%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL785-1 : 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 : 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 5.67s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-5 aty)
% Number of variables : 18 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_True_0,axiom,
v_n____ = v_i____,
file('theBenchmark.p',cls_True_0) ).
cnf(c_387,plain,
v_n____ = v_i____,
inference(clausify,[status(thm)],[cls_True_0]) ).
cnf(c_388,plain,
v_i____ = v_n____,
inference(copy,[status(thm)],[c_387]) ).
fof(cls_nT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('theBenchmark.p',cls_nT_0) ).
cnf(c_396,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(clausify,[status(thm)],[cls_nT_0]) ).
cnf(c_397,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(paramod,[status(thm)],[c_388,c_396]) ).
fof(cls_foldl__Cons_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : c_List_Ofoldl(VAR_0,VAR_1,c_List_Olist_OCons(VAR_2,VAR_3,VAR_4),VAR_5,VAR_4) = c_List_Ofoldl(VAR_0,hAPP(hAPP(VAR_0,VAR_1),VAR_2),VAR_3,VAR_5,VAR_4),
file('theBenchmark.p',cls_foldl__Cons_0) ).
cnf(c_406,plain,
c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,E),F,E) = c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,F,E),
inference(clausify,[status(thm)],[cls_foldl__Cons_0]) ).
cnf(c_407,plain,
c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,E,F) = c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,F),E,F),
inference(copy,[status(thm)],[c_406]) ).
fof(cls_Cons_0,axiom,
v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
file('theBenchmark.p',cls_Cons_0) ).
cnf(c_421,plain,
v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_Cons_0]) ).
cnf(c_422,plain,
c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) = v_rs____,
inference(copy,[status(thm)],[c_421]) ).
fof(cls_conjecture_0,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_438,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_440,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(paramod,[status(thm)],[c_388,c_438]) ).
cnf(c_441,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(paramod,[status(thm)],[c_407,c_440]) ).
cnf(c_442,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(paramod,[status(thm)],[c_422,c_441]) ).
cnf(c_439,plain,
$false,
inference(resolve,[status(thm)],[c_397,c_442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL785-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n005.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Fri Sep 25 23:33:53 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.46 % Process 533736 was started by sandbox2 on n005,
% 0.19/5.46 % Fri Sep 25 23:33:53 2026
% 0.19/5.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.47
% 0.19/5.47 % From the command line: assign(max_seconds, 300).
% 0.23/5.67
% 0.23/5.67 % SZS status Unsatisfiable for theBenchmark
% 0.23/5.67
% 0.23/5.67 % Proof 1 at 0.18 (+ 0.01) seconds.
% 0.23/5.67 % Length of proof is 10.
% 0.23/5.67 % Level of proof is 3.
% 0.23/5.67 % Maximum clause weight is 20.000.
% 0.23/5.67 % Given clauses 0.
% 0.23/5.67
% 0.23/5.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------