TSTP Solution File: LCL203-10 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL203-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 14:35:24 EDT 2022
% Result : Unsatisfiable 26.56s 26.76s
% Output : Refutation 29.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 75 RR)
% Number of literals : 75 ( 0 equ; 2 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 : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq(u,u,v,w),v),
file('LCL203-10.p',unknown),
[] ).
cnf(2,axiom,
equal(axiom(implies__dfg(or__dfg(u,u),u)),true__dfg),
file('LCL203-10.p',unknown),
[] ).
cnf(3,axiom,
equal(axiom(implies__dfg(u,or__dfg(v,u))),true__dfg),
file('LCL203-10.p',unknown),
[] ).
cnf(4,axiom,
equal(axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),true__dfg),
file('LCL203-10.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('LCL203-10.p',unknown),
[] ).
cnf(6,axiom,
equal(axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),true__dfg),
file('LCL203-10.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL203-10.p',unknown),
[] ).
cnf(8,axiom,
equal(ifeq(axiom(u),true__dfg,theorem(u),true__dfg),true__dfg),
file('LCL203-10.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('LCL203-10.p',unknown),
[] ).
cnf(10,axiom,
~ equal(theorem(implies__dfg(not__dfg(or__dfg(p,q)),or__dfg(not__dfg(p),not__dfg(q)))),true__dfg),
file('LCL203-10.p',unknown),
[] ).
cnf(11,plain,
~ equal(theorem(implies__dfg(not__dfg(or__dfg(p,q)),implies__dfg(p,not__dfg(q)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
cnf(19,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(20,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(21,plain,
equal(theorem(implies__dfg(or__dfg(u,u),u)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,19]),
[iquote('0:Rew:1.0,19.0')] ).
cnf(22,plain,
equal(theorem(implies__dfg(u,or__dfg(v,u))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,20]),
[iquote('0:Rew:1.0,20.0')] ).
cnf(38,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(41,plain,
equal(theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,38]),
[iquote('0:Rew:1.0,38.0')] ).
cnf(51,plain,
equal(theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,41]),
[iquote('0:SpR:7.0,41.0')] ).
cnf(73,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(75,plain,
equal(axiom(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(79,plain,
equal(axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[7,75]),
[iquote('0:Rew:7.0,75.0')] ).
cnf(82,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)],[1,73]),
[iquote('0:Rew:1.0,73.0')] ).
cnf(88,plain,
equal(axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(not__dfg(w),u),implies__dfg(w,v)))),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(90,plain,
equal(axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[7,88]),
[iquote('0:Rew:7.0,88.0')] ).
cnf(101,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[79,8]),
[iquote('0:SpR:79.0,8.0')] ).
cnf(106,plain,
equal(theorem(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,101]),
[iquote('0:Rew:1.0,101.0')] ).
cnf(119,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)],[22,9]),
[iquote('0:SpR:22.0,9.0')] ).
cnf(124,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)],[21,9]),
[iquote('0:SpR:21.0,9.0')] ).
cnf(125,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)],[41,9]),
[iquote('0:SpR:41.0,9.0')] ).
cnf(127,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)],[22,9]),
[iquote('0:SpR:22.0,9.0')] ).
cnf(131,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(implies__dfg(u,v)),true__dfg,theorem(or__dfg(v,not__dfg(u))),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[51,9]),
[iquote('0:SpR:51.0,9.0')] ).
cnf(132,plain,
equal(ifeq(theorem(or__dfg(u,u)),true__dfg,theorem(u),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,124]),
[iquote('0:Rew:1.0,124.0')] ).
cnf(133,plain,
equal(ifeq(theorem(u),true__dfg,theorem(or__dfg(v,u)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,127]),
[iquote('0:Rew:1.0,127.0')] ).
cnf(135,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)],[1,125]),
[iquote('0:Rew:1.0,125.0')] ).
cnf(138,plain,
equal(ifeq(theorem(implies__dfg(u,v)),true__dfg,theorem(or__dfg(v,not__dfg(u))),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,131]),
[iquote('0:Rew:1.0,131.0')] ).
cnf(140,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)],[1,119]),
[iquote('0:Rew:1.0,119.0')] ).
cnf(228,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)],[82,9]),
[iquote('0:SpR:82.0,9.0')] ).
cnf(240,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)],[1,228]),
[iquote('0:Rew:1.0,228.0')] ).
cnf(307,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[90,8]),
[iquote('0:SpR:90.0,8.0')] ).
cnf(308,plain,
equal(theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,307]),
[iquote('0:Rew:1.0,307.0')] ).
cnf(843,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(or__dfg(u,implies__dfg(v,w))),true__dfg,theorem(implies__dfg(v,or__dfg(u,w))),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[106,9]),
[iquote('0:SpR:106.0,9.0')] ).
cnf(853,plain,
equal(ifeq(theorem(or__dfg(u,implies__dfg(v,w))),true__dfg,theorem(implies__dfg(v,or__dfg(u,w))),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,843]),
[iquote('0:Rew:1.0,843.0')] ).
cnf(970,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(theorem(implies__dfg(u,v)),true__dfg,theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[308,9]),
[iquote('0:SpR:308.0,9.0')] ).
cnf(977,plain,
equal(ifeq(theorem(implies__dfg(u,v)),true__dfg,theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,970]),
[iquote('0:Rew:1.0,970.0')] ).
cnf(1358,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)],[51,140]),
[iquote('0:SpR:51.0,140.0')] ).
cnf(1367,plain,
equal(theorem(or__dfg(or__dfg(u,v),not__dfg(v))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1358]),
[iquote('0:Rew:1.0,1358.0')] ).
cnf(1734,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)],[1367,133]),
[iquote('0:SpR:1367.0,133.0')] ).
cnf(1751,plain,
equal(theorem(or__dfg(u,or__dfg(or__dfg(v,w),not__dfg(w)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1734]),
[iquote('0:Rew:1.0,1734.0')] ).
cnf(2697,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)],[1751,240]),
[iquote('0:SpR:1751.0,240.0')] ).
cnf(2722,plain,
equal(theorem(or__dfg(or__dfg(u,v),or__dfg(w,not__dfg(v)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,2697]),
[iquote('0:Rew:1.0,2697.0')] ).
cnf(3121,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)],[2722,135]),
[iquote('0:SpR:2722.0,135.0')] ).
cnf(3137,plain,
equal(theorem(or__dfg(or__dfg(u,not__dfg(v)),or__dfg(w,v))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,3121]),
[iquote('0:Rew:1.0,3121.0')] ).
cnf(3774,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)],[3137,240]),
[iquote('0:SpR:3137.0,240.0')] ).
cnf(3792,plain,
equal(theorem(or__dfg(u,or__dfg(or__dfg(v,not__dfg(w)),w))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,3774]),
[iquote('0:Rew:1.0,3774.0')] ).
cnf(3979,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)],[3792,132]),
[iquote('0:SpR:3792.0,132.0')] ).
cnf(4020,plain,
equal(theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,3979]),
[iquote('0:Rew:1.0,3979.0')] ).
cnf(4110,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)],[4020,135]),
[iquote('0:SpR:4020.0,135.0')] ).
cnf(4122,plain,
equal(theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,4110]),
[iquote('0:Rew:1.0,4110.0')] ).
cnf(4192,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)],[4122,240]),
[iquote('0:SpR:4122.0,240.0')] ).
cnf(4221,plain,
equal(theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,4192]),
[iquote('0:Rew:1.0,4192.0')] ).
cnf(4327,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(u,not__dfg(u))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4221,132]),
[iquote('0:SpR:4221.0,132.0')] ).
cnf(4369,plain,
equal(theorem(or__dfg(u,not__dfg(u))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,4327]),
[iquote('0:Rew:1.0,4327.0')] ).
cnf(4409,plain,
equal(theorem(implies__dfg(u,not__dfg(not__dfg(u)))),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,4369]),
[iquote('0:SpR:7.0,4369.0')] ).
cnf(11024,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,not__dfg(not__dfg(v))))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4409,977]),
[iquote('0:SpR:4409.0,977.0')] ).
cnf(11049,plain,
equal(theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,not__dfg(not__dfg(v))))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,11024]),
[iquote('0:Rew:1.0,11024.0')] ).
cnf(33854,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(u,not__dfg(not__dfg(or__dfg(v,u))))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[11049,140]),
[iquote('0:SpR:11049.0,140.0')] ).
cnf(33883,plain,
equal(theorem(implies__dfg(u,not__dfg(not__dfg(or__dfg(v,u))))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,33854]),
[iquote('0:Rew:1.0,33854.0')] ).
cnf(33918,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(not__dfg(not__dfg(or__dfg(u,v))),not__dfg(v))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[33883,138]),
[iquote('0:SpR:33883.0,138.0')] ).
cnf(33984,plain,
equal(theorem(implies__dfg(not__dfg(or__dfg(u,v)),not__dfg(v))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,33918,7]),
[iquote('0:Rew:1.0,33918.0,7.0,33918.0')] ).
cnf(34286,plain,
equal(ifeq(true__dfg,true__dfg,theorem(or__dfg(u,implies__dfg(not__dfg(or__dfg(v,w)),not__dfg(w)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[33984,133]),
[iquote('0:SpR:33984.0,133.0')] ).
cnf(34346,plain,
equal(theorem(or__dfg(u,implies__dfg(not__dfg(or__dfg(v,w)),not__dfg(w)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,34286]),
[iquote('0:Rew:1.0,34286.0')] ).
cnf(39913,plain,
equal(ifeq(true__dfg,true__dfg,theorem(implies__dfg(not__dfg(or__dfg(u,v)),or__dfg(w,not__dfg(v)))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[34346,853]),
[iquote('0:SpR:34346.0,853.0')] ).
cnf(40005,plain,
equal(theorem(implies__dfg(not__dfg(or__dfg(u,v)),or__dfg(w,not__dfg(v)))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,39913]),
[iquote('0:Rew:1.0,39913.0')] ).
cnf(42226,plain,
equal(theorem(implies__dfg(not__dfg(or__dfg(u,v)),implies__dfg(w,not__dfg(v)))),true__dfg),
inference(spr,[status(thm),theory(equality)],[7,40005]),
[iquote('0:SpR:7.0,40005.0')] ).
cnf(42228,plain,
$false,
inference(unc,[status(thm)],[42226,11]),
[iquote('0:UnC:42226.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL203-10 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 23:45:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 26.56/26.76
% 26.56/26.76 SPASS V 3.9
% 26.56/26.76 SPASS beiseite: Proof found.
% 26.56/26.76 % SZS status Theorem
% 26.56/26.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.56/26.76 SPASS derived 35114 clauses, backtracked 0 clauses, performed 0 splits and kept 4539 clauses.
% 26.56/26.76 SPASS allocated 106708 KBytes.
% 26.56/26.76 SPASS spent 0:0:26.40 on the problem.
% 26.56/26.76 0:00:00.04 for the input.
% 26.56/26.76 0:00:00.00 for the FLOTTER CNF translation.
% 26.56/26.76 0:00:00.29 for inferences.
% 26.56/26.76 0:00:00.00 for the backtracking.
% 26.56/26.76 0:0:25.96 for the reduction.
% 26.56/26.76
% 26.56/26.76
% 26.56/26.76 Here is a proof with depth 18, length 75 :
% 26.56/26.76 % SZS output start Refutation
% See solution above
% 29.33/29.57 Formulae used in the proof : ifeq_axiom axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2 prove_this
% 29.33/29.57
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