%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL813-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n031.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 01:08:29 PM UTC 2026
% Result : Unsatisfiable 0.65s 0.94s
% Output : Refutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 7 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(819,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL813-1.p',unknown),
[] ).
cnf(893,axiom,
equal(hAPP(c_Type_Oshift(u,v,w,x),v),w),
file('LCL813-1.p',unknown),
[] ).
cnf(895,axiom,
c_Type_Otyping(u,c_Lambda_OdB_OVar(v),hAPP(u,v)),
file('LCL813-1.p',unknown),
[] ).
cnf(936,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('LCL813-1.p',unknown),
[] ).
cnf(1120,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_Orderings_Obot__class_Obot(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(rew,[status(thm),theory(equality)],[819,936]),
[iquote('0:Rew:819.0,936.0')] ).
cnf(1255,plain,
c_Type_Otyping(c_Type_Oshift(u,v,w,x),c_Lambda_OdB_OVar(v),w),
inference(spr,[status(thm),theory(equality)],[893,895]),
[iquote('0:SpR:893.0,895.0')] ).
cnf(1257,plain,
$false,
inference(unc,[status(thm)],[1255,1120]),
[iquote('0:UnC:1255.0,1120.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL813-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n031.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 6 01:39:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.65/0.94
% 0.65/0.94 SPASS V 3.9
% 0.65/0.94 SPASS beiseite: Proof found.
% 0.65/0.94 % SZS status Theorem
% 0.65/0.94 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.65/0.94 SPASS derived 114 clauses, backtracked 0 clauses, performed 0 splits and kept 744 clauses.
% 0.65/0.94 SPASS allocated 77410 KBytes.
% 0.65/0.94 SPASS spent 0:00:00.55 on the problem.
% 0.65/0.94 0:00:00.10 for the input.
% 0.65/0.94 0:00:00.00 for the FLOTTER CNF translation.
% 0.65/0.94 0:00:00.01 for inferences.
% 0.65/0.94 0:00:00.00 for the backtracking.
% 0.65/0.94 0:00:00.31 for the reduction.
% 0.65/0.94
% 0.65/0.94
% 0.65/0.94 Here is a proof with depth 1, length 7 :
% 0.65/0.94 % SZS output start Refutation
% See solution above
% 0.65/0.94 Formulae used in the proof : cls_bot__nat__def_0 cls_shift__eq_0 cls_typing_OVar_0 cls_conjecture_0
% 0.65/0.94
%------------------------------------------------------------------------------