TSTP Solution File: LCL788-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL788-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:39:59 EDT 2022
% Result : Unsatisfiable 0.48s 0.66s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 11 unt; 0 nHn; 12 RR)
% Number of literals : 13 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(194,axiom,
( ~ c_Type_Otyping(u,c_Lambda_OdB_OVar(v),w)
| equal(hAPP(u,v),w) ),
file('LCL788-1.p',unknown),
[] ).
cnf(196,axiom,
equal(hAPP(c_Type_Oshift(u,v,w,x),v),w),
file('LCL788-1.p',unknown),
[] ).
cnf(226,axiom,
equal(c_List_Ofoldr(u,c_List_Olist_OCons(v,w,x),y,x,z),hAPP(hAPP(u,v),c_List_Ofoldr(u,w,y,x,z))),
file('LCL788-1.p',unknown),
[] ).
cnf(238,axiom,
equal(v_i____,v_n____),
file('LCL788-1.p',unknown),
[] ).
cnf(239,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('LCL788-1.p',unknown),
[] ).
cnf(242,axiom,
~ equal(hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),v_T____),
file('LCL788-1.p',unknown),
[] ).
cnf(258,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(rew,[status(thm),theory(equality)],[238,239]),
[iquote('0:Rew:238.0,239.0')] ).
cnf(265,plain,
~ equal(c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype),v_T____),
inference(rew,[status(thm),theory(equality)],[226,242]),
[iquote('0:Rew:226.0,242.0')] ).
cnf(266,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(rew,[status(thm),theory(equality)],[226,258]),
[iquote('0:Rew:226.0,258.0')] ).
cnf(1557,plain,
equal(c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype),hAPP(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_n____)),
inference(res,[status(thm),theory(equality)],[266,194]),
[iquote('0:Res:266.0,194.0')] ).
cnf(1558,plain,
equal(c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype),v_T____),
inference(rew,[status(thm),theory(equality)],[196,1557]),
[iquote('0:Rew:196.0,1557.0')] ).
cnf(1559,plain,
$false,
inference(mrr,[status(thm)],[1558,265]),
[iquote('0:MRR:1558.0,265.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : LCL788-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 3 18:21:53 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.48/0.66
% 0.48/0.66 SPASS V 3.9
% 0.48/0.66 SPASS beiseite: Proof found.
% 0.48/0.66 % SZS status Theorem
% 0.48/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.66 SPASS derived 956 clauses, backtracked 0 clauses, performed 1 splits and kept 474 clauses.
% 0.48/0.66 SPASS allocated 64716 KBytes.
% 0.48/0.66 SPASS spent 0:00:00.28 on the problem.
% 0.48/0.66 0:00:00.04 for the input.
% 0.48/0.66 0:00:00.00 for the FLOTTER CNF translation.
% 0.48/0.66 0:00:00.02 for inferences.
% 0.48/0.66 0:00:00.00 for the backtracking.
% 0.48/0.66 0:00:00.18 for the reduction.
% 0.48/0.66
% 0.48/0.66
% 0.48/0.66 Here is a proof with depth 1, length 12 :
% 0.48/0.66 % SZS output start Refutation
% See solution above
% 0.48/0.66 Formulae used in the proof : cls_typing__elims_I1_J_0 cls_shift__eq_0 cls_foldr_Osimps_I2_J_0 cls_CHAINED_0 cls_CHAINED_0_01 cls_conjecture_0
% 0.48/0.66
%------------------------------------------------------------------------------