TSTP Solution File: LCL239-10 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL239-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:35:47 EDT 2022
% Result : Unsatisfiable 1.92s 2.09s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 54 RR)
% Number of literals : 54 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq(u,u,v,w),v),
file('LCL239-10.p',unknown),
[] ).
cnf(2,axiom,
equal(axiom(implies__dfg(or__dfg(u,u),u)),true__dfg),
file('LCL239-10.p',unknown),
[] ).
cnf(3,axiom,
equal(axiom(implies__dfg(u,or__dfg(v,u))),true__dfg),
file('LCL239-10.p',unknown),
[] ).
cnf(4,axiom,
equal(axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),true__dfg),
file('LCL239-10.p',unknown),
[] ).
cnf(5,axiom,
equal(axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),true__dfg),
file('LCL239-10.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL239-10.p',unknown),
[] ).
cnf(8,axiom,
equal(ifeq(axiom(u),true__dfg,theorem(u),true__dfg),true__dfg),
file('LCL239-10.p',unknown),
[] ).
cnf(9,axiom,
equal(ifeq(theorem(implies__dfg(u,v)),true__dfg,ifeq(theorem(u),true__dfg,theorem(v),true__dfg),true__dfg),true__dfg),
file('LCL239-10.p',unknown),
[] ).
cnf(10,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL239-10.p',unknown),
[] ).
cnf(11,axiom,
~ equal(theorem(not__dfg(and__dfg(p,not__dfg(p)))),true__dfg),
file('LCL239-10.p',unknown),
[] ).
cnf(12,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
cnf(21,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(or__dfg(u,u),u)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(22,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(u,or__dfg(v,u))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(24,plain,
equal(theorem(implies__dfg(or__dfg(u,u),u)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,21]),
[iquote('0:Rew:1.0,21.0')] ).
cnf(25,plain,
equal(theorem(implies__dfg(u,or__dfg(v,u))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,22]),
[iquote('0:Rew:1.0,22.0')] ).
cnf(56,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4,8]),
[iquote('0:SpR:4.0,8.0')] ).
cnf(59,plain,
equal(theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,56]),
[iquote('0:Rew:1.0,56.0')] ).
cnf(61,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpR:5.0,8.0')] ).
cnf(70,plain,
equal(theorem(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,61]),
[iquote('0:Rew:1.0,61.0')] ).
cnf(74,plain,
equal(theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,59]),
[iquote('0:SpR:7.0,59.0')] ).
cnf(162,plain,
equal(ifeq(theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w)),true__dfg,ifeq(true__dfg,true__dfg,theorem(w),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[25,9]),
[iquote('0:SpR:25.0,9.0')] ).
cnf(168,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(or__dfg(u,u)),true__dfg,theorem(u),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[24,9]),
[iquote('0:SpR:24.0,9.0')] ).
cnf(169,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(or__dfg(u,v)),true__dfg,theorem(or__dfg(v,u)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[59,9]),
[iquote('0:SpR:59.0,9.0')] ).
cnf(171,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(u),true__dfg,theorem(or__dfg(v,u)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[25,9]),
[iquote('0:SpR:25.0,9.0')] ).
cnf(174,plain,
equal(ifeq(theorem(or__dfg(u,u)),true__dfg,theorem(u),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,168]),
[iquote('0:Rew:1.0,168.0')] ).
cnf(175,plain,
equal(ifeq(theorem(u),true__dfg,theorem(or__dfg(v,u)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,171]),
[iquote('0:Rew:1.0,171.0')] ).
cnf(177,plain,
equal(ifeq(theorem(or__dfg(u,v)),true__dfg,theorem(or__dfg(v,u)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,169]),
[iquote('0:Rew:1.0,169.0')] ).
cnf(181,plain,
equal(ifeq(theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w)),true__dfg,theorem(w),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,162]),
[iquote('0:Rew:1.0,162.0')] ).
cnf(519,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(or__dfg(u,or__dfg(v,w))),true__dfg,theorem(or__dfg(v,or__dfg(u,w))),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[70,9]),
[iquote('0:SpR:70.0,9.0')] ).
cnf(533,plain,
equal(ifeq(theorem(or__dfg(u,or__dfg(v,w))),true__dfg,theorem(or__dfg(v,or__dfg(u,w))),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,519]),
[iquote('0:Rew:1.0,519.0')] ).
cnf(2720,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(or__dfg(u,v),not__dfg(v))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[74,181]),
[iquote('0:SpR:74.0,181.0')] ).
cnf(2731,plain,
equal(theorem(or__dfg(or__dfg(u,v),not__dfg(v))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,2720]),
[iquote('0:Rew:1.0,2720.0')] ).
cnf(3105,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(u,or__dfg(or__dfg(v,w),not__dfg(w)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[2731,175]),
[iquote('0:SpR:2731.0,175.0')] ).
cnf(3131,plain,
equal(theorem(or__dfg(u,or__dfg(or__dfg(v,w),not__dfg(w)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,3105]),
[iquote('0:Rew:1.0,3105.0')] ).
cnf(4166,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(or__dfg(u,v),or__dfg(w,not__dfg(v)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[3131,533]),
[iquote('0:SpR:3131.0,533.0')] ).
cnf(4207,plain,
equal(theorem(or__dfg(or__dfg(u,v),or__dfg(w,not__dfg(v)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,4166]),
[iquote('0:Rew:1.0,4166.0')] ).
cnf(5017,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(or__dfg(u,not__dfg(v)),or__dfg(w,v))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4207,177]),
[iquote('0:SpR:4207.0,177.0')] ).
cnf(5043,plain,
equal(theorem(or__dfg(or__dfg(u,not__dfg(v)),or__dfg(w,v))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,5017]),
[iquote('0:Rew:1.0,5017.0')] ).
cnf(5500,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(u,or__dfg(or__dfg(v,not__dfg(w)),w))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[5043,533]),
[iquote('0:SpR:5043.0,533.0')] ).
cnf(5528,plain,
equal(theorem(or__dfg(u,or__dfg(or__dfg(v,not__dfg(w)),w))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,5500]),
[iquote('0:Rew:1.0,5500.0')] ).
cnf(5906,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[5528,174]),
[iquote('0:SpR:5528.0,174.0')] ).
cnf(5960,plain,
equal(theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,5906]),
[iquote('0:Rew:1.0,5906.0')] ).
cnf(6005,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[5960,177]),
[iquote('0:SpR:5960.0,177.0')] ).
cnf(6025,plain,
equal(theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,6005]),
[iquote('0:Rew:1.0,6005.0')] ).
cnf(6456,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6025,533]),
[iquote('0:SpR:6025.0,533.0')] ).
cnf(6501,plain,
equal(theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,6456]),
[iquote('0:Rew:1.0,6456.0')] ).
cnf(6581,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(u,not__dfg(u))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6501,174]),
[iquote('0:SpR:6501.0,174.0')] ).
cnf(6639,plain,
equal(theorem(or__dfg(u,not__dfg(u))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,6581]),
[iquote('0:Rew:1.0,6581.0')] ).
cnf(6697,plain,
equal(theorem(implies__dfg(u,not__dfg(not__dfg(u)))),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,6639]),
[iquote('0:SpR:7.0,6639.0')] ).
cnf(6929,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(u),true__dfg,theorem(not__dfg(not__dfg(u))),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6697,9]),
[iquote('0:SpR:6697.0,9.0')] ).
cnf(6955,plain,
equal(ifeq(theorem(u),true__dfg,theorem(not__dfg(not__dfg(u))),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,6929]),
[iquote('0:Rew:1.0,6929.0')] ).
cnf(7928,plain,
equal(ifeq(true__dfg,true__dfg,theorem(not__dfg(not__dfg(implies__dfg(u,not__dfg(not__dfg(u)))))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[6697,6955]),
[iquote('0:SpR:6697.0,6955.0')] ).
cnf(8031,plain,
equal(theorem(not__dfg(and__dfg(u,not__dfg(u)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,7928,12]),
[iquote('0:Rew:1.0,7928.0,12.0,7928.0')] ).
cnf(8032,plain,
$false,
inference(unc,[status(thm)],[8031,11]),
[iquote('0:UnC:8031.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL239-10 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n024.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jul 4 15:21:14 EDT 2022
% 0.13/0.32 % CPUTime :
% 1.92/2.09
% 1.92/2.09 SPASS V 3.9
% 1.92/2.09 SPASS beiseite: Proof found.
% 1.92/2.09 % SZS status Theorem
% 1.92/2.09 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.92/2.09 SPASS derived 6247 clauses, backtracked 0 clauses, performed 0 splits and kept 1395 clauses.
% 1.92/2.09 SPASS allocated 74135 KBytes.
% 1.92/2.09 SPASS spent 0:00:01.67 on the problem.
% 1.92/2.09 0:00:00.04 for the input.
% 1.92/2.09 0:00:00.00 for the FLOTTER CNF translation.
% 1.92/2.09 0:00:00.06 for inferences.
% 1.92/2.09 0:00:00.00 for the backtracking.
% 1.92/2.09 0:00:01.54 for the reduction.
% 1.92/2.09
% 1.92/2.09
% 1.92/2.09 Here is a proof with depth 14, length 54 :
% 1.92/2.09 % SZS output start Refutation
% See solution above
% 1.92/2.09 Formulae used in the proof : ifeq_axiom axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 implies_definition rule_1 rule_2 and_defn prove_this
% 1.92/2.09
%------------------------------------------------------------------------------