%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL805-1 : 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 : n015.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 07:59:47 AM UTC 2026
% Result : Unsatisfiable 5.55s 1.62s
% Output : CNFRefutation 5.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-5 aty)
% Number of variables : 10 ( 2 sgn 5 !; 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_1150,plain,
c_List_Olistsp(A,c_List_Olist_ONil(B),B),
inference(clausify,[status(thm)],[cls_listsp_ONil_0]) ).
fof(cls_map__is__Nil__conv_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_List_Omap(VAR_0,c_List_Olist_ONil(VAR_1),VAR_1,VAR_2) = c_List_Olist_ONil(VAR_2),
file('theBenchmark.p',cls_map__is__Nil__conv_1) ).
cnf(c_1152,plain,
c_List_Omap(A,c_List_Olist_ONil(B),B,C) = c_List_Olist_ONil(C),
inference(clausify,[status(thm)],[cls_map__is__Nil__conv_1]) ).
fof(cls_conjecture_0,axiom,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1156,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1158,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(paramod,[status(thm)],[c_1152,c_1156]) ).
cnf(c_1159,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(paramod,[status(thm)],[c_1152,c_1158]) ).
cnf(c_1157,plain,
$false,
inference(resolve,[status(thm)],[c_1150,c_1159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL805-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 23:39:43 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 2569179 was started by sandbox on n015,
% 0.09/0.36 % Fri Sep 25 23:39:43 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 5.55/1.62
% 5.55/1.62 % SZS status Unsatisfiable for theBenchmark
% 5.55/1.62
% 5.55/1.62 % Proof 1 at 0.74 (+ 0.02) seconds.
% 5.55/1.62 % Length of proof is 4.
% 5.55/1.62 % Level of proof is 1.
% 5.55/1.62 % Maximum clause weight is 15.000.
% 5.55/1.62 % Given clauses 0.
% 5.55/1.62
% 5.55/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------