%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL778-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 0.33s 0.62s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 6 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(483,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('LCL778-1.p',unknown),
[] ).
cnf(546,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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('LCL778-1.p',unknown),
[] ).
cnf(549,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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('LCL778-1.p',unknown),
[] ).
cnf(564,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(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)],[483,546]),
[iquote('0:Rew:483.0,546.0')] ).
cnf(569,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(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)],[483,549]),
[iquote('0:Rew:483.0,549.0')] ).
cnf(570,plain,
$false,
inference(mrr,[status(thm)],[569,564]),
[iquote('0:MRR:569.0,564.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL778-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 16:29:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.33/0.62
% 0.33/0.62 SPASS V 3.9
% 0.33/0.62 SPASS beiseite: Proof found.
% 0.33/0.62 % SZS status Theorem
% 0.33/0.62 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/0.62 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 327 clauses.
% 0.33/0.62 SPASS allocated 76638 KBytes.
% 0.33/0.62 SPASS spent 0:00:00.23 on the problem.
% 0.33/0.62 0:00:00.08 for the input.
% 0.33/0.62 0:00:00.00 for the FLOTTER CNF translation.
% 0.33/0.62 0:00:00.00 for inferences.
% 0.33/0.62 0:00:00.00 for the backtracking.
% 0.33/0.62 0:00:00.07 for the reduction.
% 0.33/0.62
% 0.33/0.62
% 0.33/0.62 Here is a proof with depth 0, length 6 :
% 0.33/0.62 % SZS output start Refutation
% See solution above
% 0.33/0.62 Formulae used in the proof : cls_substn__subst__0_0 cls_conjecture_1 cls_conjecture_4
% 0.33/0.62
%------------------------------------------------------------------------------