TSTP Solution File: LCL156-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 14:34:58 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 50 RR)
% Number of literals : 50 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(and_star(x__dfg,truth),x__dfg),
file('LCL156-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL156-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL156-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL156-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL156-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
file('LCL156-1.p',unknown),
[] ).
cnf(8,axiom,
equal(or__dfg(u,v),or__dfg(v,u)),
file('LCL156-1.p',unknown),
[] ).
cnf(14,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and_star(u,v)),
file('LCL156-1.p',unknown),
[] ).
cnf(17,axiom,
equal(not__dfg(truth),falsehood),
file('LCL156-1.p',unknown),
[] ).
cnf(22,plain,
equal(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),truth),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(40,plain,
equal(implies__dfg(falsehood,u),or__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[17,6]),
[iquote('0:SpR:17.0,6.0')] ).
cnf(44,plain,
equal(implies__dfg(or__dfg(u,not__dfg(truth)),u),truth),
inference(spr,[status(thm),theory(equality)],[2,22]),
[iquote('0:SpR:2.0,22.0')] ).
cnf(45,plain,
equal(implies__dfg(or__dfg(u,not__dfg(falsehood)),or__dfg(truth,u)),truth),
inference(spr,[status(thm),theory(equality)],[40,22]),
[iquote('0:SpR:40.0,22.0')] ).
cnf(50,plain,
equal(implies__dfg(or__dfg(u,falsehood),u),truth),
inference(rew,[status(thm),theory(equality)],[17,44]),
[iquote('0:Rew:17.0,44.0')] ).
cnf(54,plain,
equal(implies__dfg(or__dfg(falsehood,u),u),truth),
inference(spr,[status(thm),theory(equality)],[8,50]),
[iquote('0:SpR:8.0,50.0')] ).
cnf(56,plain,
equal(implies__dfg(or__dfg(u,not__dfg(or__dfg(falsehood,u))),truth),truth),
inference(spr,[status(thm),theory(equality)],[54,22]),
[iquote('0:SpR:54.0,22.0')] ).
cnf(77,plain,
equal(not__dfg(or__dfg(not__dfg(u),falsehood)),and_star(u,truth)),
inference(spr,[status(thm),theory(equality)],[17,14]),
[iquote('0:SpR:17.0,14.0')] ).
cnf(81,plain,
equal(not__dfg(or__dfg(falsehood,not__dfg(u))),and_star(u,truth)),
inference(rew,[status(thm),theory(equality)],[8,77]),
[iquote('0:Rew:8.0,77.0')] ).
cnf(130,plain,
equal(implies__dfg(or__dfg(not__dfg(u),and_star(u,truth)),truth),truth),
inference(spr,[status(thm),theory(equality)],[81,56]),
[iquote('0:SpR:81.0,56.0')] ).
cnf(137,plain,
equal(implies__dfg(u,u),implies__dfg(implies__dfg(u,truth),truth)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(138,plain,
equal(implies__dfg(or__dfg(truth,u),u),implies__dfg(implies__dfg(u,falsehood),falsehood)),
inference(spr,[status(thm),theory(equality)],[40,4]),
[iquote('0:SpR:40.0,4.0')] ).
cnf(146,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),truth),truth),or__dfg(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[137,6]),
[iquote('0:SpR:137.0,6.0')] ).
cnf(163,plain,
equal(implies__dfg(or__dfg(u,truth),truth),or__dfg(u,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[6,146]),
[iquote('0:Rew:6.0,146.0')] ).
cnf(241,plain,
equal(or__dfg(falsehood,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[163,54]),
[iquote('0:SpR:163.0,54.0')] ).
cnf(286,plain,
equal(implies__dfg(truth,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[241,54]),
[iquote('0:SpR:241.0,54.0')] ).
cnf(294,plain,
equal(not__dfg(falsehood),truth),
inference(rew,[status(thm),theory(equality)],[2,286]),
[iquote('0:Rew:2.0,286.0')] ).
cnf(295,plain,
equal(implies__dfg(or__dfg(u,truth),or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[294,45]),
[iquote('0:Rew:294.0,45.0')] ).
cnf(326,plain,
equal(implies__dfg(truth,u),or__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[294,6]),
[iquote('0:SpR:294.0,6.0')] ).
cnf(334,plain,
equal(or__dfg(falsehood,u),u),
inference(rew,[status(thm),theory(equality)],[2,326]),
[iquote('0:Rew:2.0,326.0')] ).
cnf(337,plain,
equal(not__dfg(not__dfg(u)),and_star(u,truth)),
inference(rew,[status(thm),theory(equality)],[334,81]),
[iquote('0:Rew:334.0,81.0')] ).
cnf(338,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[334,54]),
[iquote('0:Rew:334.0,54.0')] ).
cnf(354,plain,
equal(implies__dfg(implies__dfg(u,truth),truth),truth),
inference(rew,[status(thm),theory(equality)],[338,137]),
[iquote('0:Rew:338.0,137.0')] ).
cnf(423,plain,
equal(or__dfg(u,falsehood),u),
inference(spr,[status(thm),theory(equality)],[334,8]),
[iquote('0:SpR:334.0,8.0')] ).
cnf(445,plain,
equal(or__dfg(u,not__dfg(u)),truth),
inference(spr,[status(thm),theory(equality)],[338,6]),
[iquote('0:SpR:338.0,6.0')] ).
cnf(478,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and_star(u,truth)),v),implies__dfg(implies__dfg(v,truth),truth)),truth),
inference(spr,[status(thm),theory(equality)],[130,3]),
[iquote('0:SpR:130.0,3.0')] ).
cnf(509,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and_star(u,truth)),v),truth),truth),
inference(rew,[status(thm),theory(equality)],[354,478]),
[iquote('0:Rew:354.0,478.0')] ).
cnf(583,plain,
equal(or__dfg(not__dfg(u),and_star(u,truth)),truth),
inference(spr,[status(thm),theory(equality)],[337,445]),
[iquote('0:SpR:337.0,445.0')] ).
cnf(599,plain,
equal(implies__dfg(implies__dfg(truth,u),truth),truth),
inference(rew,[status(thm),theory(equality)],[583,509]),
[iquote('0:Rew:583.0,509.0')] ).
cnf(601,plain,
equal(implies__dfg(u,truth),truth),
inference(rew,[status(thm),theory(equality)],[2,599]),
[iquote('0:Rew:2.0,599.0')] ).
cnf(625,plain,
equal(or__dfg(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[601,6]),
[iquote('0:SpR:601.0,6.0')] ).
cnf(632,plain,
equal(implies__dfg(truth,or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[625,295]),
[iquote('0:Rew:625.0,295.0')] ).
cnf(638,plain,
equal(or__dfg(truth,u),truth),
inference(rew,[status(thm),theory(equality)],[2,632]),
[iquote('0:Rew:2.0,632.0')] ).
cnf(643,plain,
equal(implies__dfg(implies__dfg(u,falsehood),falsehood),implies__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[638,138]),
[iquote('0:Rew:638.0,138.0')] ).
cnf(652,plain,
equal(implies__dfg(implies__dfg(u,falsehood),falsehood),u),
inference(rew,[status(thm),theory(equality)],[2,643]),
[iquote('0:Rew:2.0,643.0')] ).
cnf(787,plain,
equal(implies__dfg(or__dfg(u,falsehood),falsehood),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6,652]),
[iquote('0:SpR:6.0,652.0')] ).
cnf(792,plain,
equal(implies__dfg(u,falsehood),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[423,787]),
[iquote('0:Rew:423.0,787.0')] ).
cnf(793,plain,
equal(not__dfg(implies__dfg(u,falsehood)),u),
inference(rew,[status(thm),theory(equality)],[792,652]),
[iquote('0:Rew:792.0,652.0')] ).
cnf(798,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[792,793]),
[iquote('0:Rew:792.0,793.0')] ).
cnf(799,plain,
equal(and_star(u,truth),u),
inference(rew,[status(thm),theory(equality)],[337,798]),
[iquote('0:Rew:337.0,798.0')] ).
cnf(800,plain,
$false,
inference(unc,[status(thm)],[799,1]),
[iquote('0:UnC:799.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 11:33:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 549 clauses, backtracked 0 clauses, performed 0 splits and kept 217 clauses.
% 0.20/0.49 SPASS allocated 63920 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.06 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 6, length 50 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : prove_alternative_wajsberg_axiom wajsberg_1 wajsberg_2 wajsberg_3 wajsberg_4 or_definition or_commutativity and_star_definition false_definition
% 0.20/0.49
%------------------------------------------------------------------------------