%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL826-1 : 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 : n001.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 07:55:32 AM UTC 2026
% Result : Unsatisfiable 2.73s 16.75s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 14 RR)
% Number of literals : 23 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 12 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Cons_I1_J_0,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',hAPP(hAPP(hAPP('c$uType$uOshift'('tc$uType$uOtype'),X2),X1),'v$uT')),'v$ua'),X3))
| ~ hBOOL(hAPP('c$uInductTermi$uOIT',X0))
| ~ hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',X2),X0),'v$uT'))
| hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ua'),X0),X1))) ) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',hAPP(hAPP(hAPP('c$uType$uOshift'('tc$uType$uOtype'),'v$ux'),'v$uxc'),'v$uT')),'v$ua'),'v$uxa')) ).
cnf(cls_conjecture_1,negated_conjecture,
hBOOL(hAPP('c$uInductTermi$uOIT','v$uxb')) ).
cnf(cls_conjecture_2,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping','v$ux'),'v$uxb'),'v$uT')) ).
cnf(cls_conjecture_3,negated_conjecture,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ua'),'v$uxb'),'v$uxc'))) ).
cnf(c354,plain,
( ~ hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',hAPP(hAPP(hAPP('c$uType$uOshift'('tc$uType$uOtype'),X2),X1),'v$uT')),'v$ua'),X3))
| ~ hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',X2),X0),'v$uT'))
| hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ua'),X0),X1)))
| ~ hBOOL(hAPP('c$uInductTermi$uOIT',X0)) ),
inference(clausification,[status(esa)],[cls_Cons_I1_J_0]) ).
cnf(c386,plain,
hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',hAPP(hAPP(hAPP('c$uType$uOshift'('tc$uType$uOtype'),'v$ux'),'v$uxc'),'v$uT')),'v$ua'),'v$uxa')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c387,plain,
hBOOL(hAPP('c$uInductTermi$uOIT','v$uxb')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c388,plain,
hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping','v$ux'),'v$uxb'),'v$uT')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c389,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ua'),'v$uxb'),'v$uxc'))),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(d0,plain,
( hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ua'),'v$uxb'),X0)))
| ~ hBOOL(hAPP('c$uInductTermi$uOIT','v$uxb'))
| ~ hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',hAPP(hAPP(hAPP('c$uType$uOshift'('tc$uType$uOtype'),'v$ux'),X0),'v$uT')),'v$ua'),X1)) ),
inference(resolution,[status(thm)],[c354,c388]) ).
cnf(d1,plain,
( hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ua'),'v$uxb'),X0)))
| ~ hBOOL(hAPP(hAPP(hAPP('c$uType$uOtyping',hAPP(hAPP(hAPP('c$uType$uOshift'('tc$uType$uOtype'),'v$ux'),X0),'v$uT')),'v$ua'),X1)) ),
inference(resolution,[status(thm)],[c387,d0]) ).
cnf(d2,plain,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ua'),'v$uxb'),'v$uxc'))),
inference(resolution,[status(thm)],[d1,c386]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c389,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 23:45:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.73/16.75 % SZS status Unsatisfiable for theBenchmark.p
% 2.73/16.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------