%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL793-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:59:45 AM UTC 2026
% Result : Unsatisfiable 6.16s 16.28s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 2 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_477,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_478,plain,
c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_app__Var__IT_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_InductTermi_OIT(VAR_0)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(VAR_0,c_Lambda_OdB_OVar(VAR_1))) ),
file('theBenchmark.p',cls_app__Var__IT_0) ).
cnf(c_480,plain,
( ~ c_InductTermi_OIT(A)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(A,c_Lambda_OdB_OVar(B))) ),
inference(clausify,[status(thm)],[cls_app__Var__IT_0]) ).
cnf(c_1689,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(A))),
inference(resolve,[status(thm)],[c_480,c_478]) ).
cnf(c_1690,plain,
$false,
inference(resolve,[status(thm)],[c_1689,c_477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL793-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n013.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Fri Sep 25 23:34:38 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/15.39 % Process 1468589 was started by sandbox2 on n013,
% 0.11/15.39 % Fri Sep 25 23:34:38 2026
% 0.11/15.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/15.43
% 0.15/15.43 % From the command line: assign(max_seconds, 300).
% 6.16/16.28
% 6.16/16.28 % SZS status Unsatisfiable for theBenchmark
% 6.16/16.28
% 6.16/16.28 % Proof 1 at 0.82 (+ 0.02) seconds.
% 6.16/16.28 % Length of proof is 5.
% 6.16/16.28 % Level of proof is 2.
% 6.16/16.28 % Maximum clause weight is 29.000.
% 6.16/16.28 % Given clauses 97.
% 6.16/16.28
% 6.16/16.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------