%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV114+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 1.10s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 96 ( 14 unt; 3 def)
% Number of atoms : 554 ( 72 equ)
% Maximal formula atoms : 39 ( 5 avg)
% Number of connectives : 687 ( 229 ~; 259 |; 178 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 18 con; 0-3 aty)
% Number of variables : 136 ( 98 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( ( gt(X0,X1)
& gt(X1,X2) )
=> gt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
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) ) )
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X6,X7) = a_select3(q_ds1_filter,X7,X6) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X8,X9) = a_select3(r_ds1_filter,X9,X8) )
& ! [X10,X11] :
( ( leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X10,X11) = a_select3(pminus_ds1_filter,X11,X10) )
& ! [X12] :
( ( leq(n0,X12)
& leq(X12,minus(n0,n1)) )
=> ! [X13] :
( ( leq(n0,X13)
& leq(X13,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0007) ).
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) ) )
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
=> a_select3(q_ds1_filter,X6,X7) = a_select3(q_ds1_filter,X7,X6) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
=> a_select3(r_ds1_filter,X8,X9) = a_select3(r_ds1_filter,X9,X8) )
& ! [X10,X11] :
( ( leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,X10,X11) = a_select3(pminus_ds1_filter,X11,X10) )
& ! [X12] :
( ( leq(n0,X12)
& leq(X12,minus(n0,n1)) )
=> ! [X13] :
( ( leq(n0,X13)
& leq(X13,minus(n6,n1)) )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f104,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ? [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) != a_select3(q_ds1_filter,X7,X6)
& leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
| ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& leq(n0,X13)
& leq(X13,minus(n6,n1)) )
& leq(n0,X12)
& leq(X12,minus(n0,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)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f105,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ? [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) != a_select3(q_ds1_filter,X7,X6)
& leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
| ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& leq(n0,X13)
& leq(X13,minus(n6,n1)) )
& leq(n0,X12)
& leq(X12,minus(n0,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)) ) ),
inference(flattening,[],[f104]) ).
fof(f108,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f108]) ).
fof(f120,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X0,X1)
| ~ gt(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f121,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X0,X1)
| ~ gt(X1,X2) ),
inference(flattening,[],[f120]) ).
fof(f130,definition,
( ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& leq(n0,X13)
& leq(X13,minus(n6,n1)) )
& leq(n0,X12)
& leq(X12,minus(n0,n1)) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f131,definition,
( ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f132,definition,
( ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f133,plain,
( ( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| ? [X6,X7] :
( a_select3(q_ds1_filter,X6,X7) != a_select3(q_ds1_filter,X7,X6)
& leq(n0,X6)
& leq(n0,X7)
& leq(X6,minus(n6,n1))
& leq(X7,minus(n6,n1)) )
| 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)) ) ),
inference(definition_folding,[],[f105,f132,f131,f130]) ).
fof(f134,plain,
( ? [X8,X9] :
( a_select3(r_ds1_filter,X8,X9) != a_select3(r_ds1_filter,X9,X8)
& leq(n0,X8)
& leq(n0,X9)
& leq(X8,minus(n3,n1))
& leq(X9,minus(n3,n1)) )
| ~ 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,
( ? [X10,X11] :
( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
& leq(n0,X10)
& leq(n0,X11)
& leq(X10,minus(n6,n1))
& leq(X11,minus(n6,n1)) )
| ~ 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,
( ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& leq(n0,X13)
& leq(X13,minus(n6,n1)) )
& leq(n0,X12)
& leq(X12,minus(n0,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(n0,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(n0,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(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)) ) ),
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(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)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f143]) ).
fof(f147,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
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(n0,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f159,plain,
( leq(n0,sK7)
| ~ sP0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f163,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(f164,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(f165,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(f166,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[],[f144]) ).
fof(f167,plain,
leq(n0,pv5),
inference(cnf_transformation,[],[f144]) ).
fof(f168,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(sK10,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f169,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(sK9,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f170,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(n0,sK10)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f171,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,minus(n999,n1))
| leq(n0,sK9)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f172,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(f174,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f187,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f206,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X0,X1)
| ~ gt(X1,X2) ),
inference(cnf_transformation,[],[f121]) ).
fof(f221,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f246,plain,
! [X0,X1] :
( ~ leq(X0,minus(X1,n1))
| gt(X1,X0) ),
inference(definition_unfolding,[],[f221,f187]) ).
fof(f247,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(n0,sK10)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f170,f167]) ).
fof(f248,plain,
( leq(n0,sK10)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f247,f166]) ).
fof(f249,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(n0,sK9)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f171,f167]) ).
fof(f250,plain,
( leq(n0,sK9)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f249,f166]) ).
fof(f251,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(sK10,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f168,f167]) ).
fof(f252,plain,
( leq(sK10,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f251,f166]) ).
fof(f253,plain,
( ~ leq(pv5,minus(n999,n1))
| leq(sK9,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f169,f167]) ).
fof(f254,plain,
( leq(sK9,minus(n6,n1))
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f253,f166]) ).
fof(f255,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,[],[f172,f167]) ).
fof(f256,plain,
( a_select3(q_ds1_filter,sK9,sK10) != a_select3(q_ds1_filter,sK10,sK9)
| sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f255,f166]) ).
fof(f258,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,[],[f256,f165]) ).
fof(f259,plain,
( sP2
| sP1
| sP0
| ~ leq(n0,sK9)
| ~ leq(n0,sK10)
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(trivial_inequality_removal,[],[f258]) ).
fof(f261,plain,
( sP2
| sP1
| sP0
| ~ leq(n0,sK10)
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f259,f250]) ).
fof(f263,plain,
( sP2
| sP1
| sP0
| ~ leq(sK9,minus(n6,n1))
| ~ leq(sK10,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f261,f248]) ).
fof(f265,plain,
( sP2
| sP1
| sP0
| ~ leq(sK10,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f263,f254]) ).
fof(f267,plain,
( sP2
| sP1
| sP0 ),
inference(forward_subsumption_resolution,[],[f265,f252]) ).
fof(f403,plain,
( gt(n0,sK7)
| ~ sP0 ),
inference(resolution,[],[f246,f158]) ).
fof(f480,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1) ),
inference(resolution,[],[f206,f205]) ).
fof(f507,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,f164]) ).
fof(f508,plain,
( ~ sP2
| ~ leq(n0,sK4)
| ~ leq(n0,sK3)
| ~ leq(sK4,minus(n3,n1))
| ~ leq(sK3,minus(n3,n1)) ),
inference(trivial_inequality_removal,[],[f507]) ).
fof(f510,plain,
( ~ sP2
| ~ leq(n0,sK3)
| ~ leq(sK4,minus(n3,n1))
| ~ leq(sK3,minus(n3,n1)) ),
inference(forward_subsumption_resolution,[],[f508,f150]) ).
fof(f512,plain,
( ~ sP2
| ~ leq(sK4,minus(n3,n1))
| ~ leq(sK3,minus(n3,n1)) ),
inference(forward_subsumption_resolution,[],[f510,f151]) ).
fof(f514,plain,
( ~ sP2
| ~ leq(sK3,minus(n3,n1)) ),
inference(forward_subsumption_resolution,[],[f512,f148]) ).
fof(f516,plain,
~ sP2,
inference(forward_subsumption_resolution,[],[f514,f149]) ).
fof(f518,plain,
( sP1
| sP0 ),
inference(resolution,[],[f516,f267]) ).
fof(f520,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,f163]) ).
fof(f521,plain,
( ~ sP1
| ~ leq(n0,sK6)
| ~ leq(n0,sK5)
| ~ leq(sK6,minus(n6,n1))
| ~ leq(sK5,minus(n6,n1)) ),
inference(trivial_inequality_removal,[],[f520]) ).
fof(f523,plain,
( ~ sP1
| ~ leq(n0,sK5)
| ~ leq(sK6,minus(n6,n1))
| ~ leq(sK5,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f521,f155]) ).
fof(f525,plain,
( ~ sP1
| ~ leq(sK6,minus(n6,n1))
| ~ leq(sK5,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f523,f156]) ).
fof(f527,plain,
( ~ sP1
| ~ leq(sK5,minus(n6,n1)) ),
inference(forward_subsumption_resolution,[],[f525,f153]) ).
fof(f529,plain,
~ sP1,
inference(forward_subsumption_resolution,[],[f527,f154]) ).
fof(f545,plain,
sP0,
inference(forward_subsumption_resolution,[],[f518,f529]) ).
fof(f759,plain,
gt(n0,sK7),
inference(forward_subsumption_resolution,[],[f403,f545]) ).
fof(f1337,plain,
~ gt(sK7,n0),
inference(resolution,[],[f480,f759]) ).
fof(f1391,plain,
( ~ leq(n0,sK7)
| n0 = sK7 ),
inference(resolution,[],[f1337,f174]) ).
fof(f1735,plain,
( n0 = sK7
| ~ sP0 ),
inference(resolution,[],[f1391,f159]) ).
fof(f1738,plain,
n0 = sK7,
inference(forward_subsumption_resolution,[],[f1735,f545]) ).
fof(f1806,plain,
gt(sK7,sK7),
inference(superposition,[],[f759,f1738]) ).
fof(f1813,plain,
$false,
inference(forward_subsumption_resolution,[],[f1806,f205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV114+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 09:55:56 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.07/1.10 % (1067274)Detected formulas, will run a generic FOF schedule.
% 3.07/1.10 % (1067336)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=1154121496:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.07/1.10 % (1067339)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3084820384:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.07/1.10 % (1067334)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=2716236282:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.07/1.10 % (1067335)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=974419743:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.07/1.10 % (1067337)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2270687439:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.07/1.10 % (1067338)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3709636998:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.07/1.10 % (1067340)dis-21_1_sil=8000:lcm=predicate:random_seed=2420304073: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)
% 3.07/1.10 % (1067338)First to succeed.
% 3.07/1.10 % (1067338)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1067274"
% 3.07/1.10 % (1067337)Instruction limit reached!
% 3.07/1.10 % (1067337)------------------------------
% 3.07/1.10 % (1067337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.10 % (1067337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.10 % (1067337)CaDiCaL version: 2.1.3
% 3.07/1.10 % (1067337)Termination reason: Instruction limit
% 3.07/1.10 % (1067337)Termination phase: Saturation
% 3.07/1.10 % (1067337)Time elapsed: 0.048 s
% 3.07/1.10 % (1067337)Peak memory usage: 88 MB
% 3.07/1.10 % (1067337)Instructions burned: 112 (million)
% 3.07/1.10 % (1067340)Instruction limit reached!
% 3.07/1.10 % (1067340)------------------------------
% 3.07/1.10 % (1067340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.10 % (1067340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.10 % (1067340)CaDiCaL version: 2.1.3
% 3.07/1.10 % (1067340)Termination reason: Instruction limit
% 3.07/1.10 % (1067340)Termination phase: Saturation
% 3.07/1.10 % (1067340)Time elapsed: 0.071 s
% 3.07/1.10 % (1067340)Peak memory usage: 89 MB
% 3.07/1.10 % (1067340)Instructions burned: 130 (million)
% 3.07/1.10 % (1067339)Instruction limit reached!
% 3.07/1.10 % (1067339)------------------------------
% 3.07/1.10 % (1067339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.10 % (1067339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.10 % (1067339)CaDiCaL version: 2.1.3
% 3.07/1.10 % (1067339)Termination reason: Instruction limit
% 3.07/1.10 % (1067339)Termination phase: Saturation
% 3.07/1.10 % (1067339)Time elapsed: 0.087 s
% 3.07/1.10 % (1067339)Peak memory usage: 89 MB
% 3.07/1.10 % (1067339)Instructions burned: 139 (million)
% 3.07/1.10 % (1067348)lrs+10_1_sil=8000:sp=occurrence:random_seed=1981918874:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.07/1.10 % (1067350)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3482151350:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.07/1.10 % (1067349)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4012510539:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.07/1.10 % (1067349)Refutation not found, incomplete strategy
% 3.07/1.10 % (1067349)------------------------------
% 3.07/1.10 % (1067349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.10 % (1067349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.10 % (1067349)CaDiCaL version: 2.1.3
% 3.07/1.10 % (1067349)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.10 % (1067349)Time elapsed: 0.010 s
% 3.07/1.10 % (1067349)Peak memory usage: 89 MB
% 3.07/1.10 % (1067349)Instructions burned: 16 (million)
% 3.07/1.10 % (1067338)Refutation found. Thanks to Tanya!
% 3.07/1.10 % SZS status Theorem for theBenchmark
% 3.07/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.19 % (1067338)------------------------------
% 3.62/1.19 % (1067338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.19 % (1067338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.19 % (1067338)CaDiCaL version: 2.1.3
% 3.62/1.19 % (1067338)Termination reason: Refutation
% 3.62/1.19 % (1067338)Time elapsed: 0.035 s
% 3.62/1.19 % (1067338)Peak memory usage: 89 MB
% 3.62/1.19 % (1067338)Instructions burned: 59 (million)
% 3.62/1.19 % (1067338)------------------------------
% 3.62/1.19 % (1067338)------------------------------
% 3.62/1.19 % (1067274)Success in time 0.435 s
% 3.62/1.19 % Vampire exiting
%------------------------------------------------------------------------------