%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL851-1 : 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 : n013.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 07:59:56 AM UTC 2026
% Result : Unsatisfiable 6.97s 1.41s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_843,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_App_I3_J_0,axiom,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
file('theBenchmark.p',cls_App_I3_J_0) ).
cnf(c_847,plain,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
inference(clausify,[status(thm)],[cls_App_I3_J_0]) ).
fof(cls_conjecture_0,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_848,plain,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_3778,plain,
c_Type_Otyping(c_Type_Oshift(v_ea____,A,B,tc_Type_Otype),c_Lambda_Olift(v_ta____,A),v_Ta____),
inference(resolve,[status(thm)],[c_847,c_843]) ).
cnf(c_3779,plain,
$false,
inference(resolve,[status(thm)],[c_3778,c_848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL851-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 23:42:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1475080 was started by sandbox on n013,
% 0.09/0.37 % Fri Sep 25 23:42:51 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 6.97/1.41
% 6.97/1.41 % SZS status Unsatisfiable for theBenchmark
% 6.97/1.41
% 6.97/1.41 % Proof 1 at 0.92 (+ 0.07) seconds.
% 6.97/1.41 % Length of proof is 5.
% 6.97/1.41 % Level of proof is 2.
% 6.97/1.41 % Maximum clause weight is 14.000.
% 6.97/1.41 % Given clauses 363.
% 6.97/1.41
% 6.97/1.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------