%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:14:09 AM UTC 2026
% Result : Theorem 21.57s 3.26s
% Output : CNFRefutation 21.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 18 unt; 0 def)
% Number of atoms : 46 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 14 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Orderings_Oord__class_Oless_0_arg2,axiom,
! [X0,X1,X2] :
( 'linordered$uidom'(X2)
=> ( 'ord$uless'(X2,X0,ti(X2,X1))
<=> 'ord$uless'(X2,X0,X1) ) ) ).
fof(fact_0_n1pos,axiom,
'ord$uless'(int,'zero$uzero'(int),'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))) ).
fof(fact_5_zero__eq__power2,axiom,
! [X0] :
( 'ring$u11004092258visors'(X0)
=> ! [X1] :
( 'power$upower'(X0,X1,'number$unumber$uof'(nat,bit0(bit1(pls)))) = 'zero$uzero'(X0)
<=> ti(X0,X1) = 'zero$uzero'(X0) ) ) ).
fof(fact_32_rel__simps_I2_J,axiom,
~ 'ord$uless'(int,pls,pls) ).
fof(fact_73_Pls__def,axiom,
pls = 'zero$uzero'(int) ).
fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors,axiom,
'ring$u11004092258visors'(int) ).
fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
'linordered$uidom'(int) ).
fof(conj_0,conjecture,
'power$upower'(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n)),'number$unumber$uof'(nat,bit0(bit1(pls)))) != 'zero$uzero'(int) ).
fof(negated_conjecture,negated_conjecture,
~ ( 'power$upower'(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n)),'number$unumber$uof'(nat,bit0(bit1(pls)))) != 'zero$uzero'(int) ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c23,plain,
( ~ 'ord$uless'(X0,X1,X2)
| 'ord$uless'(X0,X1,ti(X0,X2))
| ~ 'linordered$uidom'(X0) ),
inference(clausification,[status(esa)],[tsy_c_Orderings_Oord__class_Oless_0_arg2]) ).
cnf(c36,plain,
'ord$uless'(int,'zero$uzero'(int),'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))),
inference(clausification,[status(esa)],[fact_0_n1pos]) ).
cnf(c43,plain,
( ti(X0,X1) = 'zero$uzero'(X0)
| 'power$upower'(X0,X1,'number$unumber$uof'(nat,bit0(bit1(pls)))) != 'zero$uzero'(X0)
| ~ 'ring$u11004092258visors'(X0) ),
inference(clausification,[status(esa)],[fact_5_zero__eq__power2]) ).
cnf(c77,plain,
~ 'ord$uless'(int,pls,pls),
inference(clausification,[status(esa)],[fact_32_rel__simps_I2_J]) ).
cnf(c145,plain,
pls = 'zero$uzero'(int),
inference(clausification,[status(esa)],[fact_73_Pls__def]) ).
cnf(c176,plain,
'ring$u11004092258visors'(int),
inference(clausification,[status(esa)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
cnf(c178,plain,
'linordered$uidom'(int),
inference(clausification,[status(esa)],[arity_Int_Oint___Rings_Olinordered__idom]) ).
cnf(c197,plain,
'power$upower'(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n)),'number$unumber$uof'(nat,bit0(bit1(pls)))) = 'zero$uzero'(int),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'ord$uless'(int,pls,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))),
inference(demodulation,[status(thm)],[c36,c145]) ).
cnf(d1,plain,
'power$upower'(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n)),'number$unumber$uof'(nat,bit0(bit1(pls)))) = pls,
inference(demodulation,[status(thm)],[c197,c145]) ).
cnf(d2,plain,
( ~ 'ring$u11004092258visors'(int)
| ti(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))) = 'zero$uzero'(int)
| pls != 'zero$uzero'(int) ),
inference(superposition,[status(thm)],[d1,c43]) ).
cnf(d3,plain,
( ~ 'ring$u11004092258visors'(int)
| pls != 'zero$uzero'(int)
| ti(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))) = pls ),
inference(demodulation,[status(thm)],[d2,c145]) ).
cnf(d4,plain,
( ~ 'ring$u11004092258visors'(int)
| pls != pls
| ti(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))) = pls ),
inference(demodulation,[status(thm)],[d3,c145]) ).
cnf(d5,plain,
( pls != pls
| ti(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))) = pls ),
inference(resolution,[status(thm)],[c176,d4]) ).
cnf(d6,plain,
ti(int,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))) = pls,
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ 'ord$uless'(int,X0,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n)))
| ~ 'linordered$uidom'(int)
| 'ord$uless'(int,X0,pls) ),
inference(superposition,[status(thm)],[d6,c23]) ).
cnf(d8,plain,
( 'ord$uless'(int,X0,pls)
| ~ 'ord$uless'(int,X0,'plus$uplus'(int,'one$uone'(int),'semiring$u1$uof$unat'(int,n))) ),
inference(resolution,[status(thm)],[c178,d7]) ).
cnf(d9,plain,
'ord$uless'(int,pls,pls),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c77,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 04:19:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.57/3.26 % SZS status Theorem for theBenchmark.p
% 21.57/3.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------