%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL802-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 01:08:27 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.57s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 9 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(274,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('LCL802-1.p',unknown),
[] ).
cnf(285,axiom,
equal(v_i____,v_n____),
file('LCL802-1.p',unknown),
[] ).
cnf(298,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
file('LCL802-1.p',unknown),
[] ).
cnf(329,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_as____,tc_Lambda_OdB),
file('LCL802-1.p',unknown),
[] ).
cnf(330,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
inference(rew,[status(thm),theory(equality)],[285,298]),
[iquote('0:Rew:285.0,298.0')] ).
cnf(336,plain,
~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB),
inference(rew,[status(thm),theory(equality)],[285,329]),
[iquote('0:Rew:285.0,329.0')] ).
cnf(353,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,u),
inference(res,[status(thm),theory(equality)],[274,336]),
[iquote('0:Res:274.1,336.0')] ).
cnf(354,plain,
$false,
inference(unc,[status(thm)],[353,330]),
[iquote('0:UnC:353.0,330.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL802-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n003.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 : Sat Sep 5 19:22:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.31/0.57
% 0.31/0.57 SPASS V 3.9
% 0.31/0.57 SPASS beiseite: Proof found.
% 0.31/0.57 % SZS status Theorem
% 0.31/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.57 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 277 clauses.
% 0.31/0.57 SPASS allocated 76223 KBytes.
% 0.31/0.57 SPASS spent 0:00:00.19 on the problem.
% 0.31/0.57 0:00:00.07 for the input.
% 0.31/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.31/0.57 0:00:00.00 for inferences.
% 0.31/0.57 0:00:00.00 for the backtracking.
% 0.31/0.57 0:00:00.06 for the reduction.
% 0.31/0.57
% 0.31/0.57
% 0.31/0.57 Here is a proof with depth 1, length 8 :
% 0.31/0.57 % SZS output start Refutation
% See solution above
% 0.31/0.57 Formulae used in the proof : cls_lists__typings_0 cls_True_0 cls_CHAINED_0 cls_conjecture_0
% 0.31/0.57
%------------------------------------------------------------------------------