TSTP Solution File: SWW174+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW174+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:16:21 EDT 2024
% Result : Theorem 24.96s 4.18s
% Output : CNFRefutation 24.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 76 ( 62 unt; 0 def)
% Number of atoms : 90 ( 71 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 10 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
fof(f13,axiom,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(f15,axiom,
! [X5,X7,X8] :
( class_Int_Onumber__ring(X8)
=> c_Int_Onumber__class_Onumber__of(X8,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X5)) = c_Groups_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X8,X7),c_Int_Onumber__class_Onumber__of(X8,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
fof(f72,axiom,
! [X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f73,axiom,
! [X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f74,axiom,
! [X1] : c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f117,axiom,
! [X9,X12,X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X9)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f119,axiom,
! [X24,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22),X24) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f590,axiom,
! [X27] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f887,axiom,
! [X27,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X27,X27) = c_Groups_Otimes__class_Otimes(X8,c_Groups_Oplus__class_Oplus(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Oone__class_Oone(X8)),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(f944,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
fof(f971,axiom,
! [X1] : c_Int_OBit1(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),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f989,axiom,
! [X16] : c_Nat_OSuc(X16) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f1029,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f1150,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/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/sandbox/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,[],[f1200]) ).
fof(f1211,plain,
! [X0,X1,X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X0)) = c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0)) ),
inference(rectify,[],[f15]) ).
fof(f1268,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(rectify,[],[f72]) ).
fof(f1269,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(rectify,[],[f73]) ).
fof(f1270,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(rectify,[],[f74]) ).
fof(f1311,plain,
! [X0,X1,X2] : 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,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(rectify,[],[f117]) ).
fof(f1313,plain,
! [X0,X1,X2] : 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(rectify,[],[f119]) ).
fof(f1755,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f590]) ).
fof(f2048,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X0) ),
inference(rectify,[],[f887]) ).
fof(f2121,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(rectify,[],[f971]) ).
fof(f2136,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(rectify,[],[f989]) ).
fof(f2143,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(f2147,plain,
! [X0,X1,X2] :
( c_Int_Onumber__class_Onumber__of(X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X0)) = c_Groups_Otimes__class_Otimes(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,[],[f1211]) ).
fof(f3033,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f2048]) ).
fof(f3600,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(f3601,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(f3603,plain,
! [X2,X0,X1] :
( c_Int_Onumber__class_Onumber__of(X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X0)) = c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X2,X0))
| ~ class_Int_Onumber__ring(X2) ),
inference(cnf_transformation,[],[f2147]) ).
fof(f3670,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f1268]) ).
fof(f3671,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f1269]) ).
fof(f3672,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f1270]) ).
fof(f3715,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,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(cnf_transformation,[],[f1311]) ).
fof(f3717,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,[],[f1313]) ).
fof(f4576,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1755]) ).
fof(f4988,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f3033]) ).
fof(f5051,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f944]) ).
fof(f5082,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,[],[f2121]) ).
fof(f5106,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f2136]) ).
fof(f5148,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1029]) ).
fof(f5269,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f5319,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,[],[f2143]) ).
fof(f5332,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,[],[f3600,f3672,f5082]) ).
fof(f5619,plain,
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))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definition_unfolding,[],[f5051,f3672,f5082,f5106,f5106]) ).
fof(f5652,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,[],[f5319,f3672,f3672,f5082,f3672,f5082,f3672,f5082]) ).
cnf(c_62,plain,
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))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f5332]) ).
cnf(c_63,plain,
c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f3601]) ).
cnf(c_65,plain,
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Int_Onumber__class_Onumber__of(X0,X2)) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
inference(cnf_transformation,[],[f3603]) ).
cnf(c_124,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f3670]) ).
cnf(c_125,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f3671]) ).
cnf(c_168,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)),
inference(cnf_transformation,[],[f3715]) ).
cnf(c_170,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(cnf_transformation,[],[f3717]) ).
cnf(c_996,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f4576]) ).
cnf(c_1391,plain,
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Groups_Otimes__class_Otimes(X0,c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)),X1) = c_Groups_Oplus__class_Oplus(X0,X1,X1) ),
inference(cnf_transformation,[],[f4988]) ).
cnf(c_1454,plain,
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))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5619]) ).
cnf(c_1549,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5148]) ).
cnf(c_1670,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f5269]) ).
cnf(c_1720,negated_conjecture,
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))))) != 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))))),
inference(cnf_transformation,[],[f5652]) ).
cnf(c_2803,plain,
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Int_Onumber__class_Onumber__of(X0,X2)) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
cnf(c_2939,plain,
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Groups_Otimes__class_Otimes(X0,c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)),X1) = c_Groups_Oplus__class_Oplus(X0,X1,X1) ),
inference(prop_impl_just,[status(thm)],[c_1391]) ).
cnf(c_17496,plain,
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_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(demodulation,[status(thm)],[c_62,c_124,c_125,c_168,c_170]) ).
cnf(c_17818,plain,
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))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(demodulation,[status(thm)],[c_1454,c_124,c_125,c_168,c_170,c_996]) ).
cnf(c_17824,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(demodulation,[status(thm)],[c_17496,c_17818]) ).
cnf(c_18737,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_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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)))),
inference(demodulation,[status(thm)],[c_1720,c_124,c_125,c_168,c_170,c_17818,c_17824]) ).
cnf(c_28416,plain,
( X0 != tc_Int_Oint
| c_Groups_Otimes__class_Otimes(X0,c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)),X1) = c_Groups_Oplus__class_Oplus(X0,X1,X1) ),
inference(resolution_lifted,[status(thm)],[c_2939,c_1549]) ).
cnf(c_28417,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,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) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(unflattening,[status(thm)],[c_28416]) ).
cnf(c_32437,plain,
( X0 != tc_RealDef_Oreal
| c_Groups_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Int_Onumber__class_Onumber__of(X0,X2)) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
inference(resolution_lifted,[status(thm)],[c_2803,c_1670]) ).
cnf(c_32438,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X0,X1)),
inference(unflattening,[status(thm)],[c_32437]) ).
cnf(c_46416,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X0,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)),
inference(superposition,[status(thm)],[c_32438,c_63]) ).
cnf(c_47626,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,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_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))),
inference(superposition,[status(thm)],[c_170,c_28417]) ).
cnf(c_94419,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_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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)))),
inference(superposition,[status(thm)],[c_47626,c_46416]) ).
cnf(c_94684,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_94419,c_18737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW174+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jun 19 09:39:39 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.96/4.18 % SZS status Started for theBenchmark.p
% 24.96/4.18 % SZS status Theorem for theBenchmark.p
% 24.96/4.18
% 24.96/4.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.96/4.18
% 24.96/4.18 ------ iProver source info
% 24.96/4.18
% 24.96/4.18 git: date: 2024-06-12 09:56:46 +0000
% 24.96/4.18 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 24.96/4.18 git: non_committed_changes: false
% 24.96/4.18
% 24.96/4.18 ------ Parsing...
% 24.96/4.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 24.96/4.18
% 24.96/4.18 ------ Preprocessing... sup_sim: 234 sf_s rm: 21 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe:64:0s pe_e
% 24.96/4.18
% 24.96/4.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 24.96/4.18
% 24.96/4.18 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 24.96/4.18 ------ Proving...
% 24.96/4.18 ------ Problem Properties
% 24.96/4.18
% 24.96/4.18
% 24.96/4.18 clauses 1472
% 24.96/4.18 conjectures 0
% 24.96/4.18 EPR 84
% 24.96/4.18 Horn 1294
% 24.96/4.18 unary 552
% 24.96/4.18 binary 472
% 24.96/4.18 lits 2965
% 24.96/4.18 lits eq 899
% 24.96/4.18 fd_pure 0
% 24.96/4.18 fd_pseudo 0
% 24.96/4.18 fd_cond 118
% 24.96/4.18 fd_pseudo_cond 67
% 24.96/4.18 AC symbols 0
% 24.96/4.18
% 24.96/4.18 ------ Input Options Time Limit: Unbounded
% 24.96/4.18
% 24.96/4.18
% 24.96/4.18 ------
% 24.96/4.18 Current options:
% 24.96/4.18 ------
% 24.96/4.18
% 24.96/4.18
% 24.96/4.18
% 24.96/4.18
% 24.96/4.18 ------ Proving...
% 24.96/4.18
% 24.96/4.18
% 24.96/4.18 % SZS status Theorem for theBenchmark.p
% 24.96/4.18
% 24.96/4.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.96/4.18
% 24.96/4.19
%------------------------------------------------------------------------------