%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL794-1 : 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 : n010.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 07:59:45 AM UTC 2026
% Result : Unsatisfiable 186.67s 25.18s
% Output : CNFRefutation 186.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 30 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 46 ( 6 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OVar(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)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_136,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OVar(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)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_typing_OVar_0,axiom,
! [VAR_0,VAR_1] : c_Type_Otyping(VAR_0,c_Lambda_OdB_OVar(VAR_1),hAPP(VAR_0,VAR_1)),
file('theBenchmark.p',cls_typing_OVar_0) ).
cnf(c_139,plain,
c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)),
inference(clausify,[status(thm)],[cls_typing_OVar_0]) ).
fof(cls_shift__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hAPP(c_Type_Oshift(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1) = VAR_2,
file('theBenchmark.p',cls_shift__eq_0) ).
cnf(c_142,plain,
hAPP(c_Type_Oshift(A,B,C,D),B) = C,
inference(clausify,[status(thm)],[cls_shift__eq_0]) ).
fof(cls_App_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Type_Otyping(VAR_0,VAR_1,hAPP(hAPP(c_Type_Otype_OFun,VAR_4),VAR_3))
| ~ c_Type_Otyping(VAR_0,VAR_2,VAR_4)
| c_Type_Otyping(VAR_0,hAPP(hAPP(c_Lambda_OdB_OApp,VAR_1),VAR_2),VAR_3) ),
file('theBenchmark.p',cls_App_0) ).
cnf(c_146,plain,
( ~ c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,E),D))
| ~ c_Type_Otyping(A,C,E)
| c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D) ),
inference(clausify,[status(thm)],[cls_App_0]) ).
fof(cls_lift__type_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Type_Otyping(VAR_0,VAR_3,VAR_4)
| c_Type_Otyping(c_Type_Oshift(VAR_0,VAR_1,VAR_2,tc_Type_Otype),c_Lambda_Olift(VAR_3,VAR_1),VAR_4) ),
file('theBenchmark.p',cls_lift__type_0) ).
cnf(c_150,plain,
( ~ c_Type_Otyping(A,D,E)
| c_Type_Otyping(c_Type_Oshift(A,B,C,tc_Type_Otype),c_Lambda_Olift(D,B),E) ),
inference(clausify,[status(thm)],[cls_lift__type_0]) ).
fof(cls_T_0,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('theBenchmark.p',cls_T_0) ).
cnf(c_151,plain,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(clausify,[status(thm)],[cls_T_0]) ).
cnf(c_152,plain,
hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____,
inference(copy,[status(thm)],[c_151]) ).
fof(cls_uT_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('theBenchmark.p',cls_uT_0) ).
cnf(c_154,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(clausify,[status(thm)],[cls_uT_0]) ).
cnf(c_479,plain,
c_Type_Otyping(c_Type_Oshift(A,B,C,D),c_Lambda_OdB_OVar(B),C),
inference(paramod,[status(thm)],[c_142,c_139]) ).
cnf(c_484,plain,
( ~ c_Type_Otyping(A,B,v_T____)
| ~ c_Type_Otyping(A,C,v_T_H_H____)
| c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
inference(paramod,[status(thm)],[c_152,c_146]) ).
cnf(c_488,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,A,B,tc_Type_Otype),c_Lambda_Olift(v_u____,A),v_T____),
inference(resolve,[status(thm)],[c_154,c_150]) ).
cnf(c_1648,plain,
( ~ c_Type_Otyping(c_Type_Oshift(A,B,v_T_H_H____,C),D,v_T____)
| c_Type_Otyping(c_Type_Oshift(A,B,v_T_H_H____,C),hAPP(hAPP(c_Lambda_OdB_OApp,D),c_Lambda_OdB_OVar(B)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
inference(resolve,[status(thm)],[c_484,c_479]) ).
cnf(c_1646,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,A,v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,A)),c_Lambda_OdB_OVar(A)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(resolve,[status(thm)],[c_1648,c_488]) ).
cnf(c_1647,plain,
$false,
inference(resolve,[status(thm)],[c_1646,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL794-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 23:35:30 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1940854 was started by sandbox2 on n010,
% 0.16/0.44 % Fri Sep 25 23:35:30 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 186.67/25.18
% 186.67/25.18 % SZS status Unsatisfiable for theBenchmark
% 186.67/25.18
% 186.67/25.18 % Proof 1 at 0.43 (+ 0.09) seconds.
% 186.67/25.18 % Length of proof is 13.
% 186.67/25.18 % Level of proof is 4.
% 186.67/25.18 % Maximum clause weight is 25.000.
% 186.67/25.18 % Given clauses 303.
% 186.67/25.18
% 186.67/25.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------