TSTP Solution File: LCL776-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL776-1 : TPTP v8.1.0. 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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:39:52 EDT 2022
% Result : Unsatisfiable 0.45s 0.66s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 13 RR)
% Number of literals : 19 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 14 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(716,axiom,
equal(c_List_Oappend(u,c_List_Olist_OCons(v,c_List_Olist_ONil(w),w),w),c_List_Orotate1(c_List_Olist_OCons(v,u,w),w)),
file('LCL776-1.p',unknown),
[] ).
cnf(737,axiom,
equal(c_List_Ofoldl(c_Lambda_OdB_OApp,u,c_List_Oappend(v,c_List_Olist_OCons(w,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,u,v,tc_Lambda_OdB,tc_Lambda_OdB)),w)),
file('LCL776-1.p',unknown),
[] ).
cnf(768,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,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('LCL776-1.p',unknown),
[] ).
cnf(779,axiom,
equal(c_List_Ofoldl(u,v,c_List_Olist_OCons(w,x,y),z,y),c_List_Ofoldl(u,hAPP(hAPP(u,v),w),x,z,y)),
file('LCL776-1.p',unknown),
[] ).
cnf(868,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,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('LCL776-1.p',unknown),
[] ).
cnf(869,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('LCL776-1.p',unknown),
[] ).
cnf(871,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL776-1.p',unknown),
[] ).
cnf(901,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r),c_List_Olist_OCons(v_s,c_List_Orotate1(c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),v_ss,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(rew,[status(thm),theory(equality)],[779,871,716]),
[iquote('0:Rew:779.0,871.0,716.0,871.0')] ).
cnf(902,plain,
equal(c_List_Ofoldl(c_Lambda_OdB_OApp,u,c_List_Orotate1(c_List_Olist_OCons(v,w,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,u,w,tc_Lambda_OdB,tc_Lambda_OdB)),v)),
inference(rew,[status(thm),theory(equality)],[716,737]),
[iquote('0:Rew:716.0,737.0')] ).
cnf(916,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,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,c_Lambda_OdB_OAbs(v),c_List_Olist_OCons(u,w,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(rew,[status(thm),theory(equality)],[779,768]),
[iquote('0:Rew:779.0,768.2')] ).
cnf(941,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_s))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Orotate1(c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),v_ss,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(res,[status(thm),theory(equality)],[916,901]),
[iquote('0:Res:916.2,901.0')] ).
cnf(943,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_s))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,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)))) ),
inference(rew,[status(thm),theory(equality)],[902,941]),
[iquote('0:Rew:902.0,941.1')] ).
cnf(944,plain,
$false,
inference(mrr,[status(thm)],[943,869,868]),
[iquote('0:MRR:943.0,943.1,869.0,868.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL776-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 3 17:31:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.45/0.66
% 0.45/0.66 SPASS V 3.9
% 0.45/0.66 SPASS beiseite: Proof found.
% 0.45/0.66 % SZS status Theorem
% 0.45/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.66 SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 709 clauses.
% 0.45/0.66 SPASS allocated 77241 KBytes.
% 0.45/0.66 SPASS spent 0:00:00.29 on the problem.
% 0.45/0.66 0:00:00.07 for the input.
% 0.45/0.66 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.66 0:00:00.00 for inferences.
% 0.45/0.66 0:00:00.00 for the backtracking.
% 0.45/0.66 0:00:00.14 for the reduction.
% 0.45/0.66
% 0.45/0.66
% 0.45/0.66 Here is a proof with depth 1, length 13 :
% 0.45/0.66 % SZS output start Refutation
% See solution above
% 0.45/0.66 Formulae used in the proof : cls_rotate__simps_1 cls_app__last_0 cls_Beta_0 cls_foldl__Cons_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_4
% 0.45/0.66
%------------------------------------------------------------------------------