TSTP Solution File: LCL760-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL760-1 : TPTP v8.1.0. 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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:39:43 EDT 2022
% Result : Unsatisfiable 0.41s 0.57s
% Output : Refutation 0.41s
% 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 : 10 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(567,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('LCL760-1.p',unknown),
[] ).
cnf(648,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('LCL760-1.p',unknown),
[] ).
cnf(651,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(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))),
file('LCL760-1.p',unknown),
[] ).
cnf(731,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)],[567,648]),
[iquote('0:Rew:567.0,648.0')] ).
cnf(732,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(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(rew,[status(thm),theory(equality)],[567,651]),
[iquote('0:Rew:567.0,651.0')] ).
cnf(733,plain,
$false,
inference(mrr,[status(thm)],[732,731]),
[iquote('0:MRR:732.0,731.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% 0.02/0.11 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jul 2 16:04:02 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.41/0.57
% 0.41/0.57 SPASS V 3.9
% 0.41/0.57 SPASS beiseite: Proof found.
% 0.41/0.57 % SZS status Theorem
% 0.41/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.57 SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 513 clauses.
% 0.41/0.57 SPASS allocated 76848 KBytes.
% 0.41/0.57 SPASS spent 0:00:00.23 on the problem.
% 0.41/0.57 0:00:00.06 for the input.
% 0.41/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.57 0:00:00.00 for inferences.
% 0.41/0.57 0:00:00.00 for the backtracking.
% 0.41/0.57 0:00:00.11 for the reduction.
% 0.41/0.57
% 0.41/0.57
% 0.41/0.57 Here is a proof with depth 0, length 6 :
% 0.41/0.57 % SZS output start Refutation
% See solution above
% 0.41/0.57 Formulae used in the proof : cls_substn__subst__0_0 cls_conjecture_1 cls_conjecture_4
% 0.41/0.57
%------------------------------------------------------------------------------