%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL795-1 : 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 07:59:45 AM UTC 2026
% Result : Unsatisfiable 6.34s 1.18s
% Output : CNFRefutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-5 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_uT_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('theBenchmark.p',cls_uT_0) ).
cnf(c_848,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(clausify,[status(thm)],[cls_uT_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_850,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_851,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_850]) ).
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_852,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_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),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),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_conjecture_0) ).
cnf(c_857,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),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_conjecture_0]) ).
cnf(c_858,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),v_T____),
inference(paramod,[status(thm)],[c_851,c_857]) ).
cnf(c_2910,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_852,c_848]) ).
cnf(c_2911,plain,
$false,
inference(resolve,[status(thm)],[c_2910,c_858]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL795-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Fri Sep 25 23:34:51 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 3324104 was started by sandbox on n012,
% 0.03/0.31 % Fri Sep 25 23:34:51 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.33
% 0.07/0.33 % From the command line: assign(max_seconds, 300).
% 6.34/1.18
% 6.34/1.18 % SZS status Unsatisfiable for theBenchmark
% 6.34/1.18
% 6.34/1.18 % Proof 1 at 0.78 (+ 0.06) seconds.
% 6.34/1.18 % Length of proof is 8.
% 6.34/1.18 % Level of proof is 3.
% 6.34/1.18 % Maximum clause weight is 18.000.
% 6.34/1.18 % Given clauses 372.
% 6.34/1.18
% 6.34/1.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------