TSTP Solution File: SWW256+1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW256+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.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 18:31:46 EDT 2024
% Result : Theorem 1.99s 0.66s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 31 unt; 0 def)
% Number of atoms : 192 ( 56 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 211 ( 87 ~; 86 |; 18 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 126 ( 120 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6626,plain,
$false,
inference(subsumption_resolution,[],[f6625,f4064]) ).
fof(f4064,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1197]) ).
fof(f1197,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6625,plain,
~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(subsumption_resolution,[],[f6623,f5705]) ).
fof(f5705,plain,
~ sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Complex_Oii),
inference(equality_proxy_replacement,[],[f4092,f5700]) ).
fof(f5700,plain,
! [X0,X1] :
( sQ37_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ37_eqProxy])]) ).
fof(f4092,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(cnf_transformation,[],[f755]) ).
fof(f755,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6623,plain,
( sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Complex_Oii)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(resolution,[],[f6571,f5931]) ).
fof(f5931,plain,
! [X0,X1] :
( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| sQ37_eqProxy(c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(equality_proxy_replacement,[],[f4499,f5700]) ).
fof(f4499,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2560]) ).
fof(f2560,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(flattening,[],[f2559]) ).
fof(f2559,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1613]) ).
fof(f1613,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f988]) ).
fof(f988,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Groups_Ozero__class_Ozero(X5) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6571,plain,
! [X0] : c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,c_Complex_Oii),
inference(resolution,[],[f6539,f5705]) ).
fof(f6539,plain,
! [X0,X1] :
( sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)
| c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,X1) ),
inference(subsumption_resolution,[],[f6538,f4052]) ).
fof(f4052,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1217]) ).
fof(f1217,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6538,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,X1)
| sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)
| ~ class_Power_Opower(tc_Complex_Ocomplex) ),
inference(subsumption_resolution,[],[f6537,f4020]) ).
fof(f4020,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6537,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,X1)
| sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)
| ~ class_Rings_Omult__zero(tc_Complex_Ocomplex)
| ~ class_Power_Opower(tc_Complex_Ocomplex) ),
inference(subsumption_resolution,[],[f6536,f4021]) ).
fof(f4021,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1195]) ).
fof(f1195,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6536,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,X1)
| sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)
| ~ class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)
| ~ class_Rings_Omult__zero(tc_Complex_Ocomplex)
| ~ class_Power_Opower(tc_Complex_Ocomplex) ),
inference(subsumption_resolution,[],[f6533,f4022]) ).
fof(f4022,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1202]) ).
fof(f1202,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6533,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,X1)
| sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)
| ~ class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
| ~ class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)
| ~ class_Rings_Omult__zero(tc_Complex_Ocomplex)
| ~ class_Power_Opower(tc_Complex_Ocomplex) ),
inference(resolution,[],[f6530,f6289]) ).
fof(f6289,plain,
! [X2,X0,X1] :
( ~ sQ37_eqProxy(c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| sQ37_eqProxy(c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(equality_proxy_replacement,[],[f5145,f5700,f5700]) ).
fof(f5145,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(cnf_transformation,[],[f3744]) ).
fof(f3744,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(flattening,[],[f3743]) ).
fof(f3743,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(nnf_transformation,[],[f3095]) ).
fof(f3095,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(flattening,[],[f3094]) ).
fof(f3094,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(ennf_transformation,[],[f2056]) ).
fof(f2056,plain,
! [X0,X1,X2] :
( ( class_Rings_Ozero__neq__one(X2)
& class_Rings_Ono__zero__divisors(X2)
& class_Rings_Omult__zero(X2)
& class_Power_Opower(X2) )
=> ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X8,X9,X5] :
( ( class_Rings_Ozero__neq__one(X5)
& class_Rings_Ono__zero__divisors(X5)
& class_Rings_Omult__zero(X5)
& class_Power_Opower(X5) )
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X9),X8)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X8
& c_Groups_Ozero__class_Ozero(X5) = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6530,plain,
! [X0,X1] :
( sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X1,X0) ),
inference(subsumption_resolution,[],[f6524,f3955]) ).
fof(f3955,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1220]) ).
fof(f1220,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6524,plain,
! [X0,X1] :
( sQ37_eqProxy(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X1,X0)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(resolution,[],[f6518,f6371]) ).
fof(f6371,plain,
! [X2,X3,X0,X1] :
( ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| sQ37_eqProxy(c_Groups_Ozero__class_Ozero(X3),X1)
| c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ class_Rings_Oidom(X3) ),
inference(equality_proxy_replacement,[],[f5331,f5700]) ).
fof(f5331,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| c_Groups_Ozero__class_Ozero(X3) = X1
| ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Oidom(X3) ),
inference(cnf_transformation,[],[f3824]) ).
fof(f3824,plain,
! [X0,X1,X2,X3] :
( ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ( ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
& c_Groups_Ozero__class_Ozero(X3) != X1 ) )
& ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| c_Groups_Ozero__class_Ozero(X3) = X1
| ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) )
| ~ class_Rings_Oidom(X3) ),
inference(flattening,[],[f3823]) ).
fof(f3823,plain,
! [X0,X1,X2,X3] :
( ( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ( ~ c_Rings_Odvd__class_Odvd(X3,X2,X0)
& c_Groups_Ozero__class_Ozero(X3) != X1 ) )
& ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| c_Groups_Ozero__class_Ozero(X3) = X1
| ~ c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) )
| ~ class_Rings_Oidom(X3) ),
inference(nnf_transformation,[],[f3205]) ).
fof(f3205,plain,
! [X0,X1,X2,X3] :
( ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| c_Groups_Ozero__class_Ozero(X3) = X1 ) )
| ~ class_Rings_Oidom(X3) ),
inference(ennf_transformation,[],[f2142]) ).
fof(f2142,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oidom(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> ( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) ),
inference(rectify,[],[f978]) ).
fof(f978,axiom,
! [X32,X35,X9,X5] :
( class_Rings_Oidom(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X32),X35))
<=> ( c_Rings_Odvd__class_Odvd(X5,X9,X32)
| c_Groups_Ozero__class_Ozero(X5) = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6518,plain,
! [X0,X1] : c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(subsumption_resolution,[],[f6508,f3978]) ).
fof(f3978,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1223]) ).
fof(f1223,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6508,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))
| ~ class_Rings_Odvd(tc_Complex_Ocomplex) ),
inference(resolution,[],[f5701,f6385]) ).
fof(f6385,plain,
! [X2,X3,X0,X1] :
( ~ sQ37_eqProxy(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),X2)
| c_Rings_Odvd__class_Odvd(X3,X1,X2)
| ~ class_Rings_Odvd(X3) ),
inference(equality_proxy_replacement,[],[f5369,f5700]) ).
fof(f5369,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X1,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(cnf_transformation,[],[f3259]) ).
fof(f3259,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X1,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(flattening,[],[f3258]) ).
fof(f3258,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X1,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(ennf_transformation,[],[f2173]) ).
fof(f2173,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odvd(X3)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) = X2
=> c_Rings_Odvd__class_Odvd(X3,X1,X2) ) ),
inference(rectify,[],[f982]) ).
fof(f982,axiom,
! [X11,X20,X4,X5] :
( class_Rings_Odvd(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X11) = X4
=> c_Rings_Odvd__class_Odvd(X5,X20,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f5701,plain,
! [X0,X1] : sQ37_eqProxy(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(equality_proxy_replacement,[],[f5552,f5700]) ).
fof(f5552,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(definition_unfolding,[],[f3868,f4155,f4155]) ).
fof(f4155,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1323]) ).
fof(f1323,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rectify,[],[f212]) ).
fof(f212,axiom,
! [X3] : c_Nat_OSuc(X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f3868,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(cnf_transformation,[],[f2323]) ).
fof(f2323,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(ennf_transformation,[],[f1286]) ).
fof(f1286,plain,
~ ? [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(rectify,[],[f1285]) ).
fof(f1285,negated_conjecture,
~ ? [X2,X80] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X80),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X80),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(negated_conjecture,[],[f1284]) ).
fof(f1284,conjecture,
? [X2,X80] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X80),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X80),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW256+1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.09 % Command : run_vampire %s %d THM
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Wed Jun 19 04:22:53 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.14/0.30 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.30 Running first-order theorem proving
% 0.14/0.30 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.38 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (22384)lrs-1011_8:1_sil=16000:sos=all:i=346:sd=1:ep=R:ss=axioms_0 on theBenchmark for (2999ds/346Mi)
% 0.15/0.39 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (22385)lrs+1002_1:1_to=lpo:sil=2000:sp=frequency:sos=on:st=3.0:i=282:sd=2:ss=axioms_0 on theBenchmark for (2999ds/282Mi)
% 0.15/0.39 % (22384)Refutation not found, incomplete strategy% (22384)------------------------------
% 0.15/0.39 % (22384)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.15/0.39 % (22384)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.15/0.39 % (22384)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39 % (22384)Memory used [KB]: 2339
% 0.15/0.39 % (22384)Time elapsed: 0.009 s
% 0.15/0.39 % (22384)Instructions burned: 26 (million)
% 0.15/0.39 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (22382)dis+2_1:50_sil=256000:flr=on:sac=on:i=218245:fsr=off:uhcvi=on_0 on theBenchmark for (2999ds/218245Mi)
% 0.15/0.39 % (22384)------------------------------
% 0.15/0.39 % (22384)------------------------------
% 0.15/0.40 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (22381)lrs+11_1:12_to=lpo:sil=128000:sp=const_min:i=103397:ss=included:sgt=16:av=off:fsd=on:nm=16_0 on theBenchmark for (2999ds/103397Mi)
% 0.15/0.40 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (22379)lrs+10_1:628_anc=all_dependent:bsr=unit_only:sil=256000:sp=frequency:i=136310:newcnf=on_0 on theBenchmark for (2999ds/136310Mi)
% 0.15/0.40 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (22383)lrs-1010_1:1_sil=2000:i=250:sd=1:ss=axioms:sgt=32:sos=on_0 on theBenchmark for (2999ds/250Mi)
% 0.15/0.40 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (22380)lrs+2_3:1_to=lpo:sil=256000:irw=on:fde=unused:sp=unary_first:bce=on:nwc=6.0:s2agt=30:newcnf=on:s2a=on:i=140573:nm=2_0 on theBenchmark for (2999ds/140573Mi)
% 0.15/0.41 % (22383)Refutation not found, incomplete strategy% (22383)------------------------------
% 0.15/0.41 % (22383)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.15/0.41 % (22383)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.15/0.41 % (22383)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.41
% 0.15/0.41 % (22383)Memory used [KB]: 2423
% 0.15/0.41 % (22383)Time elapsed: 0.016 s
% 0.15/0.41 % (22383)Instructions burned: 35 (million)
% 0.15/0.41 % (22383)------------------------------
% 0.15/0.41 % (22383)------------------------------
% 0.15/0.43 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.43 % (22386)lrs+1010_1:1_sil=8000:sp=occurrence:urr=on:br=off:st=1.2:i=125:sd=7:ss=axioms:sgt=16_0 on theBenchmark for (2999ds/125Mi)
% 0.15/0.45 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.45 % (22387)lrs+1010_1:1_to=lpo:sil=2000:sos=on:fd=off:i=402:bd=off_0 on theBenchmark for (2999ds/402Mi)
% 0.15/0.47 % (22386)Instruction limit reached!
% 0.15/0.47 % (22386)------------------------------
% 0.15/0.47 % (22386)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.15/0.47 % (22386)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.15/0.47 % (22386)Termination reason: Time limit
% 0.15/0.47 % (22386)Termination phase: Saturation
% 0.15/0.47
% 0.15/0.47 % (22386)Memory used [KB]: 3649
% 0.15/0.47 % (22386)Time elapsed: 0.042 s
% 0.15/0.47 % (22386)Instructions burned: 125 (million)
% 0.15/0.48 % (22385)Instruction limit reached!
% 0.15/0.48 % (22385)------------------------------
% 0.15/0.48 % (22385)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.15/0.48 % (22385)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.15/0.48 % (22385)Termination reason: Time limit
% 0.15/0.48 % (22385)Termination phase: Saturation
% 0.15/0.48
% 0.15/0.48 % (22385)Memory used [KB]: 4610
% 0.15/0.48 % (22385)Time elapsed: 0.093 s
% 0.15/0.48 % (22385)Instructions burned: 282 (million)
% 0.15/0.50 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.50 % (22388)lrs+2_5:1_sil=2000:sos=on:acc=on:urr=on:alpa=false:i=325:sd=1:bd=off:nm=32:ss=axioms:br=off:sup=off:bs=on_0 on theBenchmark for (2998ds/325Mi)
% 0.15/0.51 % (22388)Refutation not found, incomplete strategy% (22388)------------------------------
% 0.15/0.51 % (22388)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.15/0.51 % (22388)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.15/0.51 % (22388)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.51
% 0.15/0.51 % (22388)Memory used [KB]: 2334
% 0.15/0.51 % (22388)Time elapsed: 0.010 s
% 0.15/0.51 % (22388)Instructions burned: 27 (million)
% 0.15/0.51 % (22388)------------------------------
% 0.15/0.51 % (22388)------------------------------
% 0.15/0.52 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.52 % (22389)lrs+1011_1:1_to=lpo:drc=encompass:sil=4000:plsq=on:plsqr=32,1:sp=occurrence:sos=on:erd=off:urr=on:lsd=100:i=267:sd=1:nm=2:ss=axioms:flr=on:sup=off_0 on theBenchmark for (2998ds/267Mi)
% 0.15/0.55 % (22377)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.55 % (22390)lrs+33_1:1_sil=4000:sp=reverse_frequency:sos=all:i=156:sd=2:bd=off:nm=2:av=off:fsr=off:ss=axioms:sgt=10:rawr=on:sup=off:to=lpo:fs=off_0 on theBenchmark for (2998ds/156Mi)
% 0.15/0.56 % (22390)Refutation not found, incomplete strategy% (22390)------------------------------
% 0.15/0.56 % (22390)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.15/0.56 % (22390)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.15/0.56 % (22390)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.56
% 0.15/0.56 % (22390)Memory used [KB]: 2450
% 0.15/0.56 % (22390)Time elapsed: 0.012 s
% 0.15/0.56 % (22390)Instructions burned: 35 (million)
% 0.15/0.56 % (22390)------------------------------
% 0.15/0.56 % (22390)------------------------------
% 0.15/0.57 % (22387)Instruction limit reached!
% 0.15/0.57 % (22387)------------------------------
% 0.15/0.57 % (22387)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.15/0.57 % (22387)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.15/0.57 % (22387)Termination reason: Time limit
% 0.15/0.57 % (22387)Termination phase: Saturation
% 0.15/0.57
% 0.15/0.57 % (22387)Memory used [KB]: 7800
% 0.15/0.57 % (22387)Time elapsed: 0.122 s
% 0.15/0.57 % (22387)Instructions burned: 404 (million)
% 1.71/0.59 % (22389)Instruction limit reached!
% 1.71/0.59 % (22389)------------------------------
% 1.71/0.59 % (22389)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.71/0.59 % (22389)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.71/0.59 % (22389)Termination reason: Time limit
% 1.71/0.59 % (22389)Termination phase: Saturation
% 1.71/0.59
% 1.71/0.59 % (22389)Memory used [KB]: 2862
% 1.71/0.59 % (22389)Time elapsed: 0.072 s
% 1.71/0.59 % (22389)Instructions burned: 268 (million)
% 1.71/0.59 % (22377)Running in auto input_syntax mode. Trying TPTP
% 1.71/0.59 % (22391)dis+1011_1:1_to=lpo:sil=4000:sp=const_max:sos=all:spb=goal:st=1.5:i=200:av=off:ss=axioms:sfv=off:bd=off:sd=2:fd=off_0 on theBenchmark for (2997ds/200Mi)
% 1.84/0.61 % (22377)Running in auto input_syntax mode. Trying TPTP
% 1.84/0.61 % (22392)dis-1010_1:4_sil=2000:tgt=ground:fd=off:i=203:sd=1:nm=4:av=off:ss=axioms:sgt=64:newcnf=on_0 on theBenchmark for (2997ds/203Mi)
% 1.84/0.62 % (22377)Running in auto input_syntax mode. Trying TPTP
% 1.84/0.62 % (22393)lrs+1002_1:8_sil=4000:sos=on:nicw=on:st=2.5:i=1027:ss=included:sd=7:ep=RS:erd=off_0 on theBenchmark for (2997ds/1027Mi)
% 1.99/0.65 % (22391)Instruction limit reached!
% 1.99/0.65 % (22391)------------------------------
% 1.99/0.65 % (22391)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.99/0.65 % (22391)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.99/0.65 % (22391)Termination reason: Time limit
% 1.99/0.65 % (22391)Termination phase: Saturation
% 1.99/0.65
% 1.99/0.65 % (22391)Memory used [KB]: 3714
% 1.99/0.65 % (22391)Time elapsed: 0.080 s
% 1.99/0.65 % (22391)Instructions burned: 200 (million)
% 1.99/0.66 % (22393)First to succeed.
% 1.99/0.66 % (22393)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22377"
% 1.99/0.66 % (22377)Running in auto input_syntax mode. Trying TPTP
% 1.99/0.66 % (22393)Refutation found. Thanks to Tanya!
% 1.99/0.66 % SZS status Theorem for theBenchmark
% 1.99/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 1.99/0.66 % (22393)------------------------------
% 1.99/0.66 % (22393)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.99/0.66 % (22393)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.99/0.66 % (22393)Termination reason: Refutation
% 1.99/0.66
% 1.99/0.66 % (22393)Memory used [KB]: 4422
% 1.99/0.66 % (22393)Time elapsed: 0.035 s
% 1.99/0.66 % (22393)Instructions burned: 124 (million)
% 1.99/0.66 % (22393)------------------------------
% 1.99/0.66 % (22393)------------------------------
% 1.99/0.66 % (22377)Success in time 0.319 s
%------------------------------------------------------------------------------