%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL815-1 : 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 : n004.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 07:59:49 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.93s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-5 aty)
% Number of variables : 22 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_240,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_241,plain,
c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_lift__types_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Type_Otypings(VAR_0,VAR_3,VAR_4)
| c_Type_Otypings(c_Type_Oshift(VAR_0,VAR_1,VAR_2,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),VAR_1),VAR_3,tc_Lambda_OdB,tc_Lambda_OdB),VAR_4) ),
file('theBenchmark.p',cls_lift__types_0) ).
cnf(c_243,plain,
( ~ c_Type_Otypings(A,D,E)
| c_Type_Otypings(c_Type_Oshift(A,B,C,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B),D,tc_Lambda_OdB,tc_Lambda_OdB),E) ),
inference(clausify,[status(thm)],[cls_lift__types_0]) ).
fof(cls_foldr__foldl_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : c_List_Ofoldr(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4) = c_List_Ofoldl(c_COMBC(VAR_0,VAR_3,VAR_4,VAR_4),VAR_2,c_List_Orev(VAR_1,VAR_3),VAR_4,VAR_3),
file('theBenchmark.p',cls_foldr__foldl_0) ).
cnf(c_294,plain,
c_List_Ofoldr(A,B,C,D,E) = c_List_Ofoldl(c_COMBC(A,D,E,E),C,c_List_Orev(B,D),E,D),
inference(clausify,[status(thm)],[cls_foldr__foldl_0]) ).
cnf(c_953,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(paramod,[status(thm)],[c_294,c_240]) ).
cnf(c_1065,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,A,B,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),A),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(resolve,[status(thm)],[c_243,c_241]) ).
cnf(c_1066,plain,
$false,
inference(resolve,[status(thm)],[c_1065,c_953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL815-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.54 % Computer : n004.cluster.edu
% 0.11/0.54 % Model : x86_64 x86_64
% 0.11/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.54 % Memory : 8046.5625MB
% 0.11/0.54 % OS : Linux 6.8.0-71-generic
% 0.11/0.55 % CPULimit : 300
% 0.11/0.55 % WCLimit : 300
% 0.11/0.55 % DateTime : Fri Sep 25 23:37:39 UTC 2026
% 0.11/0.55 % CPUTime :
% 0.11/0.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.55 % Process 255760 was started by sandbox2 on n004,
% 0.11/0.55 % Fri Sep 25 23:37:39 2026
% 0.11/0.55 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.58
% 0.14/0.58 % From the command line: assign(max_seconds, 300).
% 0.14/0.93
% 0.14/0.93 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.93
% 0.14/0.93 % Proof 1 at 0.32 (+ 0.01) seconds.
% 0.14/0.93 % Length of proof is 7.
% 0.14/0.93 % Level of proof is 2.
% 0.14/0.93 % Maximum clause weight is 49.000.
% 0.14/0.93 % Given clauses 38.
% 0.14/0.93
% 0.14/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------