%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL789-1 : 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 : n005.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 07:59:44 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.54s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 3 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_Type_Otyping(v_e____,v_u____,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_110,plain,
~ c_Type_Otyping(v_e____,v_u____,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]) ).
fof(cls_CHAINED_0_01,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_111,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_CHAINED_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_CHAINED_0) ).
cnf(c_112,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_CHAINED_0]) ).
cnf(c_113,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_112]) ).
cnf(c_462,plain,
~ c_Type_Otyping(v_e____,v_u____,v_T____),
inference(paramod,[status(thm)],[c_113,c_110]) ).
cnf(c_461,plain,
$false,
inference(resolve,[status(thm)],[c_111,c_462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL789-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n005.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 23:34:18 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 534842 was started by sandbox on n005,
% 0.20/0.46 % Fri Sep 25 23:34:18 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.23/0.54
% 0.23/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.54
% 0.23/0.54 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.23/0.54 % Length of proof is 5.
% 0.23/0.54 % Level of proof is 2.
% 0.23/0.54 % Maximum clause weight is 30.000.
% 0.23/0.54 % Given clauses 0.
% 0.23/0.54
% 0.23/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------