%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL852-1 : 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 : n002.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 31.07s 4.93s
% Output : CNFRefutation 31.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 24 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 44 ( 6 sgn 16 !; 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_530,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_typing_OApp_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Type_Otyping(VAR_0,VAR_1,hAPP(hAPP(c_Type_Otype_OFun,VAR_4),VAR_3))
| ~ c_Type_Otyping(VAR_0,VAR_2,VAR_4)
| c_Type_Otyping(VAR_0,hAPP(hAPP(c_Lambda_OdB_OApp,VAR_1),VAR_2),VAR_3) ),
file('theBenchmark.p',cls_typing_OApp_0) ).
cnf(c_534,plain,
( ~ c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,E),D))
| ~ c_Type_Otyping(A,C,E)
| c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D) ),
inference(clausify,[status(thm)],[cls_typing_OApp_0]) ).
fof(cls_shift__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hAPP(c_Type_Oshift(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1) = VAR_2,
file('theBenchmark.p',cls_shift__eq_0) ).
cnf(c_538,plain,
hAPP(c_Type_Oshift(A,B,C,D),B) = C,
inference(clausify,[status(thm)],[cls_shift__eq_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_542,plain,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
inference(clausify,[status(thm)],[cls_App_I3_J_0]) ).
fof(cls_typing_OVar_0,axiom,
! [VAR_0,VAR_1] : c_Type_Otyping(VAR_0,c_Lambda_OdB_OVar(VAR_1),hAPP(VAR_0,VAR_1)),
file('theBenchmark.p',cls_typing_OVar_0) ).
cnf(c_543,plain,
c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)),
inference(clausify,[status(thm)],[cls_typing_OVar_0]) ).
fof(cls_conjecture_0,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_547,plain,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_2056,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_542,c_530]) ).
cnf(c_2086,plain,
c_Type_Otyping(c_Type_Oshift(A,B,C,D),c_Lambda_OdB_OVar(B),C),
inference(paramod,[status(thm)],[c_538,c_543]) ).
cnf(c_8317,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_ea____,A,B,tc_Type_Otype),C,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),D))
| c_Type_Otyping(c_Type_Oshift(v_ea____,A,B,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,C),c_Lambda_Olift(v_ta____,A)),D) ),
inference(resolve,[status(thm)],[c_534,c_2056]) ).
cnf(c_8315,plain,
c_Type_Otyping(c_Type_Oshift(v_ea____,A,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),B),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A)),c_Lambda_Olift(v_ta____,A)),B),
inference(resolve,[status(thm)],[c_8317,c_2086]) ).
cnf(c_8316,plain,
$false,
inference(resolve,[status(thm)],[c_8315,c_547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL852-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 23:46:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 292104 was started by sandbox on n002,
% 0.10/0.36 % Fri Sep 25 23:46:07 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 31.07/4.93
% 31.07/4.93 % SZS status Unsatisfiable for theBenchmark
% 31.07/4.93
% 31.07/4.93 % Proof 1 at 3.77 (+ 0.56) seconds.
% 31.07/4.93 % Length of proof is 10.
% 31.07/4.93 % Level of proof is 3.
% 31.07/4.93 % Maximum clause weight is 57.000.
% 31.07/4.93 % Given clauses 442.
% 31.07/4.93
% 31.07/4.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------