%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL834-1 : 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 : n017.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 07:59:52 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.65s
% Output : CNFRefutation 0.14s
% 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 : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 13 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_beta_0,axiom,
! [VAR_0,VAR_1] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(VAR_0)),VAR_1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,VAR_0),VAR_1),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('theBenchmark.p',cls_beta_0) ).
cnf(c_552,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(clausify,[status(thm)],[cls_beta_0]) ).
fof(cls_apps__preserves__beta_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,VAR_0),VAR_2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,VAR_0,VAR_1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,VAR_2,VAR_1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_apps__preserves__beta_0) ).
cnf(c_553,plain,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(clausify,[status(thm)],[cls_apps__preserves__beta_0]) ).
fof(cls_conjecture_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_560,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1217,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(resolve,[status(thm)],[c_553,c_552]) ).
cnf(c_1218,plain,
$false,
inference(resolve,[status(thm)],[c_1217,c_560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n017.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 23:35:39 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.39 % Process 3463418 was started by sandbox on n017,
% 0.09/5.39 % Fri Sep 25 23:35:39 2026
% 0.09/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.41
% 0.14/5.41 % From the command line: assign(max_seconds, 300).
% 0.14/5.65
% 0.14/5.65 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.65
% 0.14/5.65 % Proof 1 at 0.18 (+ 0.02) seconds.
% 0.14/5.65 % Length of proof is 5.
% 0.14/5.65 % Level of proof is 2.
% 0.14/5.65 % Maximum clause weight is 71.000.
% 0.14/5.65 % Given clauses 273.
% 0.14/5.65
% 0.14/5.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------