%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 01:08:18 PM UTC 2026
% Result : Unsatisfiable 0.46s 0.72s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 11 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(307,axiom,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Suc(u)),
file('LCL748-1.p',unknown),
[] ).
cnf(332,axiom,
equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(u,c_HOL_Oplus__class_Oplus(v,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),c_Lambda_Olift(c_Lambda_OdB_OAbs(u),v)),
file('LCL748-1.p',unknown),
[] ).
cnf(339,axiom,
( ~ c_InductTermi_OIT(u)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(u)) ),
file('LCL748-1.p',unknown),
[] ).
cnf(369,axiom,
c_InductTermi_OIT(c_Lambda_Olift(v_r,u)),
file('LCL748-1.p',unknown),
[] ).
cnf(370,axiom,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
file('LCL748-1.p',unknown),
[] ).
cnf(374,plain,
equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(u,c_Suc(v))),c_Lambda_Olift(c_Lambda_OdB_OAbs(u),v)),
inference(rew,[status(thm),theory(equality)],[307,332]),
[iquote('0:Rew:307.0,332.0')] ).
cnf(571,plain,
( ~ c_InductTermi_OIT(c_Lambda_Olift(u,c_Suc(v)))
| c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(u),v)) ),
inference(spr,[status(thm),theory(equality)],[374,339]),
[iquote('0:SpR:374.0,339.1')] ).
cnf(1969,plain,
c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),u)),
inference(sor,[status(thm)],[571,369]),
[iquote('0:SoR:571.0,369.0')] ).
cnf(1970,plain,
$false,
inference(unc,[status(thm)],[1969,370]),
[iquote('0:UnC:1969.0,370.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 09:08:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.46/0.72
% 0.46/0.72 SPASS V 3.9
% 0.46/0.72 SPASS beiseite: Proof found.
% 0.46/0.72 % SZS status Theorem
% 0.46/0.72 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.72 SPASS derived 1409 clauses, backtracked 0 clauses, performed 0 splits and kept 452 clauses.
% 0.46/0.72 SPASS allocated 76957 KBytes.
% 0.46/0.72 SPASS spent 0:00:00.33 on the problem.
% 0.46/0.72 0:00:00.07 for the input.
% 0.46/0.72 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.72 0:00:00.03 for inferences.
% 0.46/0.72 0:00:00.00 for the backtracking.
% 0.46/0.72 0:00:00.17 for the reduction.
% 0.46/0.72
% 0.46/0.72
% 0.46/0.72 Here is a proof with depth 2, length 9 :
% 0.46/0.72 % SZS output start Refutation
% See solution above
% 0.46/0.72 Formulae used in the proof : cls_Suc__eq__plus1_0 cls_lift_Osimps_I3_J_0 cls_Lambda_0 cls_conjecture_1 cls_conjecture_2
% 0.46/0.72
%------------------------------------------------------------------------------