%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL855-1 : 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 : n015.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 07:55:36 AM UTC 2026
% Result : Unsatisfiable 81.82s 34.89s
% Output : CNFRefutation 81.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 7 RR)
% Number of literals : 14 ( 7 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_subst__lift_0,axiom,
'c$uLambda$uOsubst'('c$uLambda$uOlift'(X0,X1),X2,X1) = X0 ).
cnf(cls_subst__eq_0,axiom,
'c$uLambda$uOsubst'('c$uLambda$uOdB$uOVar'(X0),X1,X0) = X1 ).
cnf(cls_subst__App_0,axiom,
'c$uLambda$uOsubst'('c$uLambda$uOdB$uOApp'(X0,X1),X2,X3) = 'c$uLambda$uOdB$uOApp'('c$uLambda$uOsubst'(X0,X2,X3),'c$uLambda$uOsubst'(X1,X2,X3)) ).
cnf(cls_CHAINED_0,axiom,
'c$uInductTermi$uOIT'('c$uLambda$uOsubst'('c$uLambda$uOdB$uOApp'('c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uLambda$uOlift'('v$uta','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))),'v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$uInductTermi$uOIT'('c$uLambda$uOdB$uOApp'('v$us','v$uta')) ).
cnf(c323,plain,
'c$uLambda$uOsubst'('c$uLambda$uOlift'(X0,X1),X2,X1) = X0,
inference(clausification,[status(esa)],[cls_subst__lift_0]) ).
cnf(c339,plain,
'c$uLambda$uOsubst'('c$uLambda$uOdB$uOVar'(X0),X1,X0) = X1,
inference(clausification,[status(esa)],[cls_subst__eq_0]) ).
cnf(c342,plain,
'c$uLambda$uOsubst'('c$uLambda$uOdB$uOApp'(X0,X1),X2,X3) = 'c$uLambda$uOdB$uOApp'('c$uLambda$uOsubst'(X0,X2,X3),'c$uLambda$uOsubst'(X1,X2,X3)),
inference(clausification,[status(esa)],[cls_subst__App_0]) ).
cnf(c360,plain,
'c$uInductTermi$uOIT'('c$uLambda$uOsubst'('c$uLambda$uOdB$uOApp'('c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uLambda$uOlift'('v$uta','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))),'v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))),
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c361,plain,
~ 'c$uInductTermi$uOIT'('c$uLambda$uOdB$uOApp'('v$us','v$uta')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
'c$uLambda$uOsubst'('c$uLambda$uOdB$uOApp'('c$uLambda$uOdB$uOVar'(X0),X2),X1,X0) = 'c$uLambda$uOdB$uOApp'(X1,'c$uLambda$uOsubst'(X2,X1,X0)),
inference(superposition,[status(thm)],[c339,c342]) ).
cnf(d1,plain,
'c$uInductTermi$uOIT'('c$uLambda$uOdB$uOApp'('v$us','c$uLambda$uOsubst'('c$uLambda$uOlift'('v$uta','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')))),
inference(demodulation,[status(thm)],[c360,d0]) ).
cnf(d2,plain,
'c$uInductTermi$uOIT'('c$uLambda$uOdB$uOApp'('v$us','v$uta')),
inference(demodulation,[status(thm)],[d1,c323]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c361,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n015.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 23:47:12 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.82/34.89 % SZS status Unsatisfiable for theBenchmark.p
% 81.82/34.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------