%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW213+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 : n008.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 09:11:32 AM UTC 2026
% Result : Theorem 46.24s 22.20s
% Output : CNFRefutation 46.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 34 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 8 |; 1 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 36 ( 2 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_poly__offset__poly,axiom,
! [X0,X1,X2,X3] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X3)
=> hAPP('c$uPolynomial$uOpoly'(X3,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X3,X2,X1)),X0) = hAPP('c$uPolynomial$uOpoly'(X3,X2),'c$uGroups$uOplus$u$uclass$uOplus'(X3,X1,X0)) ) ).
fof(fact_degree__offset__poly,axiom,
! [X0,X1,X2] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X2)
=> 'c$uPolynomial$uOdegree'(X2,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X2,X1,X0)) = 'c$uPolynomial$uOdegree'(X2,X1) ) ).
fof(fact_poly__offset,axiom,
! [X0,X1] :
? [X2] :
( ! [X3] : hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X2),X3) = hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X1),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X0,X3))
& 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOpsize'('tc$uComplex$uOcomplex',X2) = 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOpsize'('tc$uComplex$uOcomplex',X1) ) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
'class$uRings$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex') ).
fof(conj_0,hypothesis,
! [X0] :
( 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex',X0) = 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')
=> ( ! [X1] : hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X0),X1) = hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$up'),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uz',X1))
=> 'v$uthesis' ) ) ).
fof(conj_1,conjecture,
'v$uthesis' ).
fof(negated_conjecture,negated_conjecture,
~ 'v$uthesis',
inference(negate_conjecture,[status(cth)],[conj_1]) ).
cnf(c2,plain,
( hAPP('c$uPolynomial$uOpoly'(X0,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X0,X1,X2)),X3) = hAPP('c$uPolynomial$uOpoly'(X0,X1),'c$uGroups$uOplus$u$uclass$uOplus'(X0,X2,X3))
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[fact_poly__offset__poly]) ).
cnf(c16,plain,
( 'c$uPolynomial$uOdegree'(X0,'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'(X0,X1,X2)) = 'c$uPolynomial$uOdegree'(X0,X1)
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[fact_degree__offset__poly]) ).
cnf(c23,plain,
hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',sK75(X0,X1)),X2) = hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X1),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X0,X2)),
inference(clausification,[status(esa)],[fact_poly__offset]) ).
cnf(c1591,plain,
'class$uRings$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(c1673,plain,
( 'v$uthesis'
| hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X0),sK2839(X0)) != hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$up'),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uz',sK2839(X0)))
| 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex',X0) != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up') ),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c1674,plain,
~ 'v$uthesis',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v$uthesis'
| 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex',X0) != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')
| hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X0),sK2839(X0)) != hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',sK75('v$uz','v$up')),sK2839(X0)) ),
inference(demodulation,[status(thm)],[c1673,c23]) ).
cnf(d1,plain,
( 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex',X0) != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')
| hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X0),sK2839(X0)) != hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',sK75('v$uz','v$up')),sK2839(X0)) ),
inference(resolution,[status(thm)],[c1674,d0]) ).
cnf(d2,plain,
hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('tc$uComplex$uOcomplex',X0,X1)),X2) = hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',X0),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X1,X2)),
inference(resolution,[status(thm)],[c1591,c2]) ).
cnf(d3,plain,
hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('tc$uComplex$uOcomplex',X0,X1)),X2) = hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',sK75(X1,X0)),X2),
inference(demodulation,[status(thm)],[d2,c23]) ).
cnf(d4,plain,
( 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('tc$uComplex$uOcomplex',X0,X1)) != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')
| hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',sK75(X1,X0)),sK2839('c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('tc$uComplex$uOcomplex',X0,X1))) != hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex',sK75('v$uz','v$up')),sK2839('c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('tc$uComplex$uOcomplex',X0,X1))) ),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('tc$uComplex$uOcomplex','v$up','v$uz')) != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up'),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOoffset$u$upoly'('tc$uComplex$uOcomplex',X0,X1)) = 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex',X0),
inference(resolution,[status(thm)],[c1591,c16]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW213+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/10.41 % Computer : n008.cluster.edu
% 0.13/10.41 % Model : x86_64 x86_64
% 0.13/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.41 % Memory : 8046.5625MB
% 0.13/10.41 % OS : Linux 6.8.0-71-generic
% 0.13/10.41 % CPULimit : 300
% 0.13/10.41 % WCLimit : 300
% 0.13/10.41 % DateTime : Sat Sep 26 15:29:51 UTC 2026
% 0.13/10.41 % CPUTime :
% 0.13/10.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.24/22.20 % SZS status Theorem for theBenchmark.p
% 46.24/22.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------