%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL846-1 : 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 : n020.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 07:59:55 AM UTC 2026
% Result : Unsatisfiable 12.67s 2.26s
% Output : CNFRefutation 12.67s
% 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 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_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_627,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_InductTermi_OIT(v_ta____),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_628,plain,
c_InductTermi_OIT(v_ta____),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_lift__IT_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_InductTermi_OIT(VAR_0)
| c_InductTermi_OIT(c_Lambda_Olift(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_lift__IT_0) ).
cnf(c_629,plain,
( ~ c_InductTermi_OIT(A)
| c_InductTermi_OIT(c_Lambda_Olift(A,B)) ),
inference(clausify,[status(thm)],[cls_lift__IT_0]) ).
cnf(c_2040,plain,
c_InductTermi_OIT(c_Lambda_Olift(v_ta____,A)),
inference(resolve,[status(thm)],[c_629,c_628]) ).
cnf(c_2041,plain,
$false,
inference(resolve,[status(thm)],[c_2040,c_627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL846-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n020.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 23:44:03 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 4095749 was started by sandbox on n020,
% 0.18/0.44 % Fri Sep 25 23:44:03 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.24/0.52
% 0.24/0.52 % From the command line: assign(max_seconds, 300).
% 12.67/2.26
% 12.67/2.26 % SZS status Unsatisfiable for theBenchmark
% 12.67/2.26
% 12.67/2.26 % Proof 1 at 1.66 (+ 0.06) seconds.
% 12.67/2.26 % Length of proof is 5.
% 12.67/2.26 % Level of proof is 2.
% 12.67/2.26 % Maximum clause weight is 20.000.
% 12.67/2.26 % Given clauses 147.
% 12.67/2.26
% 12.67/2.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------