%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL799-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 0.30s 0.57s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 10 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(269,axiom,
( ~ c_Type_Otyping(u,v,w)
| ~ c_Type_Otyping(c_Type_Oshift(u,x,w,tc_Type_Otype),y,z)
| c_Type_Otyping(u,c_Lambda_Osubst(y,v,x),z) ),
file('LCL799-1.p',unknown),
[] ).
cnf(270,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('LCL799-1.p',unknown),
[] ).
cnf(271,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('LCL799-1.p',unknown),
[] ).
cnf(294,axiom,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('LCL799-1.p',unknown),
[] ).
cnf(313,plain,
( ~ c_Type_Otyping(v_e____,v_u____,u)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,u,tc_Type_Otype),v_a____,v_T_H_H____) ),
inference(res,[status(thm),theory(equality)],[269,294]),
[iquote('0:Res:269.2,294.0')] ).
cnf(442,plain,
~ c_Type_Otyping(v_e____,v_u____,v_T____),
inference(res,[status(thm),theory(equality)],[271,313]),
[iquote('0:Res:271.0,313.1')] ).
cnf(443,plain,
$false,
inference(mrr,[status(thm)],[442,270]),
[iquote('0:MRR:442.0,270.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL799-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.37 % Computer : n015.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 5 05:35:12 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.30/0.57
% 0.30/0.57 SPASS V 3.9
% 0.30/0.57 SPASS beiseite: Proof found.
% 0.30/0.57 % SZS status Theorem
% 0.30/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.57 SPASS derived 127 clauses, backtracked 0 clauses, performed 0 splits and kept 258 clauses.
% 0.30/0.57 SPASS allocated 76224 KBytes.
% 0.30/0.57 SPASS spent 0:00:00.18 on the problem.
% 0.30/0.57 0:00:00.07 for the input.
% 0.30/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.30/0.57 0:00:00.01 for inferences.
% 0.30/0.57 0:00:00.00 for the backtracking.
% 0.30/0.57 0:00:00.05 for the reduction.
% 0.30/0.57
% 0.30/0.57
% 0.30/0.57 Here is a proof with depth 2, length 7 :
% 0.30/0.57 % SZS output start Refutation
% See solution above
% 0.30/0.57 Formulae used in the proof : cls_subst__lemma_0 cls_CHAINED_0 cls_CHAINED_0_01 cls_conjecture_0
% 0.30/0.57
%------------------------------------------------------------------------------