%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL809-1 : 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 : n018.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 07:59:48 AM UTC 2026
% Result : Unsatisfiable 8.63s 1.51s
% Output : CNFRefutation 8.63s
% 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 5 ( 2 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_548,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_549,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
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_552,plain,
( ~ c_InductTermi_OIT(A)
| c_InductTermi_OIT(c_Lambda_Olift(A,B)) ),
inference(clausify,[status(thm)],[cls_lift__IT_0]) ).
cnf(c_1867,plain,
c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),A)),
inference(resolve,[status(thm)],[c_552,c_549]) ).
cnf(c_1868,plain,
$false,
inference(resolve,[status(thm)],[c_1867,c_548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL809-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 23:39:20 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3122431 was started by sandbox2 on n018,
% 0.07/0.35 % Fri Sep 25 23:39:20 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 8.63/1.51
% 8.63/1.51 % SZS status Unsatisfiable for theBenchmark
% 8.63/1.51
% 8.63/1.51 % Proof 1 at 1.07 (+ 0.03) seconds.
% 8.63/1.51 % Length of proof is 5.
% 8.63/1.51 % Level of proof is 2.
% 8.63/1.51 % Maximum clause weight is 23.000.
% 8.63/1.51 % Given clauses 125.
% 8.63/1.51
% 8.63/1.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------