%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL847-1 : 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 07:55:35 AM UTC 2026
% Result : Unsatisfiable 117.25s 45.78s
% Output : CNFRefutation 117.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 8 unt; 4 nHn; 10 RR)
% Number of literals : 32 ( 4 equ; 11 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_set__takeWhileD_1,axiom,
( ~ 'c$uin'(X1,'c$uList$uOset'('c$uList$uOtakeWhile'(X0,X2,X3),X3),X3)
| hBOOL(hAPP(X0,X1)) ) ).
cnf(cls_in__listsp__conv__set_1,axiom,
( 'c$uin'('c$uList$uOsko$u$uList$u$uXin$u$ulistsp$u$uconv$u$uset$u$u1$u$u1'(X0,X1,X2),'c$uList$uOset'(X1,X2),X2)
| 'c$uList$uOlistsp'(X0,X1,X2) ) ).
cnf(cls_takeWhile_Osimps_I2_J_0,axiom,
( ~ hBOOL(hAPP(X0,X1))
| 'c$uList$uOtakeWhile'(X0,'c$uList$uOlist$uOCons'(X1,X2,X3),X3) = 'c$uList$uOlist$uOCons'(X1,'c$uList$uOtakeWhile'(X0,X2,X3),X3) ) ).
cnf(cls_takeWhile_Osimps_I1_J_0,axiom,
'c$uList$uOtakeWhile'(X0,'c$uList$uOlist$uONil'(X1),X1) = 'c$uList$uOlist$uONil'(X1) ).
cnf(cls_in__listsp__conv__set_2,axiom,
( ~ hBOOL(hAPP(X0,'c$uList$uOsko$u$uList$u$uXin$u$ulistsp$u$uconv$u$uset$u$u1$u$u1'(X0,X1,X2)))
| 'c$uList$uOlistsp'(X0,X1,X2) ) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')))) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$uList$uOlistsp'('c$uInductTermi$uOIT','c$uList$uOlist$uOCons'(hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB') ).
cnf(c254,plain,
( ~ 'c$uin'(X1,'c$uList$uOset'('c$uList$uOtakeWhile'(X0,X2,X3),X3),X3)
| hBOOL(hAPP(X0,X1)) ),
inference(clausification,[status(esa)],[cls_set__takeWhileD_1]) ).
cnf(c296,plain,
( 'c$uin'('c$uList$uOsko$u$uList$u$uXin$u$ulistsp$u$uconv$u$uset$u$u1$u$u1'(X0,X1,X2),'c$uList$uOset'(X1,X2),X2)
| 'c$uList$uOlistsp'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_in__listsp__conv__set_1]) ).
cnf(c348,plain,
( ~ hBOOL(hAPP(X0,X1))
| 'c$uList$uOtakeWhile'(X0,'c$uList$uOlist$uOCons'(X1,X2,X3),X3) = 'c$uList$uOlist$uOCons'(X1,'c$uList$uOtakeWhile'(X0,X2,X3),X3) ),
inference(clausification,[status(esa)],[cls_takeWhile_Osimps_I2_J_0]) ).
cnf(c359,plain,
'c$uList$uOtakeWhile'(X0,'c$uList$uOlist$uONil'(X1),X1) = 'c$uList$uOlist$uONil'(X1),
inference(clausification,[status(esa)],[cls_takeWhile_Osimps_I1_J_0]) ).
cnf(c517,plain,
( ~ hBOOL(hAPP(X0,'c$uList$uOsko$u$uList$u$uXin$u$ulistsp$u$uconv$u$uset$u$u1$u$u1'(X0,X1,X2)))
| 'c$uList$uOlistsp'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_in__listsp__conv__set_2]) ).
cnf(c585,plain,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')))),
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c586,plain,
~ 'c$uList$uOlistsp'('c$uInductTermi$uOIT','c$uList$uOlist$uOCons'(hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
( hBOOL(hAPP(X1,'c$uList$uOsko$u$uList$u$uXin$u$ulistsp$u$uconv$u$uset$u$u1$u$u1'(X0,'c$uList$uOtakeWhile'(X1,X2,X3),X3)))
| 'c$uList$uOlistsp'(X0,'c$uList$uOtakeWhile'(X1,X2,X3),X3) ),
inference(resolution,[status(thm)],[c296,c254]) ).
cnf(d1,plain,
( 'c$uList$uOlistsp'(X0,'c$uList$uOtakeWhile'(X0,X1,X2),X2)
| 'c$uList$uOlistsp'(X0,'c$uList$uOtakeWhile'(X0,X1,X2),X2) ),
inference(resolution,[status(thm)],[d0,c517]) ).
cnf(d2,plain,
( ~ hBOOL(hAPP(X0,X1))
| 'c$uList$uOlistsp'(X0,'c$uList$uOlist$uOCons'(X1,'c$uList$uOtakeWhile'(X0,X2,X3),X3),X3) ),
inference(superposition,[status(thm)],[c348,d1]) ).
cnf(d3,plain,
( ~ hBOOL(hAPP(X0,X2))
| 'c$uList$uOlistsp'(X0,'c$uList$uOlist$uOCons'(X2,'c$uList$uOlist$uONil'(X1),X1),X1) ),
inference(superposition,[status(thm)],[c359,d2]) ).
cnf(d4,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')))),
inference(resolution,[status(thm)],[d3,c586]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c585,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL847-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n009.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 23:42:59 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 117.25/45.78 % SZS status Unsatisfiable for theBenchmark.p
% 117.25/45.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------