%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SCT007-1 : 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 : n009.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 08:27:39 AM UTC 2026
% Result : Unsatisfiable 15.54s 55.64s
% Output : CNFRefutation 15.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 12 unt; 0 nHn; 13 RR)
% Number of literals : 18 ( 5 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__def_0,axiom,
'c$uCollect'(X0,X1) = X0 ).
cnf(cls_Lin__def_0,axiom,
'c$uArrow$u$uOrder$u$uMirabelle$uOLin' = 'c$uCollect'('c$uOrder$u$uRelation$uOstrict$u$ulinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),'tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')) ).
cnf(cls_strict__linear__order__on__diff__Id_0,axiom,
( ~ hBOOL('c$uOrder$u$uRelation$uOlinear$u$uorder$u$uon'(X0,X2,X1))
| hBOOL(hAPP('c$uOrder$u$uRelation$uOstrict$u$ulinear$u$uorder$u$uon'(X0,X1),'c$uHOL$uOminus$u$uclass$uOminus'(X2,'c$uRelation$uOId'(X1),'tc$ufun'('tc$uprod'(X1,X1),'tc$ubool')))) ) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL('c$uOrder$u$uRelation$uOlinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),'v$ur','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ).
cnf(cls_conjecture_2,negated_conjecture,
~ hBOOL(hAPP('c$uOrder$u$uRelation$uOstrict$u$ulinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),'tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),X0)) ).
cnf(c28,plain,
'c$uCollect'(X0,X1) = X0,
inference(clausification,[status(esa)],[cls_Collect__def_0]) ).
cnf(c561,plain,
'c$uArrow$u$uOrder$u$uMirabelle$uOLin' = 'c$uCollect'('c$uOrder$u$uRelation$uOstrict$u$ulinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),'tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),
inference(clausification,[status(esa)],[cls_Lin__def_0]) ).
cnf(c568,plain,
( ~ hBOOL('c$uOrder$u$uRelation$uOlinear$u$uorder$u$uon'(X0,X2,X1))
| hBOOL(hAPP('c$uOrder$u$uRelation$uOstrict$u$ulinear$u$uorder$u$uon'(X0,X1),'c$uHOL$uOminus$u$uclass$uOminus'(X2,'c$uRelation$uOId'(X1),'tc$ufun'('tc$uprod'(X1,X1),'tc$ubool')))) ),
inference(clausification,[status(esa)],[cls_strict__linear__order__on__diff__Id_0]) ).
cnf(c569,plain,
hBOOL('c$uOrder$u$uRelation$uOlinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),'v$ur','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c571,plain,
~ hBOOL(hAPP('c$uOrder$u$uRelation$uOstrict$u$ulinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),'tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),X0)),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(d0,plain,
'c$uArrow$u$uOrder$u$uMirabelle$uOLin' = 'c$uOrder$u$uRelation$uOstrict$u$ulinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),'tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),
inference(demodulation,[status(thm)],[c561,c28]) ).
cnf(d1,plain,
( ~ hBOOL('c$uOrder$u$uRelation$uOlinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),X0,'tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin','c$uHOL$uOminus$u$uclass$uOminus'(X0,'c$uRelation$uOId'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')))) ),
inference(superposition,[status(thm)],[d0,c568]) ).
cnf(d2,plain,
~ hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin',X0)),
inference(demodulation,[status(thm)],[c571,d0]) ).
cnf(d3,plain,
~ hBOOL('c$uOrder$u$uRelation$uOlinear$u$uorder$u$uon'('c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$ubool')),X0,'tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[d3,c569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT007-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n009.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 06:18:30 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.54/55.64 % SZS status Unsatisfiable for theBenchmark.p
% 15.54/55.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------