%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW182+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 09:11:29 AM UTC 2026
% Result : Theorem 158.61s 53.64s
% Output : CNFRefutation 158.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 49 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 47 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_offset__poly__0,axiom,
! [X0,X1] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X1)
=> 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1)),X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1)) ) ).
fof(fact_monom__0,axiom,
! [X0,X1] :
( 'class$uGroups$uOzero'(X1)
=> 'c$uPolynomial$uOmonom'(X1,X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) = 'c$uPolynomial$uOpCons'(X1,X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1))) ) ).
fof(fact_smult__0__right,axiom,
! [X0,X1] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X1)
=> 'c$uPolynomial$uOsmult'(X1,X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1)) ) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X0,X1] :
( 'class$uGroups$uOcomm$u$umonoid$u$uadd'(X1)
=> 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'(X1),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1)),X0) = X0 ) ).
fof(fact_offset__poly__pCons,axiom,
! [X0,X1,X2,X3] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X3)
=> 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X3,'c$uPolynomial$uOpCons'(X3,X2,X1),X0) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'(X3),'c$uPolynomial$uOsmult'(X3,X0,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X3,X1,X0)),'c$uPolynomial$uOpCons'(X3,X2,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X3,X1,X0))) ) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add,axiom,
! [X0] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X0)
=> 'class$uGroups$uOcomm$u$umonoid$u$uadd'(X0) ) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ozero,axiom,
! [X0] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X0)
=> 'class$uGroups$uOzero'(X0) ) ).
fof(tfree_0,hypothesis,
'class$uRings$uOcomm$u$usemiring$u$u0'('t$ua') ).
fof(conj_0,conjecture,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOpCons'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),'v$uh') = 'c$uPolynomial$uOpCons'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))) ).
fof(negated_conjecture,negated_conjecture,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOpCons'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),'v$uh') != 'c$uPolynomial$uOpCons'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c1,plain,
( 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)),X1) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0))
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[fact_offset__poly__0]) ).
cnf(c27,plain,
( 'c$uPolynomial$uOmonom'(X0,X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) = 'c$uPolynomial$uOpCons'(X0,X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)))
| ~ 'class$uGroups$uOzero'(X0) ),
inference(clausification,[status(esa)],[fact_monom__0]) ).
cnf(c50,plain,
( 'c$uPolynomial$uOsmult'(X0,X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0))
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[fact_smult__0__right]) ).
cnf(c69,plain,
( 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'(X0),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)),X1) = X1
| ~ 'class$uGroups$uOcomm$u$umonoid$u$uadd'(X0) ),
inference(clausification,[status(esa)],[fact_add__poly__code_I1_J]) ).
cnf(c76,plain,
( 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X0,'c$uPolynomial$uOpCons'(X0,X1,X2),X3) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'(X0),'c$uPolynomial$uOsmult'(X0,X3,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X0,X2,X3)),'c$uPolynomial$uOpCons'(X0,X1,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X0,X2,X3)))
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[fact_offset__poly__pCons]) ).
cnf(c937,plain,
( 'class$uGroups$uOcomm$u$umonoid$u$uadd'(X0)
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add]) ).
cnf(c940,plain,
( 'class$uGroups$uOzero'(X0)
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[clrel_Rings_Ocomm__semiring__0__Groups_Ozero]) ).
cnf(c994,plain,
'class$uRings$uOcomm$u$usemiring$u$u0'('t$ua'),
inference(clausification,[status(esa)],[tfree_0]) ).
cnf(c995,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOpCons'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),'v$uh') != 'c$uPolynomial$uOpCons'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'class$uGroups$uOzero'('t$ua'),
inference(resolution,[status(thm)],[c940,c994]) ).
cnf(d1,plain,
'c$uPolynomial$uOmonom'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) = 'c$uPolynomial$uOpCons'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),
inference(resolution,[status(thm)],[d0,c27]) ).
cnf(d2,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOmonom'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),'v$uh') != 'c$uPolynomial$uOpCons'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),
inference(demodulation,[status(thm)],[c995,d1]) ).
cnf(d3,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOmonom'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),'v$uh') != 'c$uPolynomial$uOmonom'('t$ua','v$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),
inference(resolution,[status(thm)],[c994,c1]) ).
cnf(d5,plain,
'class$uGroups$uOcomm$u$umonoid$u$uadd'('t$ua'),
inference(resolution,[status(thm)],[c937,c994]) ).
cnf(d6,plain,
'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'('t$ua'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),X0) = X0,
inference(resolution,[status(thm)],[c69,d5]) ).
cnf(d7,plain,
'c$uPolynomial$uOsmult'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),
inference(resolution,[status(thm)],[c50,c994]) ).
cnf(d8,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOpCons'('t$ua',X0,X1),X2) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'('t$ua'),'c$uPolynomial$uOsmult'('t$ua',X2,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua',X1,X2)),'c$uPolynomial$uOpCons'('t$ua',X0,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua',X1,X2))),
inference(resolution,[status(thm)],[c76,c994]) ).
cnf(d9,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOpCons'('t$ua',X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),X0) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'('t$ua'),'c$uPolynomial$uOsmult'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),'c$uPolynomial$uOpCons'('t$ua',X1,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),X0))),
inference(superposition,[status(thm)],[d4,d8]) ).
cnf(d10,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOmonom'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),X1) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'('t$ua'),'c$uPolynomial$uOsmult'('t$ua',X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),'c$uPolynomial$uOpCons'('t$ua',X0,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),X1))),
inference(demodulation,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOmonom'('t$ua',X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),X0) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uPolynomial$uOpoly'('t$ua'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),'c$uPolynomial$uOpCons'('t$ua',X1,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),X0))),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOmonom'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),X1) = 'c$uPolynomial$uOpCons'('t$ua',X0,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')),X1)),
inference(demodulation,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOmonom'('t$ua',X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),X0) = 'c$uPolynomial$uOpCons'('t$ua',X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('t$ua','c$uPolynomial$uOmonom'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),X1) = 'c$uPolynomial$uOmonom'('t$ua',X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW182+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n001.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 15:31:12 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 158.61/53.64 % SZS status Theorem for theBenchmark.p
% 158.61/53.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------