%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL756-1 : 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 : 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 07:59:39 AM UTC 2026
% Result : Unsatisfiable 2.71s 0.74s
% Output : CNFRefutation 2.71s
% 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 : 3 ( 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; 3 con; 0-3 aty)
% Number of variables : 4 ( 2 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_402,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0,VAR_1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(VAR_0),VAR_1)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_403,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(A),B)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_404,plain,
$false,
inference(resolve,[status(thm)],[c_403,c_402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL756-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n026.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Fri Sep 25 23:32:39 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.33 % Process 3728981 was started by sandbox2 on n026,
% 0.08/0.33 % Fri Sep 25 23:32:39 2026
% 0.08/0.33 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 2.71/0.74
% 2.71/0.74 % SZS status Unsatisfiable for theBenchmark
% 2.71/0.74
% 2.71/0.74 % Proof 1 at 0.37 (+ 0.00) seconds.
% 2.71/0.74 % Length of proof is 3.
% 2.71/0.74 % Level of proof is 1.
% 2.71/0.74 % Maximum clause weight is 28.000.
% 2.71/0.74 % Given clauses 0.
% 2.71/0.74
% 2.71/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------