%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : Mon Sep 7 01:08:23 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(288,axiom,
equal(c_List_Oappend(u,c_List_Olist_OCons(v,c_List_Olist_ONil(w),w),w),c_List_Orotate1(c_List_Olist_OCons(v,u,w),w)),
file('LCL777-1.p',unknown),
[] ).
cnf(313,axiom,
equal(c_List_Ofoldl(c_Lambda_OdB_OApp,u,c_List_Oappend(v,c_List_Olist_OCons(w,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,u,v,tc_Lambda_OdB,tc_Lambda_OdB)),w)),
file('LCL777-1.p',unknown),
[] ).
cnf(385,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('LCL777-1.p',unknown),
[] ).
cnf(388,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('LCL777-1.p',unknown),
[] ).
cnf(411,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(rew,[status(thm),theory(equality)],[288,388]),
[iquote('0:Rew:288.0,388.0')] ).
cnf(412,plain,
equal(c_List_Ofoldl(c_Lambda_OdB_OApp,u,c_List_Orotate1(c_List_Olist_OCons(v,w,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,u,w,tc_Lambda_OdB,tc_Lambda_OdB)),v)),
inference(rew,[status(thm),theory(equality)],[288,313]),
[iquote('0:Rew:288.0,313.0')] ).
cnf(413,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(rew,[status(thm),theory(equality)],[412,411]),
[iquote('0:Rew:412.0,411.0')] ).
cnf(414,plain,
$false,
inference(mrr,[status(thm)],[413,385]),
[iquote('0:MRR:413.0,385.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 6 01:44:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.21/0.55
% 0.21/0.55 SPASS V 3.9
% 0.21/0.55 SPASS beiseite: Proof found.
% 0.21/0.55 % SZS status Theorem
% 0.21/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.55 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 275 clauses.
% 0.21/0.55 SPASS allocated 76282 KBytes.
% 0.21/0.55 SPASS spent 0:00:00.17 on the problem.
% 0.21/0.55 0:00:00.07 for the input.
% 0.21/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.55 0:00:00.00 for inferences.
% 0.21/0.55 0:00:00.00 for the backtracking.
% 0.21/0.55 0:00:00.04 for the reduction.
% 0.21/0.55
% 0.21/0.55
% 0.21/0.55 Here is a proof with depth 0, length 8 :
% 0.21/0.55 % SZS output start Refutation
% See solution above
% 0.21/0.55 Formulae used in the proof : cls_rotate__simps_1 cls_app__last_0 cls_conjecture_1 cls_conjecture_4
% 0.21/0.55
%------------------------------------------------------------------------------