%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL789-1 : 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 01:08:25 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 5 RR)
% Number of literals : 5 ( 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 : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(298,axiom,
equal(hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),v_T____),
file('LCL789-1.p',unknown),
[] ).
cnf(299,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('LCL789-1.p',unknown),
[] ).
cnf(321,axiom,
~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('LCL789-1.p',unknown),
[] ).
cnf(327,plain,
~ c_Type_Otyping(v_e____,v_u____,v_T____),
inference(rew,[status(thm),theory(equality)],[298,321]),
[iquote('0:Rew:298.0,321.0')] ).
cnf(328,plain,
$false,
inference(mrr,[status(thm)],[327,299]),
[iquote('0:MRR:327.0,299.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL789-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 23:14:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.44
% 0.13/0.44 SPASS V 3.9
% 0.13/0.44 SPASS beiseite: Proof found.
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 102 clauses.
% 0.13/0.44 SPASS allocated 76174 KBytes.
% 0.13/0.44 SPASS spent 0:00:00.07 on the problem.
% 0.13/0.44 0:00:00.03 for the input.
% 0.13/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.44 0:00:00.00 for inferences.
% 0.13/0.44 0:00:00.00 for the backtracking.
% 0.13/0.44 0:00:00.01 for the reduction.
% 0.13/0.44
% 0.13/0.44
% 0.13/0.44 Here is a proof with depth 0, length 5 :
% 0.13/0.44 % SZS output start Refutation
% See solution above
% 0.13/0.44 Formulae used in the proof : cls_CHAINED_0 cls_CHAINED_0_01 cls_conjecture_0
% 0.13/0.44
%------------------------------------------------------------------------------