0.95 % (3742328)First to succeed.
% 1.03/0.95 % (3742328)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3742319"
% 1.03/0.95 % (3742330)dis-21_1_sil=8000:lcm=predicate:random_seed=1356707447: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)
% 1.03/0.95 % (3742329)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3366178873:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.03/0.95 % (3742325)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=541696269:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.03/0.95 % (3742327)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=91965442:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.03/0.95 % (3742324)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=2594579555:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.03/0.95 % (3742326)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=1094452643:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.03/0.95 % (3742327)Instruction limit reached!
% 1.03/0.95 % (3742327)------------------------------
% 1.03/0.95 % (3742327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.03/0.95 % (3742327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.95 % (3742327)CaDiCaL version: 2.1.3
% 1.03/0.95 % (3742327)Termination reason: Instruction limit
% 1.03/0.95 % (3742327)Termination phase: Saturation
% 1.03/0.95 % (3742327)Time elapsed: 0.063 s
% 1.03/0.95 % (3742327)Peak memory usage: 89 MB
% 1.03/0.95 % (3742327)Instructions burned: 111 (million)
% 1.03/0.95 % (3742330)Instruction limit reached!
% 1.03/0.95 % (3742330)------------------------------
% 1.03/0.95 % (3742330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.03/0.95 % (3742330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.95 % (3742330)CaDiCaL version: 2.1.3
% 1.03/0.95 % (3742330)Termination reason: Instruction limit
% 1.03/0.95 % (3742330)Termination phase: Saturation
% 1.03/0.95 % (3742330)Time elapsed: 0.072 s
% 1.03/0.95 % (3742330)Peak memory usage: 89 MB
% 1.03/0.95 % (3742330)Instructions burned: 129 (million)
% 1.03/0.95 % (3742329)Instruction limit reached!
% 1.03/0.95 % (3742329)------------------------------
% 1.03/0.95 % (3742329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.03/0.95 % (3742329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.95 % (3742329)CaDiCaL version: 2.1.3
% 1.03/0.95 % (3742329)Termination reason: Instruction limit
% 1.03/0.95 % (3742329)Termination phase: Saturation
% 1.03/0.95 % (3742329)Time elapsed: 0.090 s
% 1.03/0.95 % (3742329)Peak memory usage: 90 MB
% 1.03/0.95 % (3742329)Instructions burned: 140 (million)
% 1.03/0.95 % (3742328)Refutation found. Thanks to Tanya!
% 1.03/0.95 % SZS status Theorem for theBenchmark
% 1.03/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.04 % (3742328)------------------------------
% 2.50/1.04 % (3742328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.04 % (3742328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.04 % (3742328)CaDiCaL version: 2.1.3
% 2.50/1.04 % (3742328)Termination reason: Refutation
% 2.50/1.04 % (3742328)Time elapsed: 0.007 s
% 2.50/1.04 % (3742328)Peak memory usage: 88 MB
% 2.50/1.04 % (3742328)Instructions burned: 20 (million)
% 2.50/1.04 % (3742328)------------------------------
% 2.50/1.04 % (3742328)------------------------------
% 2.50/1.04 % (3742319)Success in time 0.273 s
% 2.50/1.04 % Vampire exiting
%------------------------------------------------------------------------------