%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL753-1 : 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 : n026.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 07:55:21 AM UTC 2026
% Result : Unsatisfiable 112.97s 19.41s
% Output : CNFRefutation 112.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 15 unt; 4 nHn; 7 RR)
% Number of literals : 27 ( 10 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 35 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Suc__eq__plus1_0,axiom,
'c$uSuc'(X0) = 'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOone$u$uclass$uOone'('tc$unat'),'tc$unat') ).
cnf(cls_gr__implies__not0_0,axiom,
~ 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat') ).
cnf(cls_subst__Abs_0,axiom,
'c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'(X0),X1,X2) = 'c$uLambda$uOdB$uOAbs'('c$uLambda$uOsubst'(X0,'c$uLambda$uOlift'(X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uHOL$uOplus$u$uclass$uOplus'(X2,'c$uHOL$uOone$u$uclass$uOone'('tc$unat'),'tc$unat'))) ).
cnf(cls_lift_Osimps_I1_J_1,axiom,
( 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$unat')
| 'c$uLambda$uOlift'('c$uLambda$uOdB$uOVar'(X0),X1) = 'c$uLambda$uOdB$uOVar'('c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOone$u$uclass$uOone'('tc$unat'),'tc$unat')) ) ).
cnf(cls_Lambda_0,axiom,
( ~ 'c$uInductTermi$uOIT'(X0)
| 'c$uInductTermi$uOIT'('c$uLambda$uOdB$uOAbs'(X0)) ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uInductTermi$uOIT'('c$uLambda$uOsubst'('v$ura','c$uLambda$uOdB$uOVar'(X0),X1)) ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$uInductTermi$uOIT'('c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'('v$ura'),'c$uLambda$uOdB$uOVar'('v$uia'),'v$uja')) ).
cnf(c148,plain,
'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOone$u$uclass$uOone'('tc$unat'),'tc$unat') = 'c$uSuc'(X0),
inference(clausification,[status(esa)],[cls_Suc__eq__plus1_0]) ).
cnf(c296,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat'),
inference(clausification,[status(esa)],[cls_gr__implies__not0_0]) ).
cnf(c594,plain,
'c$uLambda$uOdB$uOAbs'('c$uLambda$uOsubst'(X0,'c$uLambda$uOlift'(X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uHOL$uOplus$u$uclass$uOplus'(X2,'c$uHOL$uOone$u$uclass$uOone'('tc$unat'),'tc$unat'))) = 'c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'(X0),X1,X2),
inference(clausification,[status(esa)],[cls_subst__Abs_0]) ).
cnf(c602,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$unat')
| 'c$uLambda$uOdB$uOVar'('c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOone$u$uclass$uOone'('tc$unat'),'tc$unat')) = 'c$uLambda$uOlift'('c$uLambda$uOdB$uOVar'(X0),X1) ),
inference(clausification,[status(esa)],[cls_lift_Osimps_I1_J_1]) ).
cnf(c677,plain,
( ~ 'c$uInductTermi$uOIT'(X0)
| 'c$uInductTermi$uOIT'('c$uLambda$uOdB$uOAbs'(X0)) ),
inference(clausification,[status(esa)],[cls_Lambda_0]) ).
cnf(c682,plain,
'c$uInductTermi$uOIT'('c$uLambda$uOsubst'('v$ura','c$uLambda$uOdB$uOVar'(X0),X1)),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c683,plain,
~ 'c$uInductTermi$uOIT'('c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'('v$ura'),'c$uLambda$uOdB$uOVar'('v$uia'),'v$uja')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(d0,plain,
'c$uInductTermi$uOIT'('c$uLambda$uOdB$uOAbs'('c$uLambda$uOsubst'('v$ura','c$uLambda$uOdB$uOVar'(X0),X1))),
inference(resolution,[status(thm)],[c682,c677]) ).
cnf(d1,plain,
'c$uLambda$uOdB$uOAbs'('c$uLambda$uOsubst'(X1,'c$uLambda$uOlift'(X2,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uSuc'(X0))) = 'c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'(X1),X2,X0),
inference(demodulation,[status(thm)],[c594,c148]) ).
cnf(d2,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$unat')
| 'c$uLambda$uOdB$uOVar'('c$uSuc'(X0)) = 'c$uLambda$uOlift'('c$uLambda$uOdB$uOVar'(X0),X1) ),
inference(demodulation,[status(thm)],[c602,c148]) ).
cnf(d3,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat')
| 'c$uLambda$uOdB$uOAbs'('c$uLambda$uOsubst'(X1,'c$uLambda$uOdB$uOVar'('c$uSuc'(X0)),'c$uSuc'(X2))) = 'c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'(X1),'c$uLambda$uOdB$uOVar'(X0),X2) ),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'c$uLambda$uOdB$uOAbs'('c$uLambda$uOsubst'(X0,'c$uLambda$uOdB$uOVar'('c$uSuc'(X1)),'c$uSuc'(X2))) = 'c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'(X0),'c$uLambda$uOdB$uOVar'(X1),X2),
inference(resolution,[status(thm)],[c296,d3]) ).
cnf(d5,plain,
'c$uInductTermi$uOIT'('c$uLambda$uOsubst'('c$uLambda$uOdB$uOAbs'('v$ura'),'c$uLambda$uOdB$uOVar'(X0),X1)),
inference(superposition,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,c683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL753-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n026.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Fri Sep 25 23:32:55 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 112.97/19.41 % SZS status Unsatisfiable for theBenchmark.p
% 112.97/19.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------