%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL800-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n031.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 23.37s 23.68s
% Output : Refutation 23.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 0 equ; 2 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 : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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('LCL800-1.p',unknown),
[] ).
cnf(346,axiom,
equal(c_Lambda_Osubst(c_Lambda_OdB_OVar(u),v,u),v),
file('LCL800-1.p',unknown),
[] ).
cnf(352,axiom,
equal(v_i____,v_n____),
file('LCL800-1.p',unknown),
[] ).
cnf(362,axiom,
equal(c_Lambda_Osubst(c_Lambda_Olift(u,v),w,v),u),
file('LCL800-1.p',unknown),
[] ).
cnf(367,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('LCL800-1.p',unknown),
[] ).
cnf(390,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
file('LCL800-1.p',unknown),
[] ).
cnf(391,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_n____))),
inference(rew,[status(thm),theory(equality)],[352,390]),
[iquote('0:Rew:352.0,390.0')] ).
cnf(399,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_n____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(rew,[status(thm),theory(equality)],[352,367]),
[iquote('0:Rew:352.0,367.0')] ).
cnf(32196,plain,
equal(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(u,v),w),x,v),c_Lambda_OdB_OApp(u,c_Lambda_Osubst(w,x,v))),
inference(spr,[status(thm),theory(equality)],[362,343]),
[iquote('0:SpR:362.0,343.0')] ).
cnf(32219,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_n____),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(rew,[status(thm),theory(equality)],[32196,399]),
[iquote('0:Rew:32196.0,399.0')] ).
cnf(32221,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_n____))),
inference(rew,[status(thm),theory(equality)],[346,32219]),
[iquote('0:Rew:346.0,32219.0')] ).
cnf(32222,plain,
$false,
inference(mrr,[status(thm)],[32221,391]),
[iquote('0:MRR:32221.0,391.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL800-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_spass %d %s
% 0.13/0.41 % Computer : n031.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Fri Sep 4 18:28:54 UTC 2026
% 0.13/0.41 % CPUTime :
% 23.37/23.68
% 23.37/23.68 SPASS V 3.9
% 23.37/23.68 SPASS beiseite: Proof found.
% 23.37/23.68 % SZS status Theorem
% 23.37/23.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.37/23.68 SPASS derived 25564 clauses, backtracked 0 clauses, performed 0 splits and kept 4137 clauses.
% 23.37/23.68 SPASS allocated 93274 KBytes.
% 23.37/23.68 SPASS spent 0:0:22.84 on the problem.
% 23.37/23.68 0:00:00.10 for the input.
% 23.37/23.68 0:00:00.00 for the FLOTTER CNF translation.
% 23.37/23.68 0:00:00.67 for inferences.
% 23.37/23.68 0:00:00.00 for the backtracking.
% 23.37/23.68 0:0:21.89 for the reduction.
% 23.37/23.68
% 23.37/23.68
% 23.37/23.68 Here is a proof with depth 1, length 12 :
% 23.37/23.68 % SZS output start Refutation
% See solution above
% 23.37/23.68 Formulae used in the proof : cls_subst__App_0 cls_subst__eq_0 cls_True_0 cls_subst__lift_0 cls_CHAINED_0 cls_conjecture_0
% 23.37/23.68
%------------------------------------------------------------------------------