TSTP Solution File: LCL154-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:34:57 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 62 RR)
% Number of literals : 62 ( 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(xor__dfg(x__dfg,falsehood),x__dfg),
file('LCL154-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL154-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL154-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL154-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL154-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
file('LCL154-1.p',unknown),
[] ).
cnf(8,axiom,
equal(or__dfg(u,v),or__dfg(v,u)),
file('LCL154-1.p',unknown),
[] ).
cnf(9,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL154-1.p',unknown),
[] ).
cnf(11,axiom,
equal(and__dfg(u,v),and__dfg(v,u)),
file('LCL154-1.p',unknown),
[] ).
cnf(12,axiom,
equal(or__dfg(and__dfg(u,not__dfg(v)),and__dfg(not__dfg(u),v)),xor__dfg(u,v)),
file('LCL154-1.p',unknown),
[] ).
cnf(14,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and_star(u,v)),
file('LCL154-1.p',unknown),
[] ).
cnf(17,axiom,
equal(not__dfg(truth),falsehood),
file('LCL154-1.p',unknown),
[] ).
cnf(18,plain,
equal(and_star(u,v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[14,9]),
[iquote('0:Rew:14.0,9.0')] ).
cnf(20,plain,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[18,14]),
[iquote('0:Rew:18.0,14.0')] ).
cnf(23,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)],[2,23]),
[iquote('0:SpR:2.0,23.0')] ).
cnf(45,plain,
equal(implies__dfg(or__dfg(u,not__dfg(falsehood)),or__dfg(truth,u)),truth),
inference(spr,[status(thm),theory(equality)],[40,23]),
[iquote('0:SpR:40.0,23.0')] ).
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)],[54,23]),
[iquote('0:SpR:54.0,23.0')] ).
cnf(77,plain,
equal(not__dfg(or__dfg(not__dfg(u),falsehood)),and__dfg(u,truth)),
inference(spr,[status(thm),theory(equality)],[17,20]),
[iquote('0:SpR:17.0,20.0')] ).
cnf(81,plain,
equal(not__dfg(or__dfg(falsehood,not__dfg(u))),and__dfg(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__dfg(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(240,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(288,plain,
equal(implies__dfg(truth,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[240,54]),
[iquote('0:SpR:240.0,54.0')] ).
cnf(296,plain,
equal(not__dfg(falsehood),truth),
inference(rew,[status(thm),theory(equality)],[2,288]),
[iquote('0:Rew:2.0,288.0')] ).
cnf(297,plain,
equal(implies__dfg(or__dfg(u,truth),or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[296,45]),
[iquote('0:Rew:296.0,45.0')] ).
cnf(328,plain,
equal(implies__dfg(truth,u),or__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[296,6]),
[iquote('0:SpR:296.0,6.0')] ).
cnf(329,plain,
equal(not__dfg(or__dfg(truth,not__dfg(u))),and__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[296,20]),
[iquote('0:SpR:296.0,20.0')] ).
cnf(336,plain,
equal(or__dfg(falsehood,u),u),
inference(rew,[status(thm),theory(equality)],[2,328]),
[iquote('0:Rew:2.0,328.0')] ).
cnf(339,plain,
equal(not__dfg(not__dfg(u)),and__dfg(u,truth)),
inference(rew,[status(thm),theory(equality)],[336,81]),
[iquote('0:Rew:336.0,81.0')] ).
cnf(340,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[336,54]),
[iquote('0:Rew:336.0,54.0')] ).
cnf(355,plain,
equal(implies__dfg(implies__dfg(u,truth),truth),truth),
inference(rew,[status(thm),theory(equality)],[340,137]),
[iquote('0:Rew:340.0,137.0')] ).
cnf(411,plain,
equal(or__dfg(and__dfg(u,truth),and__dfg(not__dfg(u),falsehood)),xor__dfg(u,falsehood)),
inference(spr,[status(thm),theory(equality)],[296,12]),
[iquote('0:SpR:296.0,12.0')] ).
cnf(418,plain,
equal(or__dfg(and__dfg(u,truth),and__dfg(falsehood,not__dfg(u))),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[11,411]),
[iquote('0:Rew:11.0,411.0')] ).
cnf(420,plain,
equal(or__dfg(u,falsehood),u),
inference(spr,[status(thm),theory(equality)],[336,8]),
[iquote('0:SpR:336.0,8.0')] ).
cnf(442,plain,
equal(or__dfg(u,not__dfg(u)),truth),
inference(spr,[status(thm),theory(equality)],[340,6]),
[iquote('0:SpR:340.0,6.0')] ).
cnf(490,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and__dfg(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(521,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and__dfg(u,truth)),v),truth),truth),
inference(rew,[status(thm),theory(equality)],[355,490]),
[iquote('0:Rew:355.0,490.0')] ).
cnf(593,plain,
equal(or__dfg(not__dfg(u),and__dfg(u,truth)),truth),
inference(spr,[status(thm),theory(equality)],[339,442]),
[iquote('0:SpR:339.0,442.0')] ).
cnf(609,plain,
equal(implies__dfg(implies__dfg(truth,u),truth),truth),
inference(rew,[status(thm),theory(equality)],[593,521]),
[iquote('0:Rew:593.0,521.0')] ).
cnf(611,plain,
equal(implies__dfg(u,truth),truth),
inference(rew,[status(thm),theory(equality)],[2,609]),
[iquote('0:Rew:2.0,609.0')] ).
cnf(636,plain,
equal(or__dfg(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[611,6]),
[iquote('0:SpR:611.0,6.0')] ).
cnf(643,plain,
equal(implies__dfg(truth,or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[636,297]),
[iquote('0:Rew:636.0,297.0')] ).
cnf(649,plain,
equal(or__dfg(truth,u),truth),
inference(rew,[status(thm),theory(equality)],[2,643]),
[iquote('0:Rew:2.0,643.0')] ).
cnf(653,plain,
equal(and__dfg(falsehood,u),not__dfg(truth)),
inference(rew,[status(thm),theory(equality)],[649,329]),
[iquote('0:Rew:649.0,329.0')] ).
cnf(654,plain,
equal(implies__dfg(implies__dfg(u,falsehood),falsehood),implies__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[649,138]),
[iquote('0:Rew:649.0,138.0')] ).
cnf(655,plain,
equal(and__dfg(falsehood,u),falsehood),
inference(rew,[status(thm),theory(equality)],[17,653]),
[iquote('0:Rew:17.0,653.0')] ).
cnf(658,plain,
equal(or__dfg(and__dfg(u,truth),falsehood),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[655,418]),
[iquote('0:Rew:655.0,418.0')] ).
cnf(663,plain,
equal(implies__dfg(implies__dfg(u,falsehood),falsehood),u),
inference(rew,[status(thm),theory(equality)],[2,654]),
[iquote('0:Rew:2.0,654.0')] ).
cnf(672,plain,
equal(and__dfg(u,truth),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[420,658]),
[iquote('0:Rew:420.0,658.0')] ).
cnf(673,plain,
equal(not__dfg(not__dfg(u)),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[672,339]),
[iquote('0:Rew:672.0,339.0')] ).
cnf(773,plain,
equal(implies__dfg(or__dfg(u,falsehood),falsehood),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6,663]),
[iquote('0:SpR:6.0,663.0')] ).
cnf(778,plain,
equal(implies__dfg(u,falsehood),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[420,773]),
[iquote('0:Rew:420.0,773.0')] ).
cnf(779,plain,
equal(not__dfg(implies__dfg(u,falsehood)),u),
inference(rew,[status(thm),theory(equality)],[778,663]),
[iquote('0:Rew:778.0,663.0')] ).
cnf(784,plain,
equal(xor__dfg(u,falsehood),u),
inference(rew,[status(thm),theory(equality)],[673,779,778]),
[iquote('0:Rew:673.0,779.0,778.0,779.0')] ).
cnf(785,plain,
$false,
inference(unc,[status(thm)],[784,1]),
[iquote('0:UnC:784.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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 11:56:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 533 clauses, backtracked 0 clauses, performed 0 splits and kept 223 clauses.
% 0.19/0.48 SPASS allocated 63909 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.06 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 6, length 62 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : prove_alternative_wajsberg_axiom wajsberg_1 wajsberg_2 wajsberg_3 wajsberg_4 or_definition or_commutativity and_definition and_commutativity xor_definition and_star_definition false_definition
% 0.19/0.48
%------------------------------------------------------------------------------