%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL795-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 01:08:26 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.90s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 9 unt; 0 nHn; 10 RR)
% Number of literals : 11 ( 0 equ; 4 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 : 22 ( 22 usr; 15 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(815,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL795-1.p',unknown),
[] ).
cnf(848,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('LCL795-1.p',unknown),
[] ).
cnf(872,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('LCL795-1.p',unknown),
[] ).
cnf(874,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('LCL795-1.p',unknown),
[] ).
cnf(875,axiom,
( ~ c_Type_Otyping(u,v,w)
| c_Type_Otyping(c_Type_Oshift(u,x,y,tc_Type_Otype),c_Lambda_Olift(v,x),w) ),
file('LCL795-1.p',unknown),
[] ).
cnf(920,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),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('LCL795-1.p',unknown),
[] ).
cnf(1069,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)],[848,874]),
[iquote('0:Rew:848.0,874.0')] ).
cnf(1095,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat)),v_T____),
inference(rew,[status(thm),theory(equality)],[815,920,1069,848]),
[iquote('0:Rew:815.0,920.0,1069.0,920.0,848.0,920.0')] ).
cnf(1124,plain,
~ c_Type_Otyping(v_e____,v_u____,v_T____),
inference(res,[status(thm),theory(equality)],[875,1095]),
[iquote('0:Res:875.1,1095.0')] ).
cnf(1126,plain,
$false,
inference(mrr,[status(thm)],[1124,872]),
[iquote('0:MRR:1124.0,872.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL795-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n010.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 : Sat Sep 5 15:23:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.90
% 0.13/0.90 SPASS V 3.9
% 0.13/0.90 SPASS beiseite: Proof found.
% 0.13/0.90 % SZS status Theorem
% 0.13/0.90 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.90 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 725 clauses.
% 0.13/0.90 SPASS allocated 77335 KBytes.
% 0.13/0.90 SPASS spent 0:00:00.50 on the problem.
% 0.13/0.90 0:00:00.10 for the input.
% 0.13/0.90 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.90 0:00:00.00 for inferences.
% 0.13/0.90 0:00:00.00 for the backtracking.
% 0.13/0.90 0:00:00.28 for the reduction.
% 0.13/0.90
% 0.13/0.90
% 0.13/0.90 Here is a proof with depth 1, length 10 :
% 0.13/0.90 % SZS output start Refutation
% See solution above
% 0.13/0.90 Formulae used in the proof : cls_bot__nat__def_0 cls_foldr_Osimps_I2_J_0 cls_uT_0 cls_T_0 cls_lift__type_0 cls_conjecture_0
% 0.13/0.90
%------------------------------------------------------------------------------