%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW174+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 01:29:46 PM UTC 2026
% Result : Theorem 12.32s 2.57s
% Output : Refutation 13.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of formulae : 126 ( 100 unt; 11 def)
% Number of atoms : 159 ( 131 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 33 ~; 27 |; 1 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 15 con; 0-3 aty)
% Number of variables : 94 ( 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X0)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
fof(f12,axiom,
! [X0] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
fof(f13,axiom,
! [X0] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(f33,axiom,
! [X0,X1] :
( c_NthRoot_Osqrt(X1) = c_NthRoot_Osqrt(X0)
<=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).
fof(f63,axiom,
! [X0,X1,X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(f72,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f73,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f74,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f98,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).
fof(f119,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f317,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__ge__zero) ).
fof(f326,axiom,
! [X0,X1] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X0
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
=> c_NthRoot_Osqrt(X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__unique) ).
fof(f971,axiom,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f1150,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1200,conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1201,negated_conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(negated_conjecture,[status(cth)],[f1200]) ).
fof(f1202,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(flattening,[],[f1201]) ).
fof(f1240,plain,
! [X0,X1,X2] :
( c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0))
| ~ class_Int_Onumber__ring(X2) ),
inference(ennf_transformation,[],[f63]) ).
fof(f1268,plain,
! [X0,X1] :
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f98]) ).
fof(f1585,plain,
! [X0,X1] :
( c_NthRoot_Osqrt(X0) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X0 ),
inference(ennf_transformation,[],[f326]) ).
fof(f1586,plain,
! [X0,X1] :
( c_NthRoot_Osqrt(X0) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X0 ),
inference(flattening,[],[f1585]) ).
fof(f2235,plain,
! [X0,X1] :
( ( c_NthRoot_Osqrt(X1) = c_NthRoot_Osqrt(X0)
| X0 != X1 )
& ( X1 = X0
| c_NthRoot_Osqrt(X1) != c_NthRoot_Osqrt(X0) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f2638,plain,
! [X0,X1] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X0)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2650,plain,
! [X0] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f2651,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f2675,plain,
! [X0,X1] :
( c_NthRoot_Osqrt(X1) != c_NthRoot_Osqrt(X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2235]) ).
fof(f2707,plain,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0)) = c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
inference(cnf_transformation,[],[f1240]) ).
fof(f2720,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f72]) ).
fof(f2721,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f73]) ).
fof(f2722,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f74]) ).
fof(f2746,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f1268]) ).
fof(f2767,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(cnf_transformation,[],[f119]) ).
fof(f3193,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f317]) ).
fof(f3206,plain,
! [X0,X1] :
( c_NthRoot_Osqrt(X0) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X0 ),
inference(cnf_transformation,[],[f1586]) ).
fof(f4132,plain,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f971]) ).
fof(f4319,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f4369,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f1202]) ).
fof(f4382,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f2650,f2722,f4132]) ).
fof(f4410,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(definition_unfolding,[],[f2746,f2722,f4132]) ).
fof(f4439,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f3193,f2722,f4132]) ).
fof(f4451,plain,
! [X0,X1] :
( c_NthRoot_Osqrt(X0) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) != X0 ),
inference(definition_unfolding,[],[f3206,f2722,f4132]) ).
fof(f4702,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f4369,f2722,f2722,f4132,f2722,f4132,f2722,f4132]) ).
fof(f4762,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X1 ),
inference(equality_resolution,[],[f4451]) ).
fof(f4917,definition,
sF22 = c_Groups_Oone__class_Oone(tc_Int_Oint),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f4918,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = sF22,
inference(reorient_equations,[],[f4917]) ).
fof(f4919,definition,
sF23 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF22,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f4920,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF22,c_Int_OPls) = sF23,
inference(reorient_equations,[],[f4919]) ).
fof(f4921,definition,
sF24 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF23,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f4922,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF23,c_Int_OPls) = sF24,
inference(reorient_equations,[],[f4921]) ).
fof(f4923,definition,
sF25 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,sF24),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f4924,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,sF24) = sF25,
inference(reorient_equations,[],[f4923]) ).
fof(f4925,definition,
sF26 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF25,sF25),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f4926,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF25,sF25) = sF26,
inference(reorient_equations,[],[f4925]) ).
fof(f4927,definition,
sF27 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF26),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f4928,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF26) = sF27,
inference(reorient_equations,[],[f4927]) ).
fof(f4929,definition,
sF28 = c_NthRoot_Osqrt(sF27),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f4930,plain,
c_NthRoot_Osqrt(sF27) = sF28,
inference(reorient_equations,[],[f4929]) ).
fof(f4931,definition,
sF29 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f4932,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25) = sF29,
inference(reorient_equations,[],[f4931]) ).
fof(f4933,definition,
sF30 = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,sF25),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f4934,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,sF25) = sF30,
inference(reorient_equations,[],[f4933]) ).
fof(f4935,definition,
sF31 = c_Power_Opower__class_Opower(tc_RealDef_Oreal,sF29,sF30),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f4936,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,sF29,sF30) = sF31,
inference(reorient_equations,[],[f4935]) ).
fof(f4937,definition,
sF32 = c_NthRoot_Osqrt(sF31),
introduced(definition,[new_symbols(definition,[sF32])],[function_definition]) ).
fof(f4938,plain,
c_NthRoot_Osqrt(sF31) = sF32,
inference(reorient_equations,[],[f4937]) ).
fof(f4939,plain,
sF28 != sF32,
inference(definition_folding,[],[f4702,f4938,f4936,f4934,f4924,f4922,f4920,f4918,f4922,f4920,f4918,f4932,f4924,f4922,f4920,f4918,f4922,f4920,f4918,f4930,f4928,f4926,f4924,f4922,f4920,f4918,f4922,f4920,f4918,f4924,f4922,f4920,f4918,f4922,f4920,f4918]) ).
fof(f5021,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4410,f2767]) ).
fof(f5046,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f4382,f2767]) ).
fof(f5054,plain,
sF22 = sF23,
inference(forward_demodulation,[],[f4920,f2721]) ).
fof(f5055,plain,
sF23 = sF24,
inference(forward_demodulation,[],[f4922,f2721]) ).
fof(f5091,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5021,f2767]) ).
fof(f5116,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f5046,f2638]) ).
fof(f5124,plain,
sF22 = sF24,
inference(forward_demodulation,[],[f5055,f5054]) ).
fof(f5141,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5091,f2720]) ).
fof(f5164,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f5116,f2767]) ).
fof(f5180,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5141,f2720]) ).
fof(f5203,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f5164,f2720]) ).
fof(f5218,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5180,f2721]) ).
fof(f5235,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f5203,f2720]) ).
fof(f5250,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5218,f2721]) ).
fof(f5267,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),
inference(forward_demodulation,[],[f5235,f2721]) ).
fof(f5282,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF22,sF22)),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5250,f4918]) ).
fof(f5297,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f5267,f2721]) ).
fof(f5312,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,sF24)),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5282,f5124]) ).
fof(f5327,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF22,sF22))),
inference(forward_demodulation,[],[f5297,f4918]) ).
fof(f5342,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,sF25),X0) ),
inference(forward_demodulation,[],[f5312,f4924]) ).
fof(f5357,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,sF24))),
inference(forward_demodulation,[],[f5327,f5124]) ).
fof(f5385,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,sF25)),
inference(forward_demodulation,[],[f5357,f4924]) ).
fof(f5397,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),sF30),
inference(forward_demodulation,[],[f5385,f4934]) ).
fof(f5443,plain,
c_NthRoot_Osqrt(sF31) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(sF29),sF30),
inference(superposition,[],[f2638,f4936]) ).
fof(f5448,plain,
c_NthRoot_Osqrt(sF31) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sF29),
inference(forward_demodulation,[],[f5443,f5397]) ).
fof(f5449,plain,
sF32 = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sF29),
inference(forward_demodulation,[],[f5448,f4938]) ).
fof(f5453,plain,
! [X0] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(X0)),sF30) = c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),
inference(superposition,[],[f2638,f5397]) ).
fof(f5454,plain,
! [X0] : c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0)),
inference(forward_demodulation,[],[f5453,f5397]) ).
fof(f5999,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(resolution,[],[f4439,f4762]) ).
fof(f6022,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f5999,f2638]) ).
fof(f6034,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f6022,f2767]) ).
fof(f6046,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6034,f2767]) ).
fof(f6058,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f6046,f2720]) ).
fof(f6070,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f6058,f2720]) ).
fof(f6082,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls))))),
inference(forward_demodulation,[],[f6070,f2767]) ).
fof(f6094,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),
inference(forward_demodulation,[],[f6082,f2720]) ).
fof(f6104,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f6094,f2721]) ).
fof(f6114,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF22,sF22))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF22,sF22)))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF22,sF22))),
inference(forward_demodulation,[],[f6104,f4918]) ).
fof(f6124,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,sF24))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,sF24)))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF24,sF24))),
inference(forward_demodulation,[],[f6114,f5124]) ).
fof(f6129,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,sF25)),
inference(forward_demodulation,[],[f6124,f4924]) ).
fof(f6130,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25))),sF30),
inference(forward_demodulation,[],[f6129,f4934]) ).
fof(f6131,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25))),
inference(forward_demodulation,[],[f6130,f5397]) ).
fof(f6132,plain,
c_NthRoot_Osqrt(sF29) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Osqrt(sF29)),
inference(forward_demodulation,[],[f6131,f4932]) ).
fof(f6559,plain,
c_NthRoot_Osqrt(sF32) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Osqrt(sF29)),
inference(superposition,[],[f5454,f5449]) ).
fof(f6562,plain,
c_NthRoot_Osqrt(sF29) = c_NthRoot_Osqrt(sF32),
inference(forward_demodulation,[],[f6559,f6132]) ).
fof(f7173,plain,
! [X0] :
( c_NthRoot_Osqrt(X0) != c_NthRoot_Osqrt(sF29)
| sF32 = X0 ),
inference(superposition,[],[f2675,f6562]) ).
fof(f7562,plain,
sF29 = sF32,
inference(equality_resolution,[],[f7173]) ).
fof(f7595,plain,
sF28 != sF29,
inference(superposition,[],[f4939,f7562]) ).
fof(f8198,plain,
! [X0,X1] : c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)),
inference(resolution,[],[f4319,f2707]) ).
fof(f8210,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25),X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0),
inference(resolution,[],[f4319,f5342]) ).
fof(f8217,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF29,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0),
inference(forward_demodulation,[],[f8210,f4932]) ).
fof(f8368,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF29,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)),
inference(superposition,[],[f8217,f8198]) ).
fof(f8549,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF26) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF29,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF25)),
inference(superposition,[],[f8368,f4926]) ).
fof(f8564,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF26) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF29,sF29),
inference(forward_demodulation,[],[f8549,f4932]) ).
fof(f8575,plain,
sF27 = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF29,sF29),
inference(forward_demodulation,[],[f8564,f4928]) ).
fof(f10633,plain,
c_NthRoot_Osqrt(sF27) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sF29),
inference(superposition,[],[f2651,f8575]) ).
fof(f10666,plain,
c_NthRoot_Osqrt(sF27) = sF32,
inference(forward_demodulation,[],[f10633,f5449]) ).
fof(f10674,plain,
c_NthRoot_Osqrt(sF27) = sF29,
inference(forward_demodulation,[],[f10666,f7562]) ).
fof(f10678,plain,
sF28 = sF29,
inference(forward_demodulation,[],[f10674,f4930]) ).
fof(f10682,plain,
$false,
inference(forward_subsumption_resolution,[],[f10678,f7595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW174+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n003.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 13:14:27 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 12.32/2.50 % (1573984)Detected formulas, will run a generic FOF schedule.
% 12.32/2.50 % (1573992)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=946816001:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.32/2.50 % (1573992)Instruction limit reached!
% 12.32/2.50 % (1573992)------------------------------
% 12.32/2.50 % (1573992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.50 % (1573992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.50 % (1573992)CaDiCaL version: 2.1.3
% 12.32/2.50 % (1573992)Termination reason: Instruction limit
% 12.32/2.50 % (1573992)Termination phase: Saturation
% 12.32/2.50 % (1573992)Time elapsed: 0.038 s
% 12.32/2.50 % (1573992)Peak memory usage: 90 MB
% 12.32/2.50 % (1573992)Instructions burned: 109 (million)
% 12.32/2.50 % (1573994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1562767767:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.32/2.50 % (1573993)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3385145731:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.32/2.50 % (1573995)dis-21_1_sil=8000:lcm=predicate:random_seed=2803252758: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)
% 12.32/2.50 % (1573989)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=1667885396:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.32/2.50 % (1573990)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=2203628601:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.32/2.50 % (1573991)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=2929094659:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.32/2.50 % (1573995)Instruction limit reached!
% 12.32/2.50 % (1573995)------------------------------
% 12.32/2.50 % (1573995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.50 % (1573995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.50 % (1573995)CaDiCaL version: 2.1.3
% 12.32/2.50 % (1573995)Termination reason: Instruction limit
% 12.32/2.50 % (1573995)Termination phase: Saturation
% 12.32/2.50 % (1573995)Time elapsed: 0.064 s
% 12.32/2.50 % (1573995)Peak memory usage: 90 MB
% 12.32/2.50 % (1573995)Instructions burned: 129 (million)
% 12.32/2.50 % (1573993)Instruction limit reached!
% 12.32/2.50 % (1573993)------------------------------
% 12.32/2.50 % (1573993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.50 % (1573993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.50 % (1573993)CaDiCaL version: 2.1.3
% 12.32/2.50 % (1573993)Termination reason: Instruction limit
% 12.32/2.50 % (1573993)Termination phase: Saturation
% 12.32/2.50 % (1573993)Time elapsed: 0.073 s
% 12.32/2.50 % (1573993)Peak memory usage: 89 MB
% 12.32/2.50 % (1573993)Instructions burned: 120 (million)
% 12.32/2.50 % (1573994)Instruction limit reached!
% 12.32/2.50 % (1573994)------------------------------
% 12.32/2.50 % (1573994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.50 % (1573994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.50 % (1573994)CaDiCaL version: 2.1.3
% 12.32/2.50 % (1573994)Termination reason: Instruction limit
% 12.32/2.50 % (1573994)Termination phase: Saturation
% 12.32/2.50 % (1573994)Time elapsed: 0.077 s
% 12.32/2.50 % (1573994)Peak memory usage: 91 MB
% 12.32/2.50 % (1573994)Instructions burned: 140 (million)
% 12.32/2.50 % (1573997)lrs+10_1_sil=8000:sp=occurrence:random_seed=3382103244:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.32/2.50 % (1573997)Instruction limit reached!
% 12.32/2.50 % (1573997)------------------------------
% 12.32/2.50 % (1573997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.50 % (1573997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.50 % (1573997)CaDiCaL version: 2.1.3
% 12.32/2.50 % (1573997)Termination reason: Instruction limit
% 12.32/2.50 % (1573997)Termination phase: Saturation
% 12.32/2.50 % (1573997)Time elapsed: 0.095 s
% 12.32/2.50 % (1573997)Peak memory usage: 92 MB
% 12.32/2.50 % (1573997)Instructions burned: 286 (million)
% 12.32/2.57 % (1574004)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2762185702:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.32/2.57 % (1574006)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1186979542:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 12.32/2.57 % (1574005)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4034160953:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.32/2.57 % (1574008)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2334861535:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 12.32/2.57 % (1574004)Instruction limit reached!
% 12.32/2.57 % (1574004)------------------------------
% 12.32/2.57 % (1574004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574004)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574004)Termination reason: Instruction limit
% 12.32/2.57 % (1574004)Termination phase: Saturation
% 12.32/2.57 % (1574004)Time elapsed: 0.087 s
% 12.32/2.57 % (1574004)Peak memory usage: 91 MB
% 12.32/2.57 % (1574004)Instructions burned: 158 (million)
% 12.32/2.57 % (1574008)Refutation not found, incomplete strategy
% 12.32/2.57 % (1574008)------------------------------
% 12.32/2.57 % (1574008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574008)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574008)Termination reason: Refutation not found, incomplete strategy
% 12.32/2.57 % (1574008)Time elapsed: 0.027 s
% 12.32/2.57 % (1574008)Peak memory usage: 90 MB
% 12.32/2.57 % (1574008)Instructions burned: 98 (million)
% 12.32/2.57 % (1574006)Instruction limit reached!
% 12.32/2.57 % (1574006)------------------------------
% 12.32/2.57 % (1574006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574006)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574006)Termination reason: Instruction limit
% 12.32/2.57 % (1574006)Termination phase: Saturation
% 12.32/2.57 % (1574006)Time elapsed: 0.142 s
% 12.32/2.57 % (1574006)Peak memory usage: 92 MB
% 12.32/2.57 % (1574006)Instructions burned: 248 (million)
% 12.32/2.57 % (1574013)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1374964185:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 12.32/2.57 % (1574005)Instruction limit reached!
% 12.32/2.57 % (1574005)------------------------------
% 12.32/2.57 % (1574005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574005)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574005)Termination reason: Instruction limit
% 12.32/2.57 % (1574005)Termination phase: Saturation
% 12.32/2.57 % (1574005)Time elapsed: 0.205 s
% 12.32/2.57 % (1574005)Peak memory usage: 92 MB
% 12.32/2.57 % (1574005)Instructions burned: 325 (million)
% 12.32/2.57 % (1574008)------------------------------
% 12.32/2.57 % (1574008)------------------------------
% 12.32/2.57 % (1574014)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=57188591:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 12.32/2.57 % (1574017)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1950455069:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 12.32/2.57 % (1574014)Instruction limit reached!
% 12.32/2.57 % (1574014)------------------------------
% 12.32/2.57 % (1574014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574014)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574014)Termination reason: Instruction limit
% 12.32/2.57 % (1574014)Termination phase: Saturation
% 12.32/2.57 % (1574014)Time elapsed: 0.057 s
% 12.32/2.57 % (1574014)Peak memory usage: 90 MB
% 12.32/2.57 % (1574014)Instructions burned: 114 (million)
% 12.32/2.57 % (1574016)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=300477119:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 12.32/2.57 % (1574017)Instruction limit reached!
% 12.32/2.57 % (1574017)------------------------------
% 12.32/2.57 % (1574017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574017)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574017)Termination reason: Instruction limit
% 12.32/2.57 % (1574017)Termination phase: Saturation
% 12.32/2.57 % (1574017)Time elapsed: 0.030 s
% 12.32/2.57 % (1574017)Peak memory usage: 90 MB
% 12.32/2.57 % (1574017)Instructions burned: 116 (million)
% 12.32/2.57 % (1574016)Instruction limit reached!
% 12.32/2.57 % (1574016)------------------------------
% 12.32/2.57 % (1574016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574016)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574016)Termination reason: Instruction limit
% 12.32/2.57 % (1574016)Termination phase: Property scanning
% 12.32/2.57 % (1574016)Time elapsed: 0.059 s
% 12.32/2.57 % (1574016)Peak memory usage: 89 MB
% 12.32/2.57 % (1574016)Instructions burned: 130 (million)
% 12.32/2.57 % (1574020)lrs+10_1_sil=8000:sp=occurrence:random_seed=1140728728:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 12.32/2.57 % (1574022)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1433089606:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 12.32/2.57 % (1574023)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3100996062:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 12.32/2.57 % (1574022)Refutation not found, incomplete strategy
% 12.32/2.57 % (1574022)------------------------------
% 12.32/2.57 % (1574022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574022)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574022)Termination reason: Refutation not found, incomplete strategy
% 12.32/2.57 % (1574022)Time elapsed: 0.059 s
% 12.32/2.57 % (1574022)Peak memory usage: 91 MB
% 12.32/2.57 % (1574022)Instructions burned: 114 (million)
% 12.32/2.57 % (1574022)------------------------------
% 12.32/2.57 % (1574022)------------------------------
% 12.32/2.57 % (1574027)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1950304154:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 12.32/2.57 % (1574027)Instruction limit reached!
% 12.32/2.57 % (1574027)------------------------------
% 12.32/2.57 % (1574027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574027)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574027)Termination reason: Instruction limit
% 12.32/2.57 % (1574027)Termination phase: Saturation
% 12.32/2.57 % (1574027)Time elapsed: 0.068 s
% 12.32/2.57 % (1574027)Peak memory usage: 92 MB
% 12.32/2.57 % (1574027)Instructions burned: 135 (million)
% 12.32/2.57 % (1574020)Instruction limit reached!
% 12.32/2.57 % (1574020)------------------------------
% 12.32/2.57 % (1574020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574020)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574020)Termination reason: Instruction limit
% 12.32/2.57 % (1574020)Termination phase: Saturation
% 12.32/2.57 % (1574020)Time elapsed: 0.566 s
% 12.32/2.57 % (1574020)Peak memory usage: 97 MB
% 12.32/2.57 % (1574020)Instructions burned: 908 (million)
% 12.32/2.57 % (1574029)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1675824241:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 12.32/2.57 % (1574030)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1144098196:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 12.32/2.57 % (1573989)First to succeed.
% 12.32/2.57 % (1573989)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1573984"
% 12.32/2.57 % (1574029)Instruction limit reached!
% 12.32/2.57 % (1574029)------------------------------
% 12.32/2.57 % (1574029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.32/2.57 % (1574029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.32/2.57 % (1574029)CaDiCaL version: 2.1.3
% 12.32/2.57 % (1574029)Termination reason: Instruction limit
% 12.32/2.57 % (1574029)Termination phase: Saturation
% 12.32/2.57 % (1574029)Time elapsed: 0.310 s
% 12.32/2.57 % (1574029)Peak memory usage: 96 MB
% 12.32/2.57 % (1574029)Instructions burned: 595 (million)
% 12.32/2.57 % (1573989)Refutation found. Thanks to Tanya!
% 12.32/2.57 % SZS status Theorem for theBenchmark
% 12.32/2.57 % SZS output start Proof for theBenchmark
% See solution above
% 13.85/2.76 % (1573989)------------------------------
% 13.85/2.76 % (1573989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.85/2.76 % (1573989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.76 % (1573989)CaDiCaL version: 2.1.3
% 13.85/2.76 % (1573989)Termination reason: Refutation
% 13.85/2.76 % (1573989)Time elapsed: 1.463 s
% 13.85/2.76 % (1573989)Peak memory usage: 150 MB
% 13.85/2.76 % (1573989)Instructions burned: 2332 (million)
% 13.85/2.76 % (1573989)------------------------------
% 13.85/2.76 % (1573989)------------------------------
% 13.85/2.76 % (1573984)Success in time 1.913 s
% 13.85/2.76 % Vampire exiting
%------------------------------------------------------------------------------