%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL770-1 : 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 : n009.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 07:59:41 AM UTC 2026
% Result : Unsatisfiable 1.40s 0.61s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 3 ( 2 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 : 2 ( 1 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Var__IT_0,axiom,
! [VAR_0] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(VAR_0))),
file('theBenchmark.p',cls_Var__IT_0) ).
cnf(c_518,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))),
inference(clausify,[status(thm)],[cls_Var__IT_0]) ).
fof(cls_conjecture_2,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_i))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_544,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_i))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_545,plain,
$false,
inference(resolve,[status(thm)],[c_518,c_544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL770-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 23:31:29 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2827694 was started by sandbox on n009,
% 0.11/0.38 % Fri Sep 25 23:31:29 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 1.40/0.61
% 1.40/0.61 % SZS status Unsatisfiable for theBenchmark
% 1.40/0.61
% 1.40/0.61 % Proof 1 at 0.20 (+ 0.01) seconds.
% 1.40/0.61 % Length of proof is 3.
% 1.40/0.61 % Level of proof is 1.
% 1.40/0.61 % Maximum clause weight is 11.000.
% 1.40/0.61 % Given clauses 0.
% 1.40/0.61
% 1.40/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------