%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : Mon Sep 7 01:08:21 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 6 unt; 0 nHn; 8 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(198,axiom,
c_List_Olistsp(u,c_List_Olist_ONil(v),v),
file('LCL763-1.p',unknown),
[] ).
cnf(386,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,u,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v),u,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('LCL763-1.p',unknown),
[] ).
cnf(396,axiom,
equal(c_List_Ofoldl(u,v,c_List_Olist_ONil(w),x,w),v),
file('LCL763-1.p',unknown),
[] ).
cnf(421,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL763-1.p',unknown),
[] ).
cnf(424,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
inference(rew,[status(thm),theory(equality)],[396,421]),
[iquote('0:Rew:396.0,421.0')] ).
cnf(1310,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(u))) ),
inference(spr,[status(thm),theory(equality)],[396,386]),
[iquote('0:SpR:396.0,386.1')] ).
cnf(1315,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(u))),
inference(mrr,[status(thm)],[1310,198]),
[iquote('0:MRR:1310.0,198.0')] ).
cnf(1316,plain,
$false,
inference(unc,[status(thm)],[1315,424]),
[iquote('0:UnC:1315.0,424.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_spass %d %s
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 6 00:32:42 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 759 clauses, backtracked 0 clauses, performed 0 splits and kept 611 clauses.
% 0.18/0.51 SPASS allocated 77234 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.19 on the problem.
% 0.18/0.51 0:00:00.03 for the input.
% 0.18/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.10 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 1, length 8 :
% 0.18/0.51 % SZS output start Refutation
% See solution above
% 0.18/0.51 Formulae used in the proof : cls_listsp_ONil_0 cls_IT_OVar_0 cls_foldl__Nil_0 cls_conjecture_0
% 0.18/0.51
%------------------------------------------------------------------------------