%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL851-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:08:35 PM UTC 2026
% Result : Unsatisfiable 0.66s 0.94s
% Output : Refutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 8 ( 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 : 16 ( 16 usr; 11 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(855,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL851-1.p',unknown),
[] ).
cnf(901,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('LCL851-1.p',unknown),
[] ).
cnf(905,axiom,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
file('LCL851-1.p',unknown),
[] ).
cnf(946,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
file('LCL851-1.p',unknown),
[] ).
cnf(1022,plain,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_Orderings_Obot__class_Obot(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_Orderings_Obot__class_Obot(tc_nat)),v_Ta____),
inference(rew,[status(thm),theory(equality)],[855,946]),
[iquote('0:Rew:855.0,946.0')] ).
cnf(1178,plain,
~ c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
inference(res,[status(thm),theory(equality)],[901,1022]),
[iquote('0:Res:901.1,1022.0')] ).
cnf(1179,plain,
$false,
inference(mrr,[status(thm)],[1178,905]),
[iquote('0:MRR:1178.0,905.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL851-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n027.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 17:08:13 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.66/0.94
% 0.66/0.94 SPASS V 3.9
% 0.66/0.94 SPASS beiseite: Proof found.
% 0.66/0.94 % SZS status Theorem
% 0.66/0.94 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.94 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 761 clauses.
% 0.66/0.94 SPASS allocated 77434 KBytes.
% 0.66/0.94 SPASS spent 0:00:00.52 on the problem.
% 0.66/0.94 0:00:00.10 for the input.
% 0.66/0.94 0:00:00.00 for the FLOTTER CNF translation.
% 0.66/0.94 0:00:00.00 for inferences.
% 0.66/0.94 0:00:00.00 for the backtracking.
% 0.66/0.94 0:00:00.30 for the reduction.
% 0.66/0.94
% 0.66/0.94
% 0.66/0.94 Here is a proof with depth 1, length 7 :
% 0.66/0.94 % SZS output start Refutation
% See solution above
% 0.66/0.94 Formulae used in the proof : cls_bot__nat__def_0 cls_lift__type_0 cls_App_I3_J_0 cls_conjecture_0
% 0.66/0.94
%------------------------------------------------------------------------------