%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL836-1 : 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 : n007.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 07:59:53 AM UTC 2026
% Result : Unsatisfiable 8.89s 1.72s
% Output : CNFRefutation 8.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-5 aty)
% Number of variables : 12 ( 3 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_214,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0_02,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(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('theBenchmark.p',cls_CHAINED_0_02) ).
cnf(c_215,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(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(clausify,[status(thm)],[cls_CHAINED_0_02]) ).
fof(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_216,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_CHAINED_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_217,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_SI1_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Type_Otyping(c_Type_Oshift(VAR_2,VAR_1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),VAR_3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,VAR_0))
| ~ c_Type_Otyping(VAR_2,VAR_0,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),VAR_0),VAR_1))) ),
file('theBenchmark.p',cls_SI1_0) ).
cnf(c_225,plain,
( ~ c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),D)
| ~ hBOOL(hAPP(c_InductTermi_OIT,A))
| ~ c_Type_Otyping(C,A,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),A),B))) ),
inference(clausify,[status(thm)],[cls_SI1_0]) ).
cnf(c_5336,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,A,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),B)
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),A))) ),
inference(resolve,[status(thm)],[c_225,c_217]) ).
cnf(c_718,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,A,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),B)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),A))) ),
inference(resolve,[status(thm)],[c_216,c_5336]) ).
cnf(c_5337,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(resolve,[status(thm)],[c_718,c_215]) ).
cnf(c_5335,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_5337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.39 % Computer : n007.cluster.edu
% 0.16/0.39 % Model : x86_64 x86_64
% 0.16/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39 % Memory : 8046.5625MB
% 0.16/0.39 % OS : Linux 6.8.0-71-generic
% 0.16/0.39 % CPULimit : 300
% 0.16/0.39 % WCLimit : 300
% 0.16/0.39 % DateTime : Fri Sep 25 23:39:38 UTC 2026
% 0.16/0.40 % CPUTime :
% 0.16/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.40 % Process 2196807 was started by sandbox2 on n007,
% 0.16/0.40 % Fri Sep 25 23:39:38 2026
% 0.16/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.42
% 0.19/0.42 % From the command line: assign(max_seconds, 300).
% 8.89/1.72
% 8.89/1.72 % given #500 (T,wt=8): 3018 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(v_u____)))))). [resolve(2800,a,247,b)].
% 8.89/1.72
% 8.89/1.72 % SZS status Unsatisfiable for theBenchmark
% 8.89/1.72
% 8.89/1.72 % Proof 1 at 1.10 (+ 0.17) seconds.
% 8.89/1.72 % Length of proof is 7.
% 8.89/1.72 % Level of proof is 2.
% 8.89/1.72 % Maximum clause weight is 50.000.
% 8.89/1.72 % Given clauses 630.
% 8.89/1.72
% 8.89/1.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------