TSTP Solution File: GRP148-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : Sat Jul 16 11:45:56 EDT 2022
% Result : Unsatisfiable 1.61s 1.77s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 29 RR)
% Number of literals : 29 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(a,c),c),
file('GRP148-1.p',unknown),
[] ).
cnf(2,axiom,
equal(least_upper_bound(b,c),c),
file('GRP148-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(greatest_lower_bound(least_upper_bound(a,b),c),least_upper_bound(a,b)),
file('GRP148-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP148-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP148-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP148-1.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP148-1.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP148-1.p',unknown),
[] ).
cnf(10,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP148-1.p',unknown),
[] ).
cnf(14,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP148-1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP148-1.p',unknown),
[] ).
cnf(19,plain,
equal(least_upper_bound(c,b),c),
inference(rew,[status(thm),theory(equality)],[8,2]),
[iquote('0:Rew:8.0,2.0')] ).
cnf(20,plain,
~ equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[7,3]),
[iquote('0:Rew:7.0,3.0')] ).
cnf(38,plain,
equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[8,14]),
[iquote('0:SpR:8.0,14.0')] ).
cnf(151,plain,
equal(least_upper_bound(c,least_upper_bound(b,u)),least_upper_bound(c,u)),
inference(spr,[status(thm),theory(equality)],[19,10]),
[iquote('0:SpR:19.0,10.0')] ).
cnf(221,plain,
equal(greatest_lower_bound(least_upper_bound(b,u),least_upper_bound(c,u)),least_upper_bound(b,u)),
inference(spr,[status(thm),theory(equality)],[151,38]),
[iquote('0:SpR:151.0,38.0')] ).
cnf(236,plain,
equal(greatest_lower_bound(least_upper_bound(c,u),least_upper_bound(b,u)),least_upper_bound(b,u)),
inference(rew,[status(thm),theory(equality)],[7,221]),
[iquote('0:Rew:7.0,221.0')] ).
cnf(354,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(355,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,354]),
[iquote('0:Rew:4.0,354.0')] ).
cnf(358,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[355]),
[iquote('0:SpR:355.0,355.0')] ).
cnf(361,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[5,355]),
[iquote('0:SpR:5.0,355.0')] ).
cnf(363,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[358,361]),
[iquote('0:Rew:358.0,361.0')] ).
cnf(539,plain,
equal(least_upper_bound(multiply(a,u),multiply(c,u)),multiply(c,u)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(650,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(spr,[status(thm),theory(equality)],[358,355]),
[iquote('0:SpR:358.0,355.0')] ).
cnf(1000,plain,
equal(least_upper_bound(multiply(a,multiply(inverse(c),u)),u),u),
inference(spr,[status(thm),theory(equality)],[650,539]),
[iquote('0:SpR:650.0,539.0')] ).
cnf(1013,plain,
equal(least_upper_bound(u,multiply(a,multiply(inverse(c),u))),u),
inference(rew,[status(thm),theory(equality)],[8,1000]),
[iquote('0:Rew:8.0,1000.0')] ).
cnf(7881,plain,
equal(greatest_lower_bound(c,least_upper_bound(b,multiply(a,multiply(inverse(c),c)))),least_upper_bound(b,multiply(a,multiply(inverse(c),c)))),
inference(spr,[status(thm),theory(equality)],[1013,236]),
[iquote('0:SpR:1013.0,236.0')] ).
cnf(7940,plain,
equal(greatest_lower_bound(c,least_upper_bound(a,b)),least_upper_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[8,7881,363,5]),
[iquote('0:Rew:8.0,7881.0,363.0,7881.0,5.0,7881.0')] ).
cnf(7941,plain,
$false,
inference(mrr,[status(thm)],[7940,20]),
[iquote('0:MRR:7940.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP148-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 : Mon Jun 13 05:54:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.61/1.77
% 1.61/1.77 SPASS V 3.9
% 1.61/1.77 SPASS beiseite: Proof found.
% 1.61/1.77 % SZS status Theorem
% 1.61/1.77 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.61/1.77 SPASS derived 5378 clauses, backtracked 0 clauses, performed 0 splits and kept 1257 clauses.
% 1.61/1.77 SPASS allocated 72934 KBytes.
% 1.61/1.77 SPASS spent 0:00:01.37 on the problem.
% 1.61/1.77 0:00:00.04 for the input.
% 1.61/1.77 0:00:00.00 for the FLOTTER CNF translation.
% 1.61/1.77 0:00:00.04 for inferences.
% 1.61/1.77 0:00:00.00 for the backtracking.
% 1.61/1.77 0:00:01.27 for the reduction.
% 1.61/1.77
% 1.61/1.77
% 1.61/1.77 Here is a proof with depth 5, length 29 :
% 1.61/1.77 % SZS output start Refutation
% See solution above
% 1.61/1.77 Formulae used in the proof : ax_lub1c_1 ax_lub1c_2 prove_ax_lub1c left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub associativity_of_lub glb_absorbtion monotony_lub2
% 1.61/1.77
%------------------------------------------------------------------------------