%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL777-1 : 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 : n012.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 07:59:42 AM UTC 2026
% Result : Unsatisfiable 0.04s 5.38s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-5 aty)
% Number of variables : 21 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_4,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_70,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_1,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_73,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_app__last_0,axiom,
! [VAR_0,VAR_1,VAR_2] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,VAR_0,VAR_1,tc_Lambda_OdB,tc_Lambda_OdB)),VAR_2) = c_List_Ofoldl(c_Lambda_OdB_OApp,VAR_0,c_List_Oappend(VAR_1,c_List_Olist_OCons(VAR_2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_app__last_0) ).
cnf(c_135,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C) = c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_app__last_0]) ).
cnf(c_136,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),
inference(copy,[status(thm)],[c_135]) ).
fof(cls_rotate__simps_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_List_Orotate1(c_List_Olist_OCons(VAR_0,VAR_1,VAR_2),VAR_2) = c_List_Oappend(VAR_1,c_List_Olist_OCons(VAR_0,c_List_Olist_ONil(VAR_2),VAR_2),VAR_2),
file('theBenchmark.p',cls_rotate__simps_1) ).
cnf(c_166,plain,
c_List_Orotate1(c_List_Olist_OCons(A,B,C),C) = c_List_Oappend(B,c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C),
inference(clausify,[status(thm)],[cls_rotate__simps_1]) ).
cnf(c_167,plain,
c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C) = c_List_Orotate1(c_List_Olist_OCons(B,A,C),C),
inference(copy,[status(thm)],[c_166]) ).
cnf(c_488,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Orotate1(c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),v_ss,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(paramod,[status(thm)],[c_167,c_70]) ).
cnf(c_494,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Orotate1(c_List_Olist_OCons(B,C,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,C,tc_Lambda_OdB,tc_Lambda_OdB)),B),
inference(paramod,[status(thm)],[c_167,c_136]) ).
cnf(c_510,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(paramod,[status(thm)],[c_494,c_488]) ).
cnf(c_509,plain,
$false,
inference(resolve,[status(thm)],[c_73,c_510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.32 % CPULimit : 300
% 0.04/5.32 % WCLimit : 300
% 0.04/5.32 % DateTime : Fri Sep 25 23:32:40 UTC 2026
% 0.04/5.32 % CPUTime :
% 0.04/5.32 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/5.32 % Process 3321127 was started by sandbox2 on n012,
% 0.04/5.32 % Fri Sep 25 23:32:40 2026
% 0.04/5.32 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/5.33
% 0.04/5.33 % From the command line: assign(max_seconds, 300).
% 0.04/5.38
% 0.04/5.38 % SZS status Unsatisfiable for theBenchmark
% 0.04/5.38
% 0.04/5.38 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.04/5.38 % Length of proof is 9.
% 0.04/5.38 % Level of proof is 3.
% 0.04/5.38 % Maximum clause weight is 24.000.
% 0.04/5.38 % Given clauses 0.
% 0.04/5.38
% 0.04/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------