%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL773-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:59:42 AM UTC 2026
% Result : Unsatisfiable 8.61s 2.58s
% Output : CNFRefutation 8.61s
% 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 : 6 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 8 ( 4 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_479,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_0,axiom,
c_InductTermi_OIT(v_r),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_481,plain,
c_InductTermi_OIT(v_r),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_subst__Var__IT_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_InductTermi_OIT(VAR_0)
| c_InductTermi_OIT(c_Lambda_Osubst(VAR_0,c_Lambda_OdB_OVar(VAR_1),VAR_2)) ),
file('theBenchmark.p',cls_subst__Var__IT_0) ).
cnf(c_487,plain,
( ~ c_InductTermi_OIT(A)
| c_InductTermi_OIT(c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C)) ),
inference(clausify,[status(thm)],[cls_subst__Var__IT_0]) ).
cnf(c_1263,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(A),B)),
inference(resolve,[status(thm)],[c_487,c_481]) ).
cnf(c_1264,plain,
$false,
inference(resolve,[status(thm)],[c_1263,c_479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL773-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 23:34:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1399691 was started by sandbox on n003,
% 0.08/0.35 % Fri Sep 25 23:34:23 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 8.61/2.58
% 8.61/2.58 % SZS status Unsatisfiable for theBenchmark
% 8.61/2.58
% 8.61/2.58 % Proof 1 at 1.07 (+ 0.04) seconds.
% 8.61/2.58 % Length of proof is 5.
% 8.61/2.58 % Level of proof is 2.
% 8.61/2.58 % Maximum clause weight is 23.000.
% 8.61/2.58 % Given clauses 97.
% 8.61/2.58
% 8.61/2.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------