%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:20:04 PM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 23 unt; 6 def)
% Number of atoms : 316 ( 74 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 365 ( 132 ~; 136 |; 82 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 15 con; 0-3 aty)
% Number of variables : 71 ( 0 sgn 53 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',sum_plus_base) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_tptp_minus_1) ).
fof(f29,axiom,
! [X0] : plus(X0,n1) = succ(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',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(f143,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(f144,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,[],[f143]) ).
fof(f164,definition,
( ? [X6,X7] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7))
& leq(n0,X6)
& leq(X6,minus(pv10,n1)) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f165,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)) )
| sP4 )
& 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,[],[f144,f164]) ).
fof(f199,plain,
( ? [X6,X7] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7))
& leq(n0,X6)
& leq(X6,minus(pv10,n1)) )
| ~ sP4 ),
inference(nnf_transformation,[],[f164]) ).
fof(f200,plain,
( ? [X0,X1] :
( n1 != sum(n0,minus(n5,n1),a_select3(q,X0,X1))
& leq(n0,X0)
& leq(X0,minus(pv10,n1)) )
| ~ sP4 ),
inference(rectify,[],[f199]) ).
fof(f201,plain,
( ( n1 != sum(n0,minus(n5,n1),a_select3(q,sK32,sK33))
& leq(n0,sK32)
& leq(sK32,minus(pv10,n1)) )
| ~ sP4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33]),skolemize(X0,sK32),skolemize(X1,sK33)],[f200]) ).
fof(f202,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)) )
| sP4 )
& 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,[],[f165]) ).
fof(f203,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,sK34) != divide(sqrt(times(minus(a_select3(center,sK34,n0),a_select2(x,pv10)),minus(a_select3(center,sK34,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK35,n0),a_select2(x,pv10)),minus(a_select3(center,sK35,n0),a_select2(x,pv10))))))
& leq(n0,sK34)
& leq(sK34,minus(pv12,n1)) )
| sP4 )
& 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,[sK34,sK35]),skolemize(X0,sK34),skolemize(X1,sK35)],[f202]) ).
fof(f281,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f283,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f284,plain,
! [X0] : succ(X0) = plus(X0,n1),
inference(cnf_transformation,[],[f29]) ).
fof(f294,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f295,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f314,plain,
( leq(sK32,minus(pv10,n1))
| ~ sP4 ),
inference(cnf_transformation,[],[f201]) ).
fof(f315,plain,
( leq(n0,sK32)
| ~ sP4 ),
inference(cnf_transformation,[],[f201]) ).
fof(f316,plain,
( n1 != sum(n0,minus(n5,n1),a_select3(q,sK32,sK33))
| ~ sP4 ),
inference(cnf_transformation,[],[f201]) ).
fof(f317,plain,
! [X4,X5] :
( ~ leq(X4,minus(pv10,n1))
| ~ leq(n0,X4)
| n1 = sum(n0,minus(n5,n1),a_select3(q,X4,X5)) ),
inference(cnf_transformation,[],[f203]) ).
fof(f318,plain,
! [X2,X3] :
( ~ leq(X2,minus(pv12,n1))
| ~ leq(n0,X2)
| 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)))))) ),
inference(cnf_transformation,[],[f203]) ).
fof(f319,plain,
leq(pv12,minus(n5,n1)),
inference(cnf_transformation,[],[f203]) ).
fof(f320,plain,
leq(pv10,minus(n135300,n1)),
inference(cnf_transformation,[],[f203]) ).
fof(f321,plain,
leq(n0,pv12),
inference(cnf_transformation,[],[f203]) ).
fof(f322,plain,
leq(n0,pv10),
inference(cnf_transformation,[],[f203]) ).
fof(f323,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(sK34,minus(pv12,n1))
| sP4 ),
inference(cnf_transformation,[],[f203]) ).
fof(f324,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,sK34)
| sP4 ),
inference(cnf_transformation,[],[f203]) ).
fof(f325,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,sK34) != divide(sqrt(times(minus(a_select3(center,sK34,n0),a_select2(x,pv10)),minus(a_select3(center,sK34,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK35,n0),a_select2(x,pv10)),minus(a_select3(center,sK35,n0),a_select2(x,pv10))))))
| sP4 ),
inference(cnf_transformation,[],[f203]) ).
fof(f371,plain,
n0 = plus(tptp_minus_1,n1),
inference(definition_unfolding,[],[f283,f284]) ).
fof(f381,plain,
! [X0] : minus(plus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f295,f294,f284]) ).
fof(f394,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(sK34,minus(pv12,n1))
| sP4 ),
inference(global_subsumption,[],[f323,f322,f321,f320,f319]) ).
fof(f395,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,sK34)
| sP4 ),
inference(global_subsumption,[],[f324,f322,f321,f320,f319]) ).
fof(f396,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,sK34) != divide(sqrt(times(minus(a_select3(center,sK34,n0),a_select2(x,pv10)),minus(a_select3(center,sK34,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,sK35,n0),a_select2(x,pv10)),minus(a_select3(center,sK35,n0),a_select2(x,pv10))))))
| sP4 ),
inference(global_subsumption,[],[f325,f322,f321,f320,f319]) ).
fof(f398,definition,
( spl36_1
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl36_1])],[avatar_definition]) ).
fof(f399,plain,
( sP4
| ~ spl36_1 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f400,plain,
( ~ sP4
| spl36_1 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f402,definition,
( spl36_2
<=> n1 = sum(n0,minus(n5,n1),a_select3(q,sK32,sK33)) ),
introduced(definition,[new_symbols(definition,[spl36_2])],[avatar_definition]) ).
fof(f404,plain,
( n1 != sum(n0,minus(n5,n1),a_select3(q,sK32,sK33))
| spl36_2 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f405,plain,
( ~ spl36_1
| ~ spl36_2 ),
inference(avatar_split_clause,[],[f316,f402,f398]) ).
fof(f443,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,sK34)
| spl36_1 ),
inference(forward_subsumption_resolution,[],[f395,f400]) ).
fof(f445,definition,
( spl36_14
<=> leq(n0,sK34) ),
introduced(definition,[new_symbols(definition,[spl36_14])],[avatar_definition]) ).
fof(f447,plain,
( leq(n0,sK34)
| ~ spl36_14 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f449,definition,
( spl36_15
<=> 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))))) ),
introduced(definition,[new_symbols(definition,[spl36_15])],[avatar_definition]) ).
fof(f451,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)))))
| spl36_15 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f452,plain,
( spl36_14
| ~ spl36_15
| spl36_1 ),
inference(avatar_split_clause,[],[f443,f398,f449,f445]) ).
fof(f456,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(sK34,minus(pv12,n1))
| spl36_1 ),
inference(forward_subsumption_resolution,[],[f394,f400]) ).
fof(f458,definition,
( spl36_16
<=> leq(sK34,minus(pv12,n1)) ),
introduced(definition,[new_symbols(definition,[spl36_16])],[avatar_definition]) ).
fof(f460,plain,
( leq(sK34,minus(pv12,n1))
| ~ spl36_16 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f461,plain,
( spl36_16
| ~ spl36_15
| spl36_1 ),
inference(avatar_split_clause,[],[f456,f398,f449,f458]) ).
fof(f575,plain,
tptp_minus_1 = minus(n0,n1),
inference(superposition,[],[f381,f371]) ).
fof(f578,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)))))
| spl36_15 ),
inference(superposition,[],[f451,f575]) ).
fof(f579,plain,
( $false
| spl36_15 ),
inference(forward_subsumption_resolution,[],[f578,f281]) ).
fof(f580,plain,
spl36_15,
inference(avatar_contradiction_clause,[],[f579]) ).
fof(f593,plain,
( ! [X0] :
( ~ leq(n0,sK34)
| a_select3(q,pv10,sK34) = divide(sqrt(times(minus(a_select3(center,sK34,n0),a_select2(x,pv10)),minus(a_select3(center,sK34,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))))) )
| ~ spl36_16 ),
inference(resolution,[],[f460,f318]) ).
fof(f594,plain,
( ! [X0] : a_select3(q,pv10,sK34) = divide(sqrt(times(minus(a_select3(center,sK34,n0),a_select2(x,pv10)),minus(a_select3(center,sK34,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10))))))
| ~ spl36_14
| ~ spl36_16 ),
inference(forward_subsumption_resolution,[],[f593,f447]) ).
fof(f600,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)))))
| sP4
| ~ spl36_14
| ~ spl36_16 ),
inference(forward_subsumption_resolution,[],[f396,f594]) ).
fof(f601,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)))))
| sP4
| ~ spl36_14
| ~ spl36_16 ),
inference(forward_demodulation,[],[f600,f575]) ).
fof(f602,plain,
( sP4
| ~ spl36_14
| ~ spl36_16 ),
inference(forward_subsumption_resolution,[],[f601,f281]) ).
fof(f603,plain,
( spl36_1
| ~ spl36_14
| ~ spl36_16 ),
inference(avatar_split_clause,[],[f602,f458,f445,f398]) ).
fof(f620,plain,
( leq(n0,sK32)
| ~ spl36_1 ),
inference(forward_subsumption_resolution,[],[f315,f399]) ).
fof(f626,plain,
( leq(sK32,minus(pv10,n1))
| ~ spl36_1 ),
inference(forward_subsumption_resolution,[],[f314,f399]) ).
fof(f627,plain,
( ! [X0] :
( ~ leq(n0,sK32)
| n1 = sum(n0,minus(n5,n1),a_select3(q,sK32,X0)) )
| ~ spl36_1 ),
inference(resolution,[],[f626,f317]) ).
fof(f628,plain,
( ! [X0] : n1 = sum(n0,minus(n5,n1),a_select3(q,sK32,X0))
| ~ spl36_1 ),
inference(forward_subsumption_resolution,[],[f627,f620]) ).
fof(f629,plain,
( n1 != n1
| ~ spl36_1
| spl36_2 ),
inference(superposition,[],[f404,f628]) ).
fof(f630,plain,
( $false
| ~ spl36_1
| spl36_2 ),
inference(trivial_inequality_removal,[],[f629]) ).
fof(f631,plain,
( ~ spl36_1
| spl36_2 ),
inference(avatar_contradiction_clause,[],[f630]) ).
cnf(s166,plain,
( ~ spl36_1
| ~ spl36_2 ),
inference(sat_conversion,[],[f405]) ).
cnf(s204,plain,
( spl36_1
| spl36_14
| ~ spl36_15 ),
inference(sat_conversion,[],[f452]) ).
cnf(s212,plain,
( spl36_1
| ~ spl36_15
| spl36_16 ),
inference(sat_conversion,[],[f461]) ).
cnf(s329,plain,
spl36_15,
inference(sat_conversion,[],[f580]) ).
cnf(s382,plain,
( spl36_1
| ~ spl36_14
| ~ spl36_16 ),
inference(sat_conversion,[],[f603]) ).
cnf(s430,plain,
( ~ spl36_1
| spl36_2 ),
inference(sat_conversion,[],[f631]) ).
cnf(s431,plain,
( spl36_1
| spl36_16 ),
inference(rat,[],[s212,s329]) ).
cnf(s432,plain,
( spl36_1
| spl36_14 ),
inference(rat,[],[s204,s329]) ).
cnf(s433,plain,
spl36_1,
inference(rat,[],[s382,s432,s431]) ).
cnf(s434,plain,
spl36_2,
inference(rat,[],[s430,s433]) ).
cnf(s435,plain,
$false,
inference(rat,[],[s166,s434,s433]) ).
fof(f632,plain,
$false,
inference(avatar_sat_refutation,[],[s435]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 09:45:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.30 % (3890716)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (3890724)dis+10_1_sil=32000:sp=arity:random_seed=1932122769:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (3890722)% WARNING: option uhcvi not known.
% 0.19/0.30 % (3890721)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=75909781_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (3890722)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3533717017:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (3890723)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3664161689:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (3890727)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=525505067:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (3890725)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1863759891:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (3890726)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1414237493:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (3890723) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3890716-3890723"...
% 0.19/0.30 % (3890723)...printing done.
% 0.19/0.30 % (3890723)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (3890723)------------------------------
% 0.19/0.30 % (3890723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3890723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3890723)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3890723)Termination reason: Refutation
% 0.19/0.30 % (3890723)Time elapsed: 0.016 s
% 0.19/0.30 % (3890723)Peak memory usage: 13 MB
% 0.19/0.30 % (3890723)Instructions burned: 28 (million)
% 0.19/0.30 % (3890716)Success in time 0.068 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------