%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL848-1 : 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 07:59:55 AM UTC 2026
% Result : Unsatisfiable 2.81s 0.80s
% Output : CNFRefutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 42 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_473,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_474,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
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_484,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_485,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_484]) ).
fof(cls_foldl__Nil_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_List_Ofoldl(VAR_0,VAR_1,c_List_Olist_ONil(VAR_2),VAR_3,VAR_2) = VAR_1,
file('theBenchmark.p',cls_foldl__Nil_0) ).
cnf(c_491,plain,
c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C) = B,
inference(clausify,[status(thm)],[cls_foldl__Nil_0]) ).
fof(cls_IT_OVar_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_List_Olistsp(c_InductTermi_OIT,VAR_1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(VAR_0),VAR_1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_IT_OVar_0) ).
cnf(c_509,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,B,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(clausify,[status(thm)],[cls_IT_OVar_0]) ).
cnf(c_1391,plain,
hAPP(hAPP(A,B),C) = c_List_Ofoldl(A,B,c_List_Olist_OCons(C,c_List_Olist_ONil(D),D),E,D),
inference(paramod,[status(thm)],[c_491,c_485]) ).
cnf(c_1372,plain,
c_List_Ofoldl(A,B,c_List_Olist_OCons(C,c_List_Olist_ONil(D),D),E,D) = hAPP(hAPP(A,B),C),
inference(copy,[status(thm)],[c_1391]) ).
cnf(c_1373,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))))),
inference(paramod,[status(thm)],[c_1372,c_473]) ).
cnf(c_1392,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(resolve,[status(thm)],[c_509,c_474]) ).
cnf(c_1389,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A)),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))))),
inference(paramod,[status(thm)],[c_1372,c_1392]) ).
cnf(c_1390,plain,
$false,
inference(resolve,[status(thm)],[c_1389,c_1373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL848-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 23:42:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1474691 was started by sandbox on n013,
% 0.12/0.36 % Fri Sep 25 23:42:36 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 2.81/0.80
% 2.81/0.80 % SZS status Unsatisfiable for theBenchmark
% 2.81/0.80
% 2.81/0.80 % Proof 1 at 0.39 (+ 0.02) seconds.
% 2.81/0.80 % Length of proof is 10.
% 2.81/0.80 % Level of proof is 4.
% 2.81/0.80 % Maximum clause weight is 20.000.
% 2.81/0.80 % Given clauses 132.
% 2.81/0.80
% 2.81/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------