%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL763-1 : 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 : n011.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 07:59:40 AM UTC 2026
% Result : Unsatisfiable 0.84s 0.55s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 18 ( 6 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_listsp_ONil_0,axiom,
! [VAR_0,VAR_1] : c_List_Olistsp(VAR_0,c_List_Olist_ONil(VAR_1),VAR_1),
file('theBenchmark.p',cls_listsp_ONil_0) ).
cnf(c_266,plain,
c_List_Olistsp(A,c_List_Olist_ONil(B),B),
inference(clausify,[status(thm)],[cls_listsp_ONil_0]) ).
fof(cls_IT_OVar_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_List_Olistsp(c_InductTermi_OIT,VAR_1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(VAR_0),VAR_1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_IT_OVar_0) ).
cnf(c_443,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,B,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(clausify,[status(thm)],[cls_IT_OVar_0]) ).
fof(cls_foldl__Nil_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_List_Ofoldl(VAR_0,VAR_1,c_List_Olist_ONil(VAR_2),VAR_3,VAR_2) = VAR_1,
file('theBenchmark.p',cls_foldl__Nil_0) ).
cnf(c_454,plain,
c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C) = B,
inference(clausify,[status(thm)],[cls_foldl__Nil_0]) ).
fof(cls_conjecture_0,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_460,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_461,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
inference(paramod,[status(thm)],[c_454,c_460]) ).
cnf(c_1203,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(resolve,[status(thm)],[c_443,c_266]) ).
cnf(c_1201,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))),
inference(paramod,[status(thm)],[c_454,c_1203]) ).
cnf(c_1202,plain,
$false,
inference(resolve,[status(thm)],[c_1201,c_461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 23:31:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3183435 was started by sandbox2 on n011,
% 0.09/0.36 % Fri Sep 25 23:31:15 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.84/0.55
% 0.84/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.84/0.55
% 0.84/0.55 % Proof 1 at 0.14 (+ 0.02) seconds.
% 0.84/0.55 % Length of proof is 7.
% 0.84/0.55 % Level of proof is 2.
% 0.84/0.55 % Maximum clause weight is 14.000.
% 0.84/0.55 % Given clauses 241.
% 0.84/0.55
% 0.84/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------