%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SCT083-1 : 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 : 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 08:27:45 AM UTC 2026
% Result : Unsatisfiable 18.15s 10.77s
% Output : CNFRefutation 18.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 20 unt; 0 nHn; 24 RR)
% Number of literals : 49 ( 8 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 66 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__def_0,axiom,
'c$uCollect'(X0,X1) = X0 ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP('c$uCOMBC'(X0,X1,X2,X3),X4),X5) = hAPP(hAPP(X0,X5),X4) ).
cnf(cls_Collect__mem__eq_0,axiom,
'c$uCollect'(hAPP('c$uCOMBC'('c$uin'(X0),X0,'tc$ufun'(X0,'tc$ubool'),'tc$ubool'),X1),X0) = X1 ).
cnf(cls_const__Lin__Prof_0,axiom,
( ~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),X0),'c$uArrow$u$uOrder$u$uMirabelle$uOLin'))
| hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'c$uCOMBK'(X0,'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf')) ) ).
cnf(cls_funcset__mem_0,axiom,
( ~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'(X4,X0)),X1),'c$uFuncSet$uOPi'(X5,'c$uCOMBK'(X3,'tc$ufun'(X0,'tc$ubool'),X4),X4,X0)))
| ~ hBOOL(hAPP(hAPP('c$uin'(X4),X2),X5))
| hBOOL(hAPP(hAPP('c$uin'(X0),hAPP(X1,X2)),X3)) ) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL(hAPP(hAPP('c$uin'(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'v$uLab'),'c$uArrow$u$uOrder$u$uMirabelle$uOLin')) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'v$uF'),'c$uFuncSet$uOPi'('c$uArrow$u$uOrder$u$uMirabelle$uOProf','c$uCOMBK'('c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$ubool'),'tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')))) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),hAPP('v$uF','c$uCOMBK'('v$uLab','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi'))),'c$uArrow$u$uOrder$u$uMirabelle$uOLin')) ).
cnf(c393,plain,
'c$uCollect'(X0,X1) = X0,
inference(clausification,[status(esa)],[cls_Collect__def_0]) ).
cnf(c415,plain,
hAPP(hAPP('c$uCOMBC'(X0,X1,X2,X3),X4),X5) = hAPP(hAPP(X0,X5),X4),
inference(clausification,[status(esa)],[cls_COMBC__def_0]) ).
cnf(c611,plain,
'c$uCollect'(hAPP('c$uCOMBC'('c$uin'(X0),X0,'tc$ufun'(X0,'tc$ubool'),'tc$ubool'),X1),X0) = X1,
inference(clausification,[status(esa)],[cls_Collect__mem__eq_0]) ).
cnf(c709,plain,
( ~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),X0),'c$uArrow$u$uOrder$u$uMirabelle$uOLin'))
| hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'c$uCOMBK'(X0,'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf')) ),
inference(clausification,[status(esa)],[cls_const__Lin__Prof_0]) ).
cnf(c710,plain,
( ~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'(X4,X0)),X1),'c$uFuncSet$uOPi'(X5,'c$uCOMBK'(X3,'tc$ufun'(X0,'tc$ubool'),X4),X4,X0)))
| ~ hBOOL(hAPP(hAPP('c$uin'(X4),X2),X5))
| hBOOL(hAPP(hAPP('c$uin'(X0),hAPP(X1,X2)),X3)) ),
inference(clausification,[status(esa)],[cls_funcset__mem_0]) ).
cnf(c712,plain,
( ~ hBOOL(hAPP(hAPP('c$uin'(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ),
inference(clausification,[status(esa)],[cls_mem__def_0]) ).
cnf(c714,plain,
hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'v$uLab'),'c$uArrow$u$uOrder$u$uMirabelle$uOLin')),
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c715,plain,
hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'v$uF'),'c$uFuncSet$uOPi'('c$uArrow$u$uOrder$u$uMirabelle$uOProf','c$uCOMBK'('c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$ubool'),'tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')))),
inference(clausification,[status(esa)],[cls_CHAINED_0_01]) ).
cnf(c716,plain,
~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),hAPP('v$uF','c$uCOMBK'('v$uLab','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi'))),'c$uArrow$u$uOrder$u$uMirabelle$uOLin')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
hAPP('c$uCOMBC'('c$uin'(X0),X0,'tc$ufun'(X0,'tc$ubool'),'tc$ubool'),X1) = X1,
inference(demodulation,[status(thm)],[c611,c393]) ).
cnf(d1,plain,
hAPP(X1,X2) = hAPP(hAPP('c$uin'(X0),X2),X1),
inference(superposition,[status(thm)],[d0,c415]) ).
cnf(d2,plain,
( hBOOL(hAPP(hAPP('c$uin'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'c$uCOMBK'(X0,'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf'))
| ~ hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin',X0)) ),
inference(demodulation,[status(thm)],[c709,d1]) ).
cnf(d3,plain,
( hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOProf','c$uCOMBK'(X0,'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi')))
| ~ hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin',X0)) ),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
~ hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin',hAPP('v$uF','c$uCOMBK'('v$uLab','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi')))),
inference(demodulation,[status(thm)],[c716,d1]) ).
cnf(d5,plain,
( ~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'(X4,X0)),X1),'c$uFuncSet$uOPi'(X5,'c$uCOMBK'(X3,'tc$ufun'(X0,'tc$ubool'),X4),X4,X0)))
| ~ hBOOL(hAPP(hAPP('c$uin'(X4),X2),X5))
| hBOOL(hAPP(X3,hAPP(X1,X2))) ),
inference(demodulation,[status(thm)],[c710,d1]) ).
cnf(d6,plain,
( ~ hBOOL(hAPP(hAPP('c$uin'('tc$ufun'(X0,X5)),X4),'c$uFuncSet$uOPi'(X2,'c$uCOMBK'(X3,'tc$ufun'(X5,'tc$ubool'),X0),X0,X5)))
| ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X3,hAPP(X4,X1))) ),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( ~ hBOOL(hAPP('c$uFuncSet$uOPi'(X3,'c$uCOMBK'(X4,'tc$ufun'(X1,'tc$ubool'),X0),X0,X1),X2))
| ~ hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(X4,hAPP(X2,X5))) ),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
hBOOL(hAPP('c$uFuncSet$uOPi'('c$uArrow$u$uOrder$u$uMirabelle$uOProf','c$uCOMBK'('c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$ubool'),'tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))),'tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')),'v$uF')),
inference(demodulation,[status(thm)],[c715,d1]) ).
cnf(d9,plain,
( ~ hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOProf',X0))
| hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin',hAPP('v$uF',X0))) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
~ hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOProf','c$uCOMBK'('v$uLab','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi'))),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
~ hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin','v$uLab')),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin','v$uLab')),
inference(resolution,[status(thm)],[c712,c714]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT083-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n010.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sat Sep 26 06:26:15 UTC 2026
% 0.16/0.40 % CPUTime :
% 0.16/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.15/10.77 % SZS status Unsatisfiable for theBenchmark.p
% 18.15/10.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------