%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 01:08:36 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.55s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(138,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),u,tc_Lambda_OdB) ),
file('LCL856-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ c_Type_Otyping(u,v,w)
| hBOOL(hAPP(c_InductTermi_OIT,v)) ),
file('LCL856-1.p',unknown),
[] ).
cnf(186,axiom,
c_Type_Otyping(v_e,v_t,v_T),
file('LCL856-1.p',unknown),
[] ).
cnf(187,axiom,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
file('LCL856-1.p',unknown),
[] ).
cnf(197,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(res,[status(thm),theory(equality)],[186,170]),
[iquote('0:Res:186.0,170.0')] ).
cnf(199,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(res,[status(thm),theory(equality)],[138,187]),
[iquote('0:Res:138.1,187.0')] ).
cnf(209,plain,
$false,
inference(mrr,[status(thm)],[199,197]),
[iquote('0:MRR:199.0,197.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 5 03:21:10 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.22/0.55
% 0.22/0.55 SPASS V 3.9
% 0.22/0.55 SPASS beiseite: Proof found.
% 0.22/0.55 % SZS status Theorem
% 0.22/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.55 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 171 clauses.
% 0.22/0.55 SPASS allocated 75951 KBytes.
% 0.22/0.55 SPASS spent 0:00:00.14 on the problem.
% 0.22/0.55 0:00:00.07 for the input.
% 0.22/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.55 0:00:00.00 for inferences.
% 0.22/0.55 0:00:00.00 for the backtracking.
% 0.22/0.55 0:00:00.02 for the reduction.
% 0.22/0.55
% 0.22/0.55
% 0.22/0.55 Here is a proof with depth 1, length 7 :
% 0.22/0.55 % SZS output start Refutation
% See solution above
% 0.22/0.55 Formulae used in the proof : cls_IT__implies__termi_0 cls_type__implies__IT_0 cls_conjecture_0 cls_conjecture_1
% 0.22/0.55
%------------------------------------------------------------------------------