%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV053+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 : n010.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 01:08:00 PM UTC 2026
% Result : Theorem 1.06s 0.94s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 18 unt; 1 def)
% Number of atoms : 293 ( 77 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 371 ( 139 ~; 140 |; 82 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 65 ( 47 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
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,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(X0,minus(pv12,n1)) )
=> a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))))) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(X2,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1 ) )
=> ( n0 = sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(X4,minus(pv12,n1)) )
=> a_select3(q,pv10,X4) = divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X5,n0),a_select2(x,pv10)),minus(a_select3(center,X5,n0),a_select2(x,pv10)))))) )
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(X6,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X6,X7)) = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0031) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(X0,minus(pv12,n1)) )
=> a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))))) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(X2,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1 ) )
=> ( n0 = sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(X4,minus(pv12,n1)) )
=> a_select3(q,pv10,X4) = divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X5,n0),a_select2(x,pv10)),minus(a_select3(center,X5,n0),a_select2(x,pv10)))))) )
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(X6,minus(pv10,n1)) )
=> sum(n0,minus(n5,n1),a_select3(q,X6,X7)) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,plain,
( ( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| ? [X4,X5] :
( a_select3(q,pv10,X4) != divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X5,n0),a_select2(x,pv10)),minus(a_select3(center,X5,n0),a_select2(x,pv10))))))
& leq(n0,X4)
& leq(X4,minus(pv12,n1)) )
| ? [X6,X7] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7))
& leq(n0,X6)
& leq(X6,minus(pv10,n1)) ) )
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X0,X1] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10))))))
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv12,n1)) )
& ! [X2,X3] :
( sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1
| ~ leq(n0,X2)
| ~ leq(X2,minus(pv10,n1)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| ? [X4,X5] :
( a_select3(q,pv10,X4) != divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X5,n0),a_select2(x,pv10)),minus(a_select3(center,X5,n0),a_select2(x,pv10))))))
& leq(n0,X4)
& leq(X4,minus(pv12,n1)) )
| ? [X6,X7] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7))
& leq(n0,X6)
& leq(X6,minus(pv10,n1)) ) )
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X0,X1] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10))))))
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv12,n1)) )
& ! [X2,X3] :
( sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1
| ~ leq(n0,X2)
| ~ leq(X2,minus(pv10,n1)) ) ),
inference(flattening,[],[f94]) ).
fof(f118,definition,
( ? [X6,X7] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7))
& leq(n0,X6)
& leq(X6,minus(pv10,n1)) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f119,plain,
( ( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| ? [X4,X5] :
( a_select3(q,pv10,X4) != divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X5,n0),a_select2(x,pv10)),minus(a_select3(center,X5,n0),a_select2(x,pv10))))))
& leq(n0,X4)
& leq(X4,minus(pv12,n1)) )
| sP0 )
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X0,X1] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10))))))
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv12,n1)) )
& ! [X2,X3] :
( sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1
| ~ leq(n0,X2)
| ~ leq(X2,minus(pv10,n1)) ) ),
inference(definition_folding,[],[f95,f118]) ).
fof(f120,plain,
( ? [X6,X7] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7))
& leq(n0,X6)
& leq(X6,minus(pv10,n1)) )
| ~ sP0 ),
inference(nnf_transformation,[],[f118]) ).
fof(f121,plain,
( ? [X0,X1] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X0,X1))
& leq(n0,X0)
& leq(X0,minus(pv10,n1)) )
| ~ sP0 ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
( ( n1 != sum(n0,minus(n5,n1),a_select3(q,sK1,sK2))
& leq(n0,sK1)
& leq(sK1,minus(pv10,n1)) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f121]) ).
fof(f123,plain,
( ( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| ? [X0,X1] :
( a_select3(q,pv10,X0) != divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10))))))
& leq(n0,X0)
& leq(X0,minus(pv12,n1)) )
| sP0 )
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X2,X3] :
( a_select3(q,pv10,X2) = divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X3,n0),a_select2(x,pv10)),minus(a_select3(center,X3,n0),a_select2(x,pv10))))))
| ~ leq(n0,X2)
| ~ leq(X2,minus(pv12,n1)) )
& ! [X4,X5] :
( n1 = sum(n0,minus(n5,n1),a_select3(q,X4,X5))
| ~ leq(n0,X4)
| ~ leq(X4,minus(pv10,n1)) ) ),
inference(rectify,[],[f119]) ).
fof(f124,plain,
( ( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| ( a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
& leq(n0,sK3)
& leq(sK3,minus(pv12,n1)) )
| sP0 )
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,minus(n135300,n1))
& leq(pv12,minus(n5,n1))
& ! [X2,X3] :
( a_select3(q,pv10,X2) = divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X3,n0),a_select2(x,pv10)),minus(a_select3(center,X3,n0),a_select2(x,pv10))))))
| ~ leq(n0,X2)
| ~ leq(X2,minus(pv12,n1)) )
& ! [X4,X5] :
( n1 = sum(n0,minus(n5,n1),a_select3(q,X4,X5))
| ~ leq(n0,X4)
| ~ leq(X4,minus(pv10,n1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f123]) ).
fof(f128,plain,
( leq(sK1,minus(pv10,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f129,plain,
( leq(n0,sK1)
| ~ sP0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f130,plain,
( n1 != sum(n0,minus(n5,n1),a_select3(q,sK1,sK2))
| ~ sP0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f131,plain,
! [X4,X5] :
( n1 = sum(n0,minus(n5,n1),a_select3(q,X4,X5))
| ~ leq(n0,X4)
| ~ leq(X4,minus(pv10,n1)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f132,plain,
! [X2,X3] :
( a_select3(q,pv10,X2) = divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X3,n0),a_select2(x,pv10)),minus(a_select3(center,X3,n0),a_select2(x,pv10))))))
| ~ leq(n0,X2)
| ~ leq(X2,minus(pv12,n1)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f133,plain,
leq(pv12,minus(n5,n1)),
inference(cnf_transformation,[],[f124]) ).
fof(f134,plain,
leq(pv10,minus(n135300,n1)),
inference(cnf_transformation,[],[f124]) ).
fof(f135,plain,
leq(n0,pv12),
inference(cnf_transformation,[],[f124]) ).
fof(f136,plain,
leq(n0,pv10),
inference(cnf_transformation,[],[f124]) ).
fof(f137,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| leq(sK3,minus(pv12,n1))
| sP0 ),
inference(cnf_transformation,[],[f124]) ).
fof(f138,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| leq(n0,sK3)
| sP0 ),
inference(cnf_transformation,[],[f124]) ).
fof(f139,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv10)
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
| sP0 ),
inference(cnf_transformation,[],[f124]) ).
fof(f145,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f157,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f174,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f198,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f202,plain,
! [X0] : minus(succ(X0),n1) = X0,
inference(definition_unfolding,[],[f198,f157]) ).
fof(f207,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| leq(n0,sK3)
| sP0 ),
inference(forward_subsumption_resolution,[],[f138,f136]) ).
fof(f208,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| leq(n0,sK3)
| sP0 ),
inference(forward_subsumption_resolution,[],[f207,f135]) ).
fof(f209,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(pv12,minus(n5,n1))
| leq(n0,sK3)
| sP0 ),
inference(forward_subsumption_resolution,[],[f208,f134]) ).
fof(f210,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| leq(n0,sK3)
| sP0 ),
inference(forward_subsumption_resolution,[],[f209,f133]) ).
fof(f211,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| leq(sK3,minus(pv12,n1))
| sP0 ),
inference(forward_subsumption_resolution,[],[f137,f136]) ).
fof(f212,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| leq(sK3,minus(pv12,n1))
| sP0 ),
inference(forward_subsumption_resolution,[],[f211,f135]) ).
fof(f213,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(pv12,minus(n5,n1))
| leq(sK3,minus(pv12,n1))
| sP0 ),
inference(forward_subsumption_resolution,[],[f212,f134]) ).
fof(f214,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| leq(sK3,minus(pv12,n1))
| sP0 ),
inference(forward_subsumption_resolution,[],[f213,f133]) ).
fof(f222,plain,
tptp_minus_1 = minus(n0,n1),
inference(superposition,[],[f202,f174]) ).
fof(f228,plain,
( n0 != sum(n0,tptp_minus_1,sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| leq(sK3,minus(pv12,n1))
| sP0 ),
inference(superposition,[],[f214,f222]) ).
fof(f229,plain,
( n0 != sum(n0,tptp_minus_1,sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| leq(n0,sK3)
| sP0 ),
inference(superposition,[],[f210,f222]) ).
fof(f232,plain,
( leq(n0,sK3)
| sP0 ),
inference(forward_subsumption_resolution,[],[f229,f145]) ).
fof(f233,plain,
( leq(sK3,minus(pv12,n1))
| sP0 ),
inference(forward_subsumption_resolution,[],[f228,f145]) ).
fof(f370,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(n0,pv12)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
| sP0 ),
inference(forward_subsumption_resolution,[],[f139,f136]) ).
fof(f371,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv12,minus(n5,n1))
| a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
| sP0 ),
inference(forward_subsumption_resolution,[],[f370,f135]) ).
fof(f372,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| ~ leq(pv12,minus(n5,n1))
| a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
| sP0 ),
inference(forward_subsumption_resolution,[],[f371,f134]) ).
fof(f373,plain,
( n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
| sP0 ),
inference(forward_subsumption_resolution,[],[f372,f133]) ).
fof(f374,plain,
( n0 != sum(n0,tptp_minus_1,sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10)))))
| a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
| sP0 ),
inference(forward_demodulation,[],[f373,f222]) ).
fof(f375,plain,
( a_select3(q,pv10,sK3) != divide(sqrt(times(minus(a_select3(center,sK3,n0),a_select2(x,pv10)),minus(a_select3(center,sK3,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10))))))
| sP0 ),
inference(forward_subsumption_resolution,[],[f374,f145]) ).
fof(f376,plain,
( a_select3(q,pv10,sK3) != a_select3(q,pv10,sK3)
| sP0
| ~ leq(n0,sK3)
| ~ leq(sK3,minus(pv12,n1)) ),
inference(superposition,[],[f375,f132]) ).
fof(f377,plain,
( sP0
| ~ leq(n0,sK3)
| ~ leq(sK3,minus(pv12,n1)) ),
inference(trivial_inequality_removal,[],[f376]) ).
fof(f378,plain,
( sP0
| ~ leq(sK3,minus(pv12,n1)) ),
inference(forward_subsumption_resolution,[],[f377,f232]) ).
fof(f379,plain,
sP0,
inference(forward_subsumption_resolution,[],[f378,f233]) ).
fof(f450,plain,
n1 != sum(n0,minus(n5,n1),a_select3(q,sK1,sK2)),
inference(forward_subsumption_resolution,[],[f130,f379]) ).
fof(f451,plain,
( n1 != n1
| ~ leq(n0,sK1)
| ~ leq(sK1,minus(pv10,n1)) ),
inference(superposition,[],[f450,f131]) ).
fof(f452,plain,
( ~ leq(sK1,minus(pv10,n1))
| ~ leq(n0,sK1) ),
inference(trivial_inequality_removal,[],[f451]) ).
fof(f453,plain,
( ~ leq(n0,sK1)
| ~ sP0 ),
inference(resolution,[],[f452,f128]) ).
fof(f457,plain,
~ sP0,
inference(forward_subsumption_resolution,[],[f453,f129]) ).
fof(f458,plain,
$false,
inference(forward_subsumption_resolution,[],[f457,f379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV053+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 09:45:47 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.24 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
% 1.06/0.94 % (1813243)Detected formulas, will run a generic FOF schedule.
% 1.06/0.94 % (1813252)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3067794169:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.06/0.94 % (1813252)First to succeed.
% 1.06/0.94 % (1813252)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1813243"
% 1.06/0.94 % (1813250)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=3136922235:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.06/0.94 % (1813253)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2058151874:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.06/0.94 % (1813248)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=3248897301:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.06/0.94 % (1813249)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=1000224856:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.06/0.94 % (1813251)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3794872864:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.06/0.94 % (1813254)dis-21_1_sil=8000:lcm=predicate:random_seed=4148883926: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)
% 1.06/0.94 % (1813251)Instruction limit reached!
% 1.06/0.94 % (1813251)------------------------------
% 1.06/0.94 % (1813251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.94 % (1813251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.94 % (1813251)CaDiCaL version: 2.1.3
% 1.06/0.94 % (1813251)Termination reason: Instruction limit
% 1.06/0.94 % (1813251)Termination phase: Saturation
% 1.06/0.94 % (1813251)Time elapsed: 0.054 s
% 1.06/0.94 % (1813251)Peak memory usage: 89 MB
% 1.06/0.94 % (1813251)Instructions burned: 110 (million)
% 1.06/0.94 % (1813254)Instruction limit reached!
% 1.06/0.94 % (1813254)------------------------------
% 1.06/0.94 % (1813254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.94 % (1813254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.94 % (1813254)CaDiCaL version: 2.1.3
% 1.06/0.94 % (1813254)Termination reason: Instruction limit
% 1.06/0.94 % (1813254)Termination phase: Saturation
% 1.06/0.94 % (1813254)Time elapsed: 0.065 s
% 1.06/0.94 % (1813254)Peak memory usage: 89 MB
% 1.06/0.94 % (1813254)Instructions burned: 130 (million)
% 1.06/0.94 % (1813253)Instruction limit reached!
% 1.06/0.94 % (1813253)------------------------------
% 1.06/0.94 % (1813253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.06/0.94 % (1813253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.94 % (1813253)CaDiCaL version: 2.1.3
% 1.06/0.94 % (1813253)Termination reason: Instruction limit
% 1.06/0.94 % (1813253)Termination phase: Saturation
% 1.06/0.94 % (1813253)Time elapsed: 0.088 s
% 1.06/0.94 % (1813253)Peak memory usage: 90 MB
% 1.06/0.94 % (1813253)Instructions burned: 139 (million)
% 1.06/0.94 % (1813252)Refutation found. Thanks to Tanya!
% 1.06/0.94 % SZS status Theorem for theBenchmark
% 1.06/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.14 % (1813252)------------------------------
% 0.21/1.14 % (1813252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.14 % (1813252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.14 % (1813252)CaDiCaL version: 2.1.3
% 0.21/1.14 % (1813252)Termination reason: Refutation
% 0.21/1.14 % (1813252)Time elapsed: 0.006 s
% 0.21/1.14 % (1813252)Peak memory usage: 88 MB
% 0.21/1.14 % (1813252)Instructions burned: 18 (million)
% 0.21/1.14 % (1813252)------------------------------
% 0.21/1.14 % (1813252)------------------------------
% 0.21/1.14 % (1813243)Success in time 0.266 s
% 0.21/1.14 % Vampire exiting
%------------------------------------------------------------------------------