%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL858-1 : 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 07:59:57 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.57s
% Output : CNFRefutation 0.17s
% 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 : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_IT__implies__termi_0,axiom,
! [VAR_0] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,VAR_0))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),VAR_0)) ),
file('theBenchmark.p',cls_IT__implies__termi_0) ).
cnf(c_187,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,A))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),A)) ),
inference(clausify,[status(thm)],[cls_IT__implies__termi_0]) ).
fof(cls_CHAINED_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_215,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_conjecture_0,axiom,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_216,plain,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_804,plain,
hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
inference(resolve,[status(thm)],[c_215,c_187]) ).
cnf(c_803,plain,
$false,
inference(resolve,[status(thm)],[c_216,c_804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL858-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.50 % Computer : n009.cluster.edu
% 0.13/0.50 % Model : x86_64 x86_64
% 0.13/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.50 % Memory : 8046.5625MB
% 0.13/0.50 % OS : Linux 6.8.0-71-generic
% 0.13/0.50 % CPULimit : 300
% 0.13/0.50 % WCLimit : 300
% 0.13/0.50 % DateTime : Fri Sep 25 23:43:44 UTC 2026
% 0.13/0.50 % CPUTime :
% 0.13/0.51 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.51 % Process 2858906 was started by sandbox on n009,
% 0.13/0.51 % Fri Sep 25 23:43:44 2026
% 0.13/0.51 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.52
% 0.17/0.52 % From the command line: assign(max_seconds, 300).
% 0.17/0.57
% 0.17/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.57
% 0.17/0.57 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.17/0.57 % Length of proof is 4.
% 0.17/0.57 % Level of proof is 1.
% 0.17/0.57 % Maximum clause weight is 33.000.
% 0.17/0.57 % Given clauses 176.
% 0.17/0.57
% 0.17/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------