%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL808-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 01:08:29 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.55s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 9 unt; 0 nHn; 12 RR)
% Number of literals : 18 ( 0 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(58,axiom,
equal(v_i____,v_n____),
file('LCL808-1.p',unknown),
[] ).
cnf(65,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
file('LCL808-1.p',unknown),
[] ).
cnf(66,axiom,
( ~ c_InductTermi_OIT(u)
| ~ c_Type_Otyping(v,u,v_T____)
| ~ c_Type_Otyping(c_Type_Oshift(v,w,v_T____,tc_Type_Otype),v_b____,x)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,u,w)) ),
file('LCL808-1.p',unknown),
[] ).
cnf(67,axiom,
c_InductTermi_OIT(v_u____),
file('LCL808-1.p',unknown),
[] ).
cnf(68,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('LCL808-1.p',unknown),
[] ).
cnf(75,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
file('LCL808-1.p',unknown),
[] ).
cnf(76,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____)),
inference(rew,[status(thm),theory(equality)],[58,75]),
[iquote('0:Rew:58.0,75.0')] ).
cnf(77,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
inference(rew,[status(thm),theory(equality)],[58,65]),
[iquote('0:Rew:58.0,65.0')] ).
cnf(497,plain,
( ~ c_InductTermi_OIT(u)
| ~ c_Type_Otyping(v_e____,u,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,u,v_n____)) ),
inference(res,[status(thm),theory(equality)],[77,66]),
[iquote('0:Res:77.0,66.2')] ).
cnf(511,plain,
( ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(res,[status(thm),theory(equality)],[497,76]),
[iquote('0:Res:497.2,76.0')] ).
cnf(512,plain,
~ c_Type_Otyping(v_e____,v_u____,v_T____),
inference(ssi,[status(thm)],[511,67]),
[iquote('0:SSi:511.0,67.0')] ).
cnf(513,plain,
$false,
inference(mrr,[status(thm)],[512,68]),
[iquote('0:MRR:512.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL808-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n013.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
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 05:25:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.23/0.55
% 0.23/0.55 SPASS V 3.9
% 0.23/0.55 SPASS beiseite: Proof found.
% 0.23/0.55 % SZS status Theorem
% 0.23/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.55 SPASS derived 424 clauses, backtracked 0 clauses, performed 0 splits and kept 278 clauses.
% 0.23/0.55 SPASS allocated 76192 KBytes.
% 0.23/0.55 SPASS spent 0:00:00.18 on the problem.
% 0.23/0.55 0:00:00.06 for the input.
% 0.23/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.55 0:00:00.01 for inferences.
% 0.23/0.55 0:00:00.00 for the backtracking.
% 0.23/0.55 0:00:00.06 for the reduction.
% 0.23/0.55
% 0.23/0.55
% 0.23/0.55 Here is a proof with depth 2, length 12 :
% 0.23/0.55 % SZS output start Refutation
% See solution above
% 0.23/0.55 Formulae used in the proof : cls_True_0 cls_CHAINED_0 cls_CHAINED_0_01 cls_CHAINED_0_02 cls_CHAINED_0_03 cls_conjecture_0
% 0.23/0.55
%------------------------------------------------------------------------------