%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG391-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 06:48:25 AM UTC 2026
% Result : Unsatisfiable 106.99s 35.73s
% Output : CNFRefutation 106.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 10 unt; 0 nHn; 11 RR)
% Number of literals : 32 ( 19 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf__absorb2_0,axiom,
( ~ 'c$ulessequals'(X2,X1,X0)
| 'c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X1,X2,X0) = X2
| ~ 'class$uLattices$uOlower$u$usemilattice'(X0) ) ).
cnf(cls_inf__idem_0,axiom,
( 'c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X1,X1,X0) = X1
| ~ 'class$uLattices$uOlower$u$usemilattice'(X0) ) ).
cnf(cls_eq__imp__le_0,axiom,
'c$ulessequals'(X0,X0,'tc$unat') ).
cnf(cls_conjecture_0,negated_conjecture,
'v$ucs' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')) ).
cnf(cls_conjecture_2,negated_conjecture,
( X0 = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua'))
| 'c$uPolynomial$uOdegree'(X0,'t$ua') != 'c$uPolynomial$uOdegree'('v$ucs','t$ua')
| 'c$uPolynomial$uOpoly'('v$ucs',hAPP('v$ux',X0),'t$ua') != 'c$uPolynomial$uOpoly'(X0,hAPP('v$ux',X0),'t$ua') ) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
'class$uLattices$uOlower$u$usemilattice'('tc$unat') ).
cnf(c639,plain,
( ~ 'c$ulessequals'(X1,X0,X2)
| ~ 'class$uLattices$uOlower$u$usemilattice'(X2)
| 'c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X0,X1,X2) = X1 ),
inference(clausification,[status(esa)],[cls_inf__absorb2_0]) ).
cnf(c929,plain,
( 'c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X1,X1,X0) = X1
| ~ 'class$uLattices$uOlower$u$usemilattice'(X0) ),
inference(clausification,[status(esa)],[cls_inf__idem_0]) ).
cnf(c946,plain,
'c$ulessequals'(X0,X0,'tc$unat'),
inference(clausification,[status(esa)],[cls_eq__imp__le_0]) ).
cnf(c1103,plain,
'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')) != 'v$ucs',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1105,plain,
( 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')) = X0
| 'c$uPolynomial$uOpoly'(X0,hAPP('v$ux',X0),'t$ua') != 'c$uPolynomial$uOpoly'('v$ucs',hAPP('v$ux',X0),'t$ua')
| 'c$uPolynomial$uOdegree'('v$ucs','t$ua') != 'c$uPolynomial$uOdegree'(X0,'t$ua') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c1151,plain,
'class$uLattices$uOlower$u$usemilattice'('tc$unat'),
inference(clausification,[status(esa)],[clsarity_nat__Lattices_Olower__semilattice]) ).
cnf(d0,plain,
( 'c$uPolynomial$uOpoly'('v$ucs',hAPP('v$ux','v$ucs'),'t$ua') != 'c$uPolynomial$uOpoly'('v$ucs',hAPP('v$ux','v$ucs'),'t$ua')
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('t$ua')) = 'v$ucs' ),
inference(equality_resolution,[status(thm)],[c1105]) ).
cnf(d1,plain,
'c$uPolynomial$uOpoly'('v$ucs',hAPP('v$ux','v$ucs'),'t$ua') != 'c$uPolynomial$uOpoly'('v$ucs',hAPP('v$ux','v$ucs'),'t$ua'),
inference(resolution,[status(thm)],[c1103,d0]) ).
cnf(d2,plain,
'c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X0,X0,'tc$unat') = X0,
inference(resolution,[status(thm)],[c929,c1151]) ).
cnf(d3,plain,
( ~ 'class$uLattices$uOlower$u$usemilattice'('tc$unat')
| 'c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X0,X0,'tc$unat') = X0 ),
inference(resolution,[status(thm)],[c639,c946]) ).
cnf(d4,plain,
( ~ 'class$uLattices$uOlower$u$usemilattice'('tc$unat')
| X0 = X0 ),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
X0 = X0,
inference(resolution,[status(thm)],[c1151,d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG391-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 22:02:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 106.99/35.73 % SZS status Unsatisfiable for theBenchmark.p
% 106.99/35.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------