%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL796-1 : 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 01:08:26 PM UTC 2026
% Result : Unsatisfiable 0.77s 1.11s
% Output : Refutation 0.77s
% 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 : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(928,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL796-1.p',unknown),
[] ).
cnf(972,axiom,
equal(hAPP(c_Type_Oshift(u,v,w,x),v),w),
file('LCL796-1.p',unknown),
[] ).
cnf(974,axiom,
c_Type_Otyping(u,c_Lambda_OdB_OVar(v),hAPP(u,v)),
file('LCL796-1.p',unknown),
[] ).
cnf(1016,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_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____),
file('LCL796-1.p',unknown),
[] ).
cnf(1059,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_OdB_OVar(c_Orderings_Obot__class_Obot(tc_nat)),v_T_H_H____),
inference(rew,[status(thm),theory(equality)],[928,1016]),
[iquote('0:Rew:928.0,1016.0')] ).
cnf(1351,plain,
c_Type_Otyping(c_Type_Oshift(u,v,w,x),c_Lambda_OdB_OVar(v),w),
inference(spr,[status(thm),theory(equality)],[972,974]),
[iquote('0:SpR:972.0,974.0')] ).
cnf(1353,plain,
$false,
inference(unc,[status(thm)],[1351,1059]),
[iquote('0:UnC:1351.0,1059.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL796-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n031.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 08:27:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.77/1.11
% 0.77/1.11 SPASS V 3.9
% 0.77/1.11 SPASS beiseite: Proof found.
% 0.77/1.11 % SZS status Theorem
% 0.77/1.11 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/1.11 SPASS derived 94 clauses, backtracked 0 clauses, performed 0 splits and kept 831 clauses.
% 0.77/1.11 SPASS allocated 77690 KBytes.
% 0.77/1.11 SPASS spent 0:00:00.70 on the problem.
% 0.77/1.11 0:00:00.11 for the input.
% 0.77/1.11 0:00:00.00 for the FLOTTER CNF translation.
% 0.77/1.11 0:00:00.00 for inferences.
% 0.77/1.11 0:00:00.00 for the backtracking.
% 0.77/1.11 0:00:00.42 for the reduction.
% 0.77/1.11
% 0.77/1.11
% 0.77/1.11 Here is a proof with depth 1, length 7 :
% 0.77/1.11 % SZS output start Refutation
% See solution above
% 0.77/1.11 Formulae used in the proof : cls_bot__nat__def_0 cls_shift__eq_0 cls_typing_OVar_0 cls_conjecture_0
% 0.77/1.11
%------------------------------------------------------------------------------