%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW246+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 : n010.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 09:11:35 AM UTC 2026
% Result : Theorem 150.11s 45.61s
% Output : CNFRefutation 150.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 51 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 16 ~; 12 |; 0 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 10 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_poly__0,axiom,
! [X0,X1] :
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X1)
=> hAPP('c$uPolynomial$uOpoly'(X1,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1))),X0) = 'c$uGroups$uOzero$u$uclass$uOzero'(X1) ) ).
fof(fact_constant__def,axiom,
! [X0,X1,X2] :
( 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'(X2,X1,X0)
<=> ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4) ) ).
fof(fact__C0_C,axiom,
( 'class$uRings$uOidom'('t$ua')
=> ~ 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'('t$ua','t$ua','c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')))) ) ).
fof(fact_lessI,axiom,
! [X0] : 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,hAPP('c$uNat$uOSuc',X0)) ).
fof(fact_not__less__eq,axiom,
! [X0,X1] :
( ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X1,X0)
<=> 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,hAPP('c$uNat$uOSuc',X1)) ) ).
fof(fact_order__less__irrefl,axiom,
! [X0,X1] :
( 'class$uOrderings$uOpreorder'(X1)
=> ~ 'c$uOrderings$uOord$u$uclass$uOless'(X1,X0,X0) ) ).
fof(fact_mod__less,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X1,X0)
=> 'c$uDivides$uOdiv$u$uclass$uOmod'('tc$uNat$uOnat',X1,X0) = X1 ) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__0,axiom,
! [X0] :
( 'class$uRings$uOidom'(X0)
=> 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
'class$uOrderings$uOpreorder'('tc$uNat$uOnat') ).
fof(tfree_0,hypothesis,
'class$uRings$uOidom'('t$ua') ).
cnf(c7,plain,
( 'c$uGroups$uOzero$u$uclass$uOzero'(X0) = hAPP('c$uPolynomial$uOpoly'(X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0))),X1)
| ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[fact_poly__0]) ).
cnf(c26,plain,
( hAPP(X2,sK49(X2)) != hAPP(X2,sK48(X2))
| 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'(X0,X1,X2) ),
inference(clausification,[status(esa)],[fact_constant__def]) ).
cnf(c62,plain,
( ~ 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'('t$ua','t$ua','c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))))
| ~ 'class$uRings$uOidom'('t$ua') ),
inference(clausification,[status(esa)],[fact__C0_C]) ).
cnf(c760,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,hAPP('c$uNat$uOSuc',X0)),
inference(clausification,[status(esa)],[fact_lessI]) ).
cnf(c853,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X1,hAPP('c$uNat$uOSuc',X0))
| 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1) ),
inference(clausification,[status(esa)],[fact_not__less__eq]) ).
cnf(c857,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'(X0,X1,X1)
| ~ 'class$uOrderings$uOpreorder'(X0) ),
inference(clausification,[status(esa)],[fact_order__less__irrefl]) ).
cnf(c873,plain,
( 'c$uDivides$uOdiv$u$uclass$uOmod'('tc$uNat$uOnat',X0,X1) = X0
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1) ),
inference(clausification,[status(esa)],[fact_mod__less]) ).
cnf(c1121,plain,
( 'class$uRings$uOcomm$u$usemiring$u$u0'(X0)
| ~ 'class$uRings$uOidom'(X0) ),
inference(clausification,[status(esa)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0]) ).
cnf(c1180,plain,
'class$uOrderings$uOpreorder'('tc$uNat$uOnat'),
inference(clausification,[status(esa)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(c1236,plain,
'class$uRings$uOidom'('t$ua'),
inference(clausification,[status(esa)],[tfree_0]) ).
cnf(d0,plain,
~ 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'('t$ua','t$ua','c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')))),
inference(resolution,[status(thm)],[c1236,c62]) ).
cnf(d1,plain,
'class$uRings$uOcomm$u$usemiring$u$u0'('t$ua'),
inference(resolution,[status(thm)],[c1121,c1236]) ).
cnf(d2,plain,
'c$uGroups$uOzero$u$uclass$uOzero'('t$ua') = hAPP('c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),X0),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'(X0,X1,'c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))))
| hAPP('c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))),sK49('c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))))) != 'c$uGroups$uOzero$u$uclass$uOzero'('t$ua') ),
inference(superposition,[status(thm)],[d2,c26]) ).
cnf(d4,plain,
( 'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'(X0,X1,'c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))))
| 'c$uGroups$uOzero$u$uclass$uOzero'('t$ua') != 'c$uGroups$uOzero$u$uclass$uOzero'('t$ua') ),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
'c$uDivides$uOdiv$u$uclass$uOmod'('tc$uNat$uOnat',X0,hAPP('c$uNat$uOSuc',X0)) = X0,
inference(resolution,[status(thm)],[c873,c760]) ).
cnf(d6,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X1,X0)
| 'c$uDivides$uOdiv$u$uclass$uOmod'('tc$uNat$uOnat',X0,hAPP('c$uNat$uOSuc',X1)) = X0 ),
inference(resolution,[status(thm)],[c873,c853]) ).
cnf(d7,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uNat$uOnat')
| 'c$uDivides$uOdiv$u$uclass$uOmod'('tc$uNat$uOnat',X0,hAPP('c$uNat$uOSuc',X0)) = X0 ),
inference(resolution,[status(thm)],[d6,c857]) ).
cnf(d8,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uNat$uOnat')
| X0 = X0 ),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
X0 = X0,
inference(resolution,[status(thm)],[c1180,d8]) ).
cnf(d10,plain,
'c$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$uOconstant'(X0,X1,'c$uPolynomial$uOpoly'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')))),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/20.44 % Computer : n010.cluster.edu
% 0.14/20.44 % Model : x86_64 x86_64
% 0.14/20.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/20.44 % Memory : 8046.5625MB
% 0.14/20.44 % OS : Linux 6.8.0-71-generic
% 0.14/20.44 % CPULimit : 300
% 0.14/20.44 % WCLimit : 300
% 0.14/20.44 % DateTime : Sat Sep 26 15:32:52 UTC 2026
% 0.14/20.44 % CPUTime :
% 0.14/20.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 150.11/45.61 % SZS status Theorem for theBenchmark.p
% 150.11/45.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------