%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV053+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:16:18 PM UTC 2026
% Result : Theorem 1.87s 1.20s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 51 unt; 1 def)
% Number of atoms : 325 ( 106 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 347 ( 126 ~; 129 |; 82 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 60 !; 18 ?; 11 :)
% 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(f30,axiom,
! [X0] : plus(n1,X0) = succ(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_l) ).
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,
( ( ! [X2,X3] :
( ( leq(X2,minus(pv10,n1))
& leq(n0,X2) )
=> sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1 )
& ! [X0,X1] :
( ( leq(X0,minus(pv12,n1))
& leq(n0,X0) )
=> 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(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) )
=> ( ! [X6,X7] :
( ( leq(X6,minus(pv10,n1))
& leq(n0,X6) )
=> sum(n0,minus(n5,n1),a_select3(q,X6,X7)) = n1 )
& ! [X4,X5] :
( ( leq(X4,minus(pv12,n1))
& leq(n0,X4) )
=> 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(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& 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))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0031) ).
fof(f54,negated_conjecture,
~ ( ( ! [X2,X3] :
( ( leq(X2,minus(pv10,n1))
& leq(n0,X2) )
=> sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1 )
& ! [X0,X1] :
( ( leq(X0,minus(pv12,n1))
& leq(n0,X0) )
=> 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(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) )
=> ( ! [X6,X7] :
( ( leq(X6,minus(pv10,n1))
& leq(n0,X6) )
=> sum(n0,minus(n5,n1),a_select3(q,X6,X7)) = n1 )
& ! [X4,X5] :
( ( leq(X4,minus(pv12,n1))
& leq(n0,X4) )
=> 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(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& 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))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f89,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(f90,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
fof(f91,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f92,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f93,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
fof(f94,plain,
( ! [X2,X3] :
( ~ leq(X2,minus(pv10,n1))
| ~ leq(n0,X2)
| sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1 )
& ! [X0,X1] :
( ~ leq(X0,minus(pv12,n1))
| ~ leq(n0,X0)
| 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(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& ( ? [X6,X7] :
( leq(X6,minus(pv10,n1))
& leq(n0,X6)
& n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7)) )
| ? [X4,X5] :
( leq(X4,minus(pv12,n1))
& leq(n0,X4)
& 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(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ! [X2,X3] :
( ~ leq(X2,minus(pv10,n1))
| ~ leq(n0,X2)
| sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1 )
& ! [X0,X1] :
( ~ leq(X0,minus(pv12,n1))
| ~ leq(n0,X0)
| 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(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& ( ? [X6,X7] :
( leq(X6,minus(pv10,n1))
& leq(n0,X6)
& n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7)) )
| ? [X4,X5] :
( leq(X4,minus(pv12,n1))
& leq(n0,X4)
& 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(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ) ),
inference(flattening,[],[f94]) ).
fof(f123,plain,
( ! [X4,X5] :
( ~ leq(X4,minus(pv10,n1))
| ~ leq(n0,X4)
| n1 = sum(n0,minus(n5,n1),a_select3(q,X4,X5)) )
& ! [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)))))) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& ( sP0
| ? [X0,X1] :
( leq(X0,minus(pv12,n1))
& leq(n0,X0)
& 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(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ) ),
inference(rectify,[],[f119]) ).
fof(f124,plain,
( ! [X4,X5] :
( ~ leq(X4,minus(pv10,n1))
| ~ leq(n0,X4)
| n1 = sum(n0,minus(n5,n1),a_select3(q,X4,X5)) )
& ! [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)))))) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& ( sP0
| ( leq(sK3,minus(pv12,n1))
& leq(n0,sK3)
& 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(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f123]) ).
fof(f131,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,[],[f124]) ).
fof(f132,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,[],[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,
( sP0
| leq(sK3,minus(pv12,n1))
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ),
inference(cnf_transformation,[],[f124]) ).
fof(f138,plain,
( sP0
| leq(n0,sK3)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ),
inference(cnf_transformation,[],[f124]) ).
fof(f139,plain,
( sP0
| 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(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ),
inference(cnf_transformation,[],[f124]) ).
fof(f152,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f153,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f164,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(cnf_transformation,[],[f90]) ).
fof(f174,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f189,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f190,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f92]) ).
fof(f196,plain,
n3 = succ(succ(succ(n0))),
inference(cnf_transformation,[],[f93]) ).
fof(f201,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f89]) ).
fof(f205,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f208,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f217,plain,
n1 = plus(n1,n0),
inference(definition_unfolding,[],[f153,f205]) ).
fof(f218,plain,
n5 = plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,n0))))),
inference(definition_unfolding,[],[f164,f205,f205,f205,f205,f205]) ).
fof(f222,plain,
n0 = plus(n1,tptp_minus_1),
inference(definition_unfolding,[],[f189,f205]) ).
fof(f223,plain,
n2 = plus(n1,plus(n1,n0)),
inference(definition_unfolding,[],[f190,f205,f205]) ).
fof(f226,plain,
n3 = plus(n1,plus(n1,plus(n1,n0))),
inference(definition_unfolding,[],[f196,f205,f205,f205]) ).
fof(f229,plain,
n4 = plus(n1,plus(n1,plus(n1,plus(n1,n0)))),
inference(definition_unfolding,[],[f201,f205,f205,f205,f205]) ).
fof(f234,plain,
! [X0] : minus(plus(n1,X0),n1) = X0,
inference(definition_unfolding,[],[f208,f174,f205]) ).
tcf(c_52,negated_conjecture,
( sP0
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ( 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))))) != n0 )
| ( 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)))))) != a_select3(q,pv10,sK3) ) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_53,negated_conjecture,
( sP0
| leq(n0,sK3)
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ( 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))))) != n0 ) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_54,negated_conjecture,
( sP0
| leq(sK3,minus(pv12,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ( 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))))) != n0 ) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_55,negated_conjecture,
leq(n0,pv10),
inference(cnf_transformation,[],[f136]) ).
tcf(c_56,negated_conjecture,
leq(n0,pv12),
inference(cnf_transformation,[],[f135]) ).
tcf(c_57,negated_conjecture,
leq(pv10,minus(n135300,n1)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_58,negated_conjecture,
leq(pv12,minus(n5,n1)),
inference(cnf_transformation,[],[f133]) ).
tcf(c_59,negated_conjecture,
! [X0: $i,X1: $i] :
( ( 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)))))) = a_select3(q,pv10,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv12,n1)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_60,negated_conjecture,
! [X0: $i,X1: $i] :
( ( sum(n0,minus(n5,n1),a_select3(q,X0,X1)) = n1 )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv10,n1)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_73,plain,
! [X0: $i] : sum(n0,tptp_minus_1,X0) = n0,
inference(cnf_transformation,[],[f152]) ).
tcf(c_74,plain,
plus(n1,n0) = n1,
inference(cnf_transformation,[],[f217]) ).
tcf(c_85,plain,
plus(n1,plus(n1,plus(n1,plus(n1,plus(n1,n0))))) = n5,
inference(cnf_transformation,[],[f218]) ).
tcf(c_109,plain,
plus(n1,tptp_minus_1) = n0,
inference(cnf_transformation,[],[f222]) ).
tcf(c_110,plain,
plus(n1,plus(n1,n0)) = n2,
inference(cnf_transformation,[],[f223]) ).
tcf(c_116,plain,
plus(n1,plus(n1,plus(n1,n0))) = n3,
inference(cnf_transformation,[],[f226]) ).
tcf(c_121,plain,
plus(n1,plus(n1,plus(n1,plus(n1,n0)))) = n4,
inference(cnf_transformation,[],[f229]) ).
tcf(c_127,plain,
! [X0: $i] : minus(plus(n1,X0),n1) = X0,
inference(cnf_transformation,[],[f234]) ).
tcf(c_159,negated_conjecture,
( sP0
| leq(n0,sK3)
| ( 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))))) != n0 ) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_56,c_55,c_58,c_57,c_53]) ).
tcf(c_161,negated_conjecture,
( sP0
| leq(sK3,minus(pv12,n1))
| ( 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))))) != n0 ) ),
inference(global_subsumption_just,[status(thm)],[c_54,c_56,c_55,c_58,c_57,c_54]) ).
tcf(c_163,negated_conjecture,
( sP0
| ( 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))))) != n0 )
| ( 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)))))) != a_select3(q,pv10,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_56,c_55,c_58,c_57,c_52]) ).
tcf(c_603,plain,
plus(n1,n1) = n2,
inference(light_normalisation,[status(thm)],[c_110,c_74]) ).
tcf(c_632,plain,
plus(n1,n2) = n3,
inference(light_normalisation,[status(thm)],[c_116,c_74,c_603]) ).
tcf(c_665,plain,
plus(n1,n3) = n4,
inference(light_normalisation,[status(thm)],[c_121,c_74,c_603,c_632]) ).
tcf(c_676,plain,
plus(n1,n4) = n5,
inference(light_normalisation,[status(thm)],[c_85,c_74,c_603,c_632,c_665]) ).
tcf(c_2090,plain,
minus(n0,n1) = tptp_minus_1,
inference(superposition,[status(thm)],[c_109,c_127]) ).
tcf(c_2094,plain,
minus(n5,n1) = n4,
inference(superposition,[status(thm)],[c_676,c_127]) ).
tcf(c_2096,plain,
( sP0
| ( 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))))) != n0 )
| ( 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)))))) != a_select3(q,pv10,sK3) ) ),
inference(demodulation,[status(thm)],[c_163,c_2090]) ).
tcf(c_2097,plain,
( sP0
| leq(sK3,minus(pv12,n1))
| ( 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))))) != n0 ) ),
inference(demodulation,[status(thm)],[c_161,c_2090]) ).
tcf(c_2098,plain,
( sP0
| leq(n0,sK3)
| ( 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))))) != n0 ) ),
inference(demodulation,[status(thm)],[c_159,c_2090]) ).
tcf(c_2099,plain,
( sP0
| leq(n0,sK3) ),
inference(ground_joinability,[status(thm)],[c_2098,c_73]) ).
tcf(c_2102,plain,
( sP0
| leq(sK3,minus(pv12,n1)) ),
inference(ground_joinability,[status(thm)],[c_2097,c_73]) ).
tcf(c_2105,plain,
( sP0
| ( 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)))))) != a_select3(q,pv10,sK3) ) ),
inference(ground_joinability,[status(thm)],[c_2096,c_73]) ).
tcf(c_2111,plain,
! [X0: $i,X1: $i] :
( ( 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,n4,sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))))) = a_select3(q,pv10,X0) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv12,n1)) ),
inference(demodulation,[status(thm)],[c_59,c_2094]) ).
tcf(c_2155,plain,
! [X0: $i] :
( sP0
| ( 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,n4,sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))))) = a_select3(q,pv10,sK3) )
| ~ leq(n0,sK3) ),
inference(superposition,[status(thm)],[c_2102,c_2111]) ).
tcf(c_2168,plain,
( sP0
| ( 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,n4,sqrt(times(minus(a_select3(center,sK4,n0),a_select2(x,pv10)),minus(a_select3(center,sK4,n0),a_select2(x,pv10)))))) != a_select3(q,pv10,sK3) ) ),
inference(light_normalisation,[status(thm)],[c_2105,c_2094]) ).
tcf(c_2226,plain,
! [X0: $i] :
( sP0
| ( 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,n4,sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))))) = a_select3(q,pv10,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_2155,c_2099,c_2155]) ).
tcf(c_2233,plain,
sP0,
inference(backward_subsumption_resolution,[status(thm)],[c_2168,c_2226]) ).
tcf(c_2339,plain,
! [X0: $i] :
( ( sum(n0,minus(n5,n1),a_select3(q,sK1,X0)) = n1 )
| ~ leq(n0,sK1)
| ~ leq(sK1,minus(pv10,n1)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_3711,plain,
( ( sum(n0,minus(n5,n1),a_select3(q,sK1,sK2)) = n1 )
| ~ leq(n0,sK1)
| ~ leq(sK1,minus(pv10,n1)) ),
inference(instantiation,[status(thm)],[c_2339]) ).
fof(f118,definition,
( ~ sP0
| ? [X6,X7] :
( leq(X6,minus(pv10,n1))
& leq(n0,X6)
& n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7)) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f119,plain,
( ! [X2,X3] :
( ~ leq(X2,minus(pv10,n1))
| ~ leq(n0,X2)
| sum(n0,minus(n5,n1),a_select3(q,X2,X3)) = n1 )
& ! [X0,X1] :
( ~ leq(X0,minus(pv12,n1))
| ~ leq(n0,X0)
| 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(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& ( sP0
| ? [X4,X5] :
( leq(X4,minus(pv12,n1))
& leq(n0,X4)
& 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(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| 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))))) ) ),
inference(definition_folding,[],[f95,f118]) ).
fof(f120,plain,
( ~ sP0
| ? [X6,X7] :
( leq(X6,minus(pv10,n1))
& leq(n0,X6)
& n1 != sum(n0,minus(n5,n1),a_select3(q,X6,X7)) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f121,plain,
( ~ sP0
| ? [X0,X1] :
( leq(X0,minus(pv10,n1))
& leq(n0,X0)
& n1 != sum(n0,minus(n5,n1),a_select3(q,X0,X1)) ) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
( ~ sP0
| ( leq(sK1,minus(pv10,n1))
& leq(n0,sK1)
& n1 != sum(n0,minus(n5,n1),a_select3(q,sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f121]) ).
fof(f128,plain,
( ~ sP0
| leq(sK1,minus(pv10,n1)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f129,plain,
( ~ sP0
| leq(n0,sK1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f130,plain,
( ~ sP0
| n1 != sum(n0,minus(n5,n1),a_select3(q,sK1,sK2)) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_49,plain,
( ~ sP0
| ( sum(n0,minus(n5,n1),a_select3(q,sK1,sK2)) != n1 ) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_50,plain,
( leq(n0,sK1)
| ~ sP0 ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_51,plain,
( leq(sK1,minus(pv10,n1))
| ~ sP0 ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_3712,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3711,c_2233,c_49,c_51,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV053+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 18:24:11 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 1.87/1.20 % SZS status Started for theBenchmark.p
% 1.87/1.20 % SZS status Theorem for theBenchmark.p
% 1.87/1.20
% 1.87/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.87/1.20
% 1.87/1.20 % ------ iProver source info
% 1.87/1.20
% 1.87/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.87/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.87/1.20 % git: non_committed_changes: false
% 1.87/1.20
% 1.87/1.20 % ------ Parsing...
% 1.87/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.87/1.20
% 1.87/1.20 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.87/1.20
% 1.87/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.87/1.20
% 1.87/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.87/1.20 % ------ Proving...
% 1.87/1.20 % ------ Problem Properties
% 1.87/1.20
% 1.87/1.20 %
% 1.87/1.20 % clauses 81
% 1.87/1.20 % conjectures 9
% 1.87/1.20 % EPR 44
% 1.87/1.20 % Horn 72
% 1.87/1.20 % unary 53
% 1.87/1.20 % binary 13
% 1.87/1.20 % lits 139
% 1.87/1.20 % lits eq 48
% 1.87/1.20 % fd_pure 0
% 1.87/1.20 % fd_pseudo 0
% 1.87/1.20 % fd_cond 6
% 1.87/1.20 % fd_pseudo_cond 2
% 1.87/1.20 % AC symbols 0
% 1.87/1.20
% 1.87/1.20 % ------ Schedule dynamic 5 is on
% 1.87/1.20
% 1.87/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.87/1.20
% 1.87/1.20
% 1.87/1.20 % ------
% 1.87/1.20 % Current options:
% 1.87/1.20 % ------
% 1.87/1.20
% 1.87/1.20
% 1.87/1.20 %
% 1.87/1.20
% 1.87/1.20 % ------ Proving...
% 1.87/1.20 %
% 1.87/1.20
% 1.87/1.20 % SZS status Theorem for theBenchmark.p
% 1.87/1.20
% 1.87/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.87/1.20
% 1.87/1.20
%------------------------------------------------------------------------------