%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW288+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 09:11:38 AM UTC 2026
% Result : Theorem 53.38s 7.19s
% Output : CNFRefutation 53.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 28 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 7 ~; 5 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 7 ( 2 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096,axiom,
( ( 'class$uRings$uOidom'('t$ua')
& 'class$uInt$uOring$u$uchar$u$u0'('t$ua') )
=> 'v$up' = 'c$uPolynomial$uOpCons'('t$ua',hAPP('c$uPolynomial$uOpoly'('t$ua','v$up'),'c$uGroups$uOzero$u$uclass$uOzero'('t$ua')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))) ) ).
fof(fact_degree__pCons__0,axiom,
! [X0,X1] :
( 'class$uGroups$uOzero'(X1)
=> 'c$uPolynomial$uOdegree'(X1,'c$uPolynomial$uOpCons'(X1,X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1)))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ) ).
fof(clrel_Int_Oring__char__0__Groups_Ozero,axiom,
! [X0] :
( 'class$uInt$uOring$u$uchar$u$u0'(X0)
=> 'class$uGroups$uOzero'(X0) ) ).
fof(tfree_0,hypothesis,
'class$uInt$uOring$u$uchar$u$u0'('t$ua') ).
fof(tfree_1,hypothesis,
'class$uRings$uOidom'('t$ua') ).
fof(conj_0,conjecture,
'c$uPolynomial$uOdegree'('t$ua','v$up') = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ).
fof(negated_conjecture,negated_conjecture,
'c$uPolynomial$uOdegree'('t$ua','v$up') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c15,plain,
( 'v$up' = 'c$uPolynomial$uOpCons'('t$ua',hAPP('c$uPolynomial$uOpoly'('t$ua','v$up'),'c$uGroups$uOzero$u$uclass$uOzero'('t$ua')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')))
| ~ 'class$uRings$uOidom'('t$ua')
| ~ 'class$uInt$uOring$u$uchar$u$u0'('t$ua') ),
inference(clausification,[status(esa)],[fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096]) ).
cnf(c44,plain,
( 'c$uPolynomial$uOdegree'(X0,'c$uPolynomial$uOpCons'(X0,X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')
| ~ 'class$uGroups$uOzero'(X0) ),
inference(clausification,[status(esa)],[fact_degree__pCons__0]) ).
cnf(c1489,plain,
( 'class$uGroups$uOzero'(X0)
| ~ 'class$uInt$uOring$u$uchar$u$u0'(X0) ),
inference(clausification,[status(esa)],[clrel_Int_Oring__char__0__Groups_Ozero]) ).
cnf(c1693,plain,
'class$uInt$uOring$u$uchar$u$u0'('t$ua'),
inference(clausification,[status(esa)],[tfree_0]) ).
cnf(c1694,plain,
'class$uRings$uOidom'('t$ua'),
inference(clausification,[status(esa)],[tfree_1]) ).
cnf(c1695,plain,
'c$uPolynomial$uOdegree'('t$ua','v$up') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'class$uGroups$uOzero'('t$ua'),
inference(resolution,[status(thm)],[c1489,c1693]) ).
cnf(d1,plain,
'c$uPolynomial$uOdegree'('t$ua','c$uPolynomial$uOpCons'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(resolution,[status(thm)],[d0,c44]) ).
cnf(d2,plain,
( ~ 'class$uRings$uOidom'('t$ua')
| 'v$up' = 'c$uPolynomial$uOpCons'('t$ua',hAPP('c$uPolynomial$uOpoly'('t$ua','v$up'),'c$uGroups$uOzero$u$uclass$uOzero'('t$ua')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))) ),
inference(resolution,[status(thm)],[c1693,c15]) ).
cnf(d3,plain,
'v$up' = 'c$uPolynomial$uOpCons'('t$ua',hAPP('c$uPolynomial$uOpoly'('t$ua','v$up'),'c$uGroups$uOzero$u$uclass$uOzero'('t$ua')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),
inference(resolution,[status(thm)],[c1694,d2]) ).
cnf(d4,plain,
'c$uPolynomial$uOdegree'('t$ua','v$up') = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c1695,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW288+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 15:39:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.38/7.19 % SZS status Theorem for theBenchmark.p
% 53.38/7.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------