%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL762-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 5 RR)
% Number of literals : 5 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(396,axiom,
equal(c_List_Ofoldl(u,v,c_List_Olist_ONil(w),x,w),v),
file('LCL762-1.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('LCL762-1.p',unknown),
[] ).
cnf(422,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
file('LCL762-1.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(425,plain,
$false,
inference(mrr,[status(thm)],[424,422]),
[iquote('0:MRR:424.0,422.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL762-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 05:18:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.20/0.55
% 0.20/0.55 SPASS V 3.9
% 0.20/0.55 SPASS beiseite: Proof found.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.55 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 72 clauses.
% 0.20/0.55 SPASS allocated 76362 KBytes.
% 0.20/0.55 SPASS spent 0:00:00.16 on the problem.
% 0.20/0.55 0:00:00.07 for the input.
% 0.20/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.55 0:00:00.00 for inferences.
% 0.20/0.55 0:00:00.00 for the backtracking.
% 0.20/0.55 0:00:00.02 for the reduction.
% 0.20/0.55
% 0.20/0.55
% 0.20/0.55 Here is a proof with depth 0, length 5 :
% 0.20/0.55 % SZS output start Refutation
% See solution above
% 0.20/0.55 Formulae used in the proof : cls_foldl__Nil_0 cls_conjecture_0 cls_conjecture_1
% 0.20/0.55
%------------------------------------------------------------------------------