%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL762-1 : 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 : n012.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 0.07s 5.40s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 8 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(cls_conjecture_1,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_462,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_463,plain,
$false,
inference(resolve,[status(thm)],[c_461,c_462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL762-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Fri Sep 25 23:30:25 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/5.31 % Process 3318727 was started by sandbox on n012,
% 0.04/5.31 % Fri Sep 25 23:30:25 2026
% 0.04/5.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/5.32
% 0.04/5.32 % From the command line: assign(max_seconds, 300).
% 0.07/5.40
% 0.07/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.07/5.40
% 0.07/5.40 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.07/5.40 % Length of proof is 5.
% 0.07/5.40 % Level of proof is 2.
% 0.07/5.40 % Maximum clause weight is 9.000.
% 0.07/5.40 % Given clauses 0.
% 0.07/5.40
% 0.07/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------