%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP177-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:46:07 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 36 ( 0 equ; 8 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(greatest_lower_bound(identity,a),identity),
file('GRP177-2.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(identity,b),identity),
file('GRP177-2.p',unknown),
[] ).
cnf(3,axiom,
equal(greatest_lower_bound(identity,c),identity),
file('GRP177-2.p',unknown),
[] ).
cnf(4,axiom,
~ equal(greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),greatest_lower_bound(a,multiply(b,c))),
file('GRP177-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(identity,u),u),
file('GRP177-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP177-2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP177-2.p',unknown),
[] ).
cnf(8,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP177-2.p',unknown),
[] ).
cnf(10,axiom,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(u,greatest_lower_bound(v,w))),
file('GRP177-2.p',unknown),
[] ).
cnf(13,axiom,
equal(greatest_lower_bound(u,u),u),
file('GRP177-2.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP177-2.p',unknown),
[] ).
cnf(19,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP177-2.p',unknown),
[] ).
cnf(20,plain,
~ equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,c),multiply(b,c)))))),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[10,4,19,17]),
[iquote('0:Rew:10.0,4.0,10.0,4.0,19.0,4.0,19.0,4.0,17.0,4.0')] ).
cnf(146,plain,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(v,greatest_lower_bound(u,w))),
inference(spr,[status(thm),theory(equality)],[8,10]),
[iquote('0:SpR:8.0,10.0')] ).
cnf(149,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(v,w)),greatest_lower_bound(v,greatest_lower_bound(u,w))),
inference(rew,[status(thm),theory(equality)],[10,146]),
[iquote('0:Rew:10.0,146.0')] ).
cnf(150,plain,
~ equal(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,c),multiply(b,c)))))),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[149,20]),
[iquote('0:Rew:149.0,20.0')] ).
cnf(153,plain,
~ equal(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(b,c),multiply(b,c)))))),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[149,150]),
[iquote('0:Rew:149.0,150.0,149.0,150.0,149.0,150.0')] ).
cnf(154,plain,
~ equal(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,a),multiply(b,c))))),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[13,153]),
[iquote('0:Rew:13.0,153.0')] ).
cnf(206,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(207,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[5,206]),
[iquote('0:Rew:5.0,206.0')] ).
cnf(210,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[207]),
[iquote('0:SpR:207.0,207.0')] ).
cnf(213,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[6,207]),
[iquote('0:SpR:6.0,207.0')] ).
cnf(215,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[210,213]),
[iquote('0:Rew:210.0,213.0')] ).
cnf(245,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[2,19]),
[iquote('0:SpR:2.0,19.0')] ).
cnf(246,plain,
equal(greatest_lower_bound(multiply(identity,u),multiply(a,u)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[1,19]),
[iquote('0:SpR:1.0,19.0')] ).
cnf(259,plain,
equal(greatest_lower_bound(u,multiply(b,u)),u),
inference(rew,[status(thm),theory(equality)],[5,245]),
[iquote('0:Rew:5.0,245.0')] ).
cnf(260,plain,
equal(greatest_lower_bound(u,multiply(a,u)),u),
inference(rew,[status(thm),theory(equality)],[5,246]),
[iquote('0:Rew:5.0,246.0')] ).
cnf(321,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(multiply(b,u),v)),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[259,10]),
[iquote('0:SpR:259.0,10.0')] ).
cnf(361,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(multiply(a,u),v)),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[260,10]),
[iquote('0:SpR:260.0,10.0')] ).
cnf(368,plain,
~ equal(greatest_lower_bound(a,greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,a),multiply(b,c)))),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[361,154]),
[iquote('0:Rew:361.0,154.0')] ).
cnf(425,plain,
equal(greatest_lower_bound(multiply(u,identity),multiply(u,c)),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(446,plain,
equal(greatest_lower_bound(u,multiply(u,c)),u),
inference(rew,[status(thm),theory(equality)],[215,425]),
[iquote('0:Rew:215.0,425.0')] ).
cnf(495,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(multiply(u,c),v)),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[446,10]),
[iquote('0:SpR:446.0,10.0')] ).
cnf(511,plain,
~ equal(greatest_lower_bound(a,greatest_lower_bound(multiply(b,a),multiply(b,c))),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[495,368]),
[iquote('0:Rew:495.0,368.0')] ).
cnf(515,plain,
~ equal(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[321,511]),
[iquote('0:Rew:321.0,511.0')] ).
cnf(516,plain,
$false,
inference(obv,[status(thm),theory(equality)],[515]),
[iquote('0:Obv:515.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP177-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 14:38:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 358 clauses, backtracked 0 clauses, performed 0 splits and kept 143 clauses.
% 0.20/0.47 SPASS allocated 63650 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.04 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 2, length 36 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : p08b_1 p08b_2 p08b_3 prove_p08b left_identity left_inverse associativity symmetry_of_glb associativity_of_glb idempotence_of_gld monotony_glb1 monotony_glb2
% 0.20/0.47
%------------------------------------------------------------------------------