%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 21.95s 22.30s
% Output : Refutation 21.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 9 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(324,axiom,
equal(c_Lambda_Osubst(c_Lambda_Olift(u,v),w,v),u),
file('LCL855-1.p',unknown),
[] ).
cnf(340,axiom,
equal(c_Lambda_Osubst(c_Lambda_OdB_OVar(u),v,u),v),
file('LCL855-1.p',unknown),
[] ).
cnf(343,axiom,
equal(c_Lambda_OdB_OApp(c_Lambda_Osubst(u,v,w),c_Lambda_Osubst(x,v,w)),c_Lambda_Osubst(c_Lambda_OdB_OApp(u,x),v,w)),
file('LCL855-1.p',unknown),
[] ).
cnf(361,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('LCL855-1.p',unknown),
[] ).
cnf(384,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
file('LCL855-1.p',unknown),
[] ).
cnf(31242,plain,
equal(c_Lambda_OdB_OApp(u,c_Lambda_Osubst(v,u,w)),c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(w),v),u,w)),
inference(spr,[status(thm),theory(equality)],[340,343]),
[iquote('0:SpR:340.0,343.0')] ).
cnf(31266,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(rew,[status(thm),theory(equality)],[31242,361]),
[iquote('0:Rew:31242.0,361.0')] ).
cnf(31268,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(rew,[status(thm),theory(equality)],[324,31266]),
[iquote('0:Rew:324.0,31266.0')] ).
cnf(31269,plain,
$false,
inference(mrr,[status(thm)],[31268,384]),
[iquote('0:MRR:31268.0,384.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n008.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 : Fri Sep 4 18:35:38 UTC 2026
% 0.14/0.36 % CPUTime :
% 21.95/22.30
% 21.95/22.30 SPASS V 3.9
% 21.95/22.30 SPASS beiseite: Proof found.
% 21.95/22.30 % SZS status Theorem
% 21.95/22.30 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.95/22.30 SPASS derived 24956 clauses, backtracked 0 clauses, performed 0 splits and kept 4142 clauses.
% 21.95/22.30 SPASS allocated 92715 KBytes.
% 21.95/22.30 SPASS spent 0:0:21.50 on the problem.
% 21.95/22.30 0:00:00.07 for the input.
% 21.95/22.30 0:00:00.00 for the FLOTTER CNF translation.
% 21.95/22.30 0:00:00.51 for inferences.
% 21.95/22.30 0:00:00.00 for the backtracking.
% 21.95/22.30 0:0:20.76 for the reduction.
% 21.95/22.30
% 21.95/22.30
% 21.95/22.30 Here is a proof with depth 1, length 9 :
% 21.95/22.30 % SZS output start Refutation
% See solution above
% 21.95/22.30 Formulae used in the proof : cls_subst__lift_0 cls_subst__eq_0 cls_subst__App_0 cls_CHAINED_0 cls_conjecture_0
% 21.95/22.30
%------------------------------------------------------------------------------