TSTP Solution File: LCL443-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL443-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:37:02 EDT 2022
% Result : Unsatisfiable 0.37s 0.60s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq(u,u,v,w),v),
file('LCL443-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(u,v,w),c_PropLog_Othms(x,w),tc_PropLog_Opl(w)),true__dfg,ifeq(c_in(u,c_PropLog_Othms(x,w),tc_PropLog_Opl(w)),true__dfg,c_in(v,c_PropLog_Othms(x,w),tc_PropLog_Opl(w)),true__dfg),true__dfg),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(3,axiom,
equal(ifeq(c_in(u,c_PropLog_Othms(c_insert(v,w,tc_PropLog_Opl(x)),x),tc_PropLog_Opl(x)),true__dfg,c_in(c_PropLog_Opl_Oop_A_N_62(v,u,x),c_PropLog_Othms(w,x),tc_PropLog_Opl(x)),true__dfg),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(4,axiom,
equal(ifeq(c_in(u,v,tc_PropLog_Opl(w)),true__dfg,c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)),true__dfg),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(5,axiom,
equal(ifeq(c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)),true__dfg,c_in(u,c_PropLog_Othms(c_insert(x,v,tc_PropLog_Opl(w)),w),tc_PropLog_Opl(w)),true__dfg),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(6,axiom,
equal(c_in(u,c_insert(u,v,w),w),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(7,axiom,
equal(c_in(v,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(8,axiom,
equal(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(9,axiom,
~ equal(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true__dfg),
file('LCL443-10.p',unknown),
[] ).
cnf(19,plain,
equal(ifeq(true__dfg,true__dfg,c_in(u,c_PropLog_Othms(c_insert(u,v,tc_PropLog_Opl(w)),w),tc_PropLog_Opl(w)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(21,plain,
equal(c_in(u,c_PropLog_Othms(c_insert(u,v,tc_PropLog_Opl(w)),w),tc_PropLog_Opl(w)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,19]),
[iquote('0:Rew:1.0,19.0')] ).
cnf(35,plain,
equal(ifeq(true__dfg,true__dfg,c_in(v,c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(36,plain,
equal(ifeq(true__dfg,true__dfg,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(39,plain,
equal(c_in(v,c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,35]),
[iquote('0:Rew:1.0,35.0')] ).
cnf(41,plain,
equal(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,36]),
[iquote('0:Rew:1.0,36.0')] ).
cnf(120,plain,
equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v,u,t_a),c_PropLog_Othms(c_insert(v,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg,ifeq(true__dfg,true__dfg,c_in(u,c_PropLog_Othms(c_insert(v,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[39,2]),
[iquote('0:SpR:39.0,2.0')] ).
cnf(146,plain,
equal(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v,u,t_a),c_PropLog_Othms(c_insert(v,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg,c_in(u,c_PropLog_Othms(c_insert(v,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,120]),
[iquote('0:Rew:1.0,120.0')] ).
cnf(204,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[41,2]),
[iquote('0:SpR:41.0,2.0')] ).
cnf(216,plain,
equal(ifeq(c_in(v_q,c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(u,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,204]),
[iquote('0:Rew:1.0,204.0')] ).
cnf(1091,plain,
equal(ifeq(true__dfg,true__dfg,c_in(u,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v,u,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[21,146]),
[iquote('0:SpR:21.0,146.0')] ).
cnf(1096,plain,
equal(c_in(u,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v,u,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1091]),
[iquote('0:Rew:1.0,1091.0')] ).
cnf(1110,plain,
equal(ifeq(true__dfg,true__dfg,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[1096,216]),
[iquote('0:SpR:1096.0,216.0')] ).
cnf(1128,plain,
equal(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1110]),
[iquote('0:Rew:1.0,1110.0')] ).
cnf(1167,plain,
equal(ifeq(true__dfg,true__dfg,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[1128,3]),
[iquote('0:SpR:1128.0,3.0')] ).
cnf(1169,plain,
equal(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1167]),
[iquote('0:Rew:1.0,1167.0')] ).
cnf(1170,plain,
$false,
inference(mrr,[status(thm)],[1169,9]),
[iquote('0:MRR:1169.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL443-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 2 21:55:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.37/0.60
% 0.37/0.60 SPASS V 3.9
% 0.37/0.60 SPASS beiseite: Proof found.
% 0.37/0.60 % SZS status Theorem
% 0.37/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.60 SPASS derived 834 clauses, backtracked 0 clauses, performed 0 splits and kept 233 clauses.
% 0.37/0.60 SPASS allocated 64855 KBytes.
% 0.37/0.60 SPASS spent 0:00:00.23 on the problem.
% 0.37/0.60 0:00:00.04 for the input.
% 0.37/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.60 0:00:00.02 for inferences.
% 0.37/0.60 0:00:00.00 for the backtracking.
% 0.37/0.60 0:00:00.15 for the reduction.
% 0.37/0.60
% 0.37/0.60
% 0.37/0.60 Here is a proof with depth 5, length 26 :
% 0.37/0.60 % SZS output start Refutation
% See solution above
% 0.37/0.60 Formulae used in the proof : ifeq_axiom cls_PropLog_Othms_OMP_0 cls_PropLog_Odeduction_0 cls_PropLog_Othms_OH_0 cls_PropLog_Oweaken__left__insert_0 cls_Set_OinsertCI_1 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.37/0.60
%------------------------------------------------------------------------------