%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 01:08:20 PM UTC 2026
% Result : Unsatisfiable 0.46s 0.74s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 14 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(542,axiom,
equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,u),v),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubstn(u,v,c_HOL_Ozero__class_Ozero(tc_nat))),
file('LCL759-1.p',unknown),
[] ).
cnf(584,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v),u),c_HOL_Ozero__class_Ozero(tc_nat)),w,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v)),u),w,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('LCL759-1.p',unknown),
[] ).
cnf(634,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(u))),c_Suc(v))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(u)),v)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(u),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL759-1.p',unknown),
[] ).
cnf(636,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(u)),v))),
file('LCL759-1.p',unknown),
[] ).
cnf(637,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL759-1.p',unknown),
[] ).
cnf(704,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v,u,c_HOL_Ozero__class_Ozero(tc_nat)),w,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v)),u),w,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(rew,[status(thm),theory(equality)],[542,584]),
[iquote('0:Rew:542.0,584.1')] ).
cnf(709,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(u))),c_Suc(v)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(u)),v),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(u),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(rew,[status(thm),theory(equality)],[542,634]),
[iquote('0:Rew:542.0,634.0')] ).
cnf(732,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(res,[status(thm),theory(equality)],[704,637]),
[iquote('0:Res:704.2,637.0')] ).
cnf(743,plain,
$false,
inference(mrr,[status(thm)],[732,636,709]),
[iquote('0:MRR:732.0,732.1,636.0,709.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n029.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 : Fri Sep 4 21:58:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.46/0.74
% 0.46/0.74 SPASS V 3.9
% 0.46/0.74 SPASS beiseite: Proof found.
% 0.46/0.74 % SZS status Theorem
% 0.46/0.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.74 SPASS derived 19 clauses, backtracked 0 clauses, performed 0 splits and kept 518 clauses.
% 0.46/0.74 SPASS allocated 76823 KBytes.
% 0.46/0.74 SPASS spent 0:00:00.34 on the problem.
% 0.46/0.74 0:00:00.08 for the input.
% 0.46/0.74 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.74 0:00:00.00 for inferences.
% 0.46/0.74 0:00:00.00 for the backtracking.
% 0.46/0.74 0:00:00.16 for the reduction.
% 0.46/0.74
% 0.46/0.74
% 0.46/0.74 Here is a proof with depth 1, length 9 :
% 0.46/0.74 % SZS output start Refutation
% See solution above
% 0.46/0.74 Formulae used in the proof : cls_substn__subst__0_0 cls_Beta_0 cls_conjecture_1 cls_conjecture_3 cls_conjecture_4
% 0.46/0.74
%------------------------------------------------------------------------------