%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL821-1 : 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 : n001.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 07:59:50 AM UTC 2026
% Result : Unsatisfiable 1.05s 0.67s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-5 aty)
% Number of variables : 11 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_var__app__typesE_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Type_Otyping(VAR_0,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(VAR_3),VAR_1,tc_Lambda_OdB,tc_Lambda_OdB),VAR_2)
| c_Type_Otypings(VAR_0,VAR_1,c_Type_Osko__Type__Xvar__app__typesE__1__1(VAR_2,VAR_0,VAR_3,VAR_1)) ),
file('theBenchmark.p',cls_var__app__typesE_1) ).
cnf(c_374,plain,
( ~ c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),B,tc_Lambda_OdB,tc_Lambda_OdB),C)
| c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,D,B)) ),
inference(clausify,[status(thm)],[cls_var__app__typesE_1]) ).
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_385,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]) ).
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_387,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,VAR_0)
| v_thesis____ ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_388,plain,
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,A)
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_389,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,A),
inference(resolve,[status(thm)],[c_387,c_388]) ).
cnf(c_1317,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_n____,v_rs____)),
inference(resolve,[status(thm)],[c_385,c_374]) ).
cnf(c_1316,plain,
$false,
inference(resolve,[status(thm)],[c_389,c_1317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL821-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 23:44:42 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 350826 was started by sandbox2 on n001,
% 0.12/0.38 % Fri Sep 25 23:44:42 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 1.05/0.67
% 1.05/0.67 % SZS status Unsatisfiable for theBenchmark
% 1.05/0.67
% 1.05/0.67 % Proof 1 at 0.21 (+ 0.03) seconds.
% 1.05/0.67 % Length of proof is 6.
% 1.05/0.67 % Level of proof is 2.
% 1.05/0.67 % Maximum clause weight is 18.000.
% 1.05/0.67 % Given clauses 178.
% 1.05/0.67
% 1.05/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------