%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL822-1 : 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 01:08:31 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 6 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(189,axiom,
( ~ c_Type_Otypings(u,v,w)
| c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(u),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v,tc_Lambda_OdB) ),
file('LCL822-1.p',unknown),
[] ).
cnf(210,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,v_Ts____),
file('LCL822-1.p',unknown),
[] ).
cnf(231,axiom,
~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_rs____,tc_Lambda_OdB),
file('LCL822-1.p',unknown),
[] ).
cnf(239,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,u),
inference(res,[status(thm),theory(equality)],[189,231]),
[iquote('0:Res:189.1,231.0')] ).
cnf(240,plain,
$false,
inference(unc,[status(thm)],[239,210]),
[iquote('0:UnC:239.0,210.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL822-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.11/0.35 % Computer : n027.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 5 20:35:43 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.14/0.45
% 0.14/0.45 SPASS V 3.9
% 0.14/0.45 SPASS beiseite: Proof found.
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45 SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 193 clauses.
% 0.14/0.45 SPASS allocated 76020 KBytes.
% 0.14/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.14/0.45 0:00:00.03 for the input.
% 0.14/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.45 0:00:00.00 for inferences.
% 0.14/0.45 0:00:00.00 for the backtracking.
% 0.14/0.45 0:00:00.01 for the reduction.
% 0.14/0.45
% 0.14/0.45
% 0.14/0.45 Here is a proof with depth 1, length 5 :
% 0.14/0.45 % SZS output start Refutation
% See solution above
% 0.14/0.45 Formulae used in the proof : cls_lists__typings_0 cls_CHAINED_0 cls_conjecture_0
% 0.14/0.45
%------------------------------------------------------------------------------