%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 07:55:24 AM UTC 2026
% Result : Unsatisfiable 30.03s 4.23s
% Output : CNFRefutation 30.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 7 RR)
% Number of literals : 12 ( 5 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-5 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_rotate__simps_1,axiom,
'c$uList$uOrotate1'('c$uList$uOlist$uOCons'(X0,X1,X2),X2) = 'c$uList$uOappend'(X1,'c$uList$uOlist$uOCons'(X0,'c$uList$uOlist$uONil'(X2),X2),X2) ).
cnf(cls_app__last_0,axiom,
hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X0,X1,'tc$uLambda$uOdB','tc$uLambda$uOdB')),X2) = 'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X0,'c$uList$uOappend'(X1,'c$uList$uOlist$uOCons'(X2,'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB') ).
cnf(cls_conjecture_1,negated_conjecture,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubst'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP('c$uInductTermi$uOIT','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubst'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOappend'('v$uss','c$uList$uOlist$uOCons'('c$uLambda$uOdB$uOVar'('v$ui'),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'))) ).
cnf(c287,plain,
'c$uList$uOrotate1'('c$uList$uOlist$uOCons'(X0,X1,X2),X2) = 'c$uList$uOappend'(X1,'c$uList$uOlist$uOCons'(X0,'c$uList$uOlist$uONil'(X2),X2),X2),
inference(clausification,[status(esa)],[cls_rotate__simps_1]) ).
cnf(c312,plain,
hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X0,X1,'tc$uLambda$uOdB','tc$uLambda$uOdB')),X2) = 'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X0,'c$uList$uOappend'(X1,'c$uList$uOlist$uOCons'(X2,'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'),
inference(clausification,[status(esa)],[cls_app__last_0]) ).
cnf(c361,plain,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubst'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c364,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubst'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOappend'('v$uss','c$uList$uOlist$uOCons'('c$uLambda$uOdB$uOVar'('v$ui'),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'))),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(d0,plain,
hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X2,X0,'tc$uLambda$uOdB','tc$uLambda$uOdB')),X1) = 'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X2,'c$uList$uOrotate1'('c$uList$uOlist$uOCons'(X1,X0,'tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'),
inference(demodulation,[status(thm)],[c312,c287]) ).
cnf(d1,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubst'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOrotate1'('c$uList$uOlist$uOCons'('c$uLambda$uOdB$uOVar'('v$ui'),'v$uss','tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'))),
inference(demodulation,[status(thm)],[c364,c287]) ).
cnf(d2,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubst'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c361,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 23:32:47 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.03/4.23 % SZS status Unsatisfiable for theBenchmark.p
% 30.03/4.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------