TSTP Solution File: RNG008-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Mon Jul 18 20:41:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 3 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,u),u),
file('RNG008-4.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(a,b),c),
file('RNG008-4.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),c),
file('RNG008-4.p',unknown),
[] ).
cnf(4,axiom,
equal(add(additive_identity,u),u),
file('RNG008-4.p',unknown),
[] ).
cnf(5,axiom,
equal(add(additive_inverse(u),u),additive_identity),
file('RNG008-4.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG008-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG008-4.p',unknown),
[] ).
cnf(9,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG008-4.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
file('RNG008-4.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
file('RNG008-4.p',unknown),
[] ).
cnf(15,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG008-4.p',unknown),
[] ).
cnf(16,axiom,
equal(add(u,v),add(v,u)),
file('RNG008-4.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('RNG008-4.p',unknown),
[] ).
cnf(18,plain,
equal(add(u,additive_inverse(u)),additive_identity),
inference(rew,[status(thm),theory(equality)],[16,5]),
[iquote('0:Rew:16.0,5.0')] ).
cnf(36,plain,
equal(add(u,additive_identity),u),
inference(spr,[status(thm),theory(equality)],[16,4]),
[iquote('0:SpR:16.0,4.0')] ).
cnf(47,plain,
equal(additive_inverse(multiply(u,additive_inverse(u))),additive_inverse(u)),
inference(spr,[status(thm),theory(equality)],[14,1]),
[iquote('0:SpR:14.0,1.0')] ).
cnf(52,plain,
equal(additive_inverse(additive_inverse(multiply(u,u))),additive_inverse(u)),
inference(rew,[status(thm),theory(equality)],[13,47]),
[iquote('0:Rew:13.0,47.0')] ).
cnf(53,plain,
equal(additive_inverse(u),u),
inference(rew,[status(thm),theory(equality)],[9,52,1]),
[iquote('0:Rew:9.0,52.0,1.0,52.0')] ).
cnf(56,plain,
equal(add(u,u),additive_identity),
inference(rew,[status(thm),theory(equality)],[53,18]),
[iquote('0:Rew:53.0,18.0')] ).
cnf(69,plain,
equal(multiply(u,multiply(v,multiply(u,v))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[17,1]),
[iquote('0:SpR:17.0,1.0')] ).
cnf(75,plain,
equal(multiply(u,multiply(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(118,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[16,15]),
[iquote('0:SpR:16.0,15.0')] ).
cnf(121,plain,
equal(add(additive_identity,u),add(v,add(v,u))),
inference(spr,[status(thm),theory(equality)],[56,15]),
[iquote('0:SpR:56.0,15.0')] ).
cnf(124,plain,
equal(add(u,add(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,121]),
[iquote('0:Rew:4.0,121.0')] ).
cnf(125,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[15,118]),
[iquote('0:Rew:15.0,118.0')] ).
cnf(270,plain,
equal(add(multiply(u,add(u,v)),multiply(v,add(u,v))),add(u,v)),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(296,plain,
equal(add(add(multiply(u,u),multiply(u,v)),add(multiply(v,u),multiply(v,v))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[6,270]),
[iquote('0:Rew:6.0,270.0,6.0,270.0')] ).
cnf(297,plain,
equal(add(u,add(multiply(u,v),add(v,multiply(v,u)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[15,296,1,16]),
[iquote('0:Rew:15.0,296.0,1.0,296.0,16.0,296.0,1.0,296.0')] ).
cnf(298,plain,
equal(add(u,add(v,add(multiply(u,v),multiply(v,u)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[125,297]),
[iquote('0:Rew:125.0,297.0')] ).
cnf(1038,plain,
equal(add(u,add(multiply(v,u),multiply(u,v))),add(v,add(v,u))),
inference(spr,[status(thm),theory(equality)],[298,124]),
[iquote('0:SpR:298.0,124.0')] ).
cnf(1107,plain,
equal(add(u,add(multiply(v,u),multiply(u,v))),u),
inference(rew,[status(thm),theory(equality)],[124,1038]),
[iquote('0:Rew:124.0,1038.0')] ).
cnf(1204,plain,
equal(add(multiply(u,multiply(v,u)),add(multiply(v,u),multiply(multiply(u,multiply(v,u)),v))),multiply(u,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[69,1107]),
[iquote('0:SpR:69.0,1107.0')] ).
cnf(1206,plain,
equal(add(multiply(u,v),add(multiply(u,v),multiply(multiply(u,v),u))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[75,1107]),
[iquote('0:SpR:75.0,1107.0')] ).
cnf(1278,plain,
equal(multiply(u,multiply(v,u)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[124,1206,17]),
[iquote('0:Rew:124.0,1206.0,17.0,1206.0')] ).
cnf(1294,plain,
equal(add(multiply(u,v),add(multiply(v,multiply(u,v)),multiply(v,multiply(u,multiply(v,u))))),multiply(v,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[125,1204,17]),
[iquote('0:Rew:125.0,1204.0,17.0,1204.0,17.0,1204.0')] ).
cnf(1295,plain,
equal(add(multiply(u,v),add(multiply(v,u),multiply(v,u))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[1278,1294]),
[iquote('0:Rew:1278.0,1294.0,1278.0,1294.0,1278.0,1294.0')] ).
cnf(1296,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[36,1295,56]),
[iquote('0:Rew:36.0,1295.0,56.0,1295.0')] ).
cnf(1297,plain,
~ equal(multiply(a,b),c),
inference(rew,[status(thm),theory(equality)],[1296,3]),
[iquote('0:Rew:1296.0,3.0')] ).
cnf(1301,plain,
~ equal(c,c),
inference(rew,[status(thm),theory(equality)],[2,1297]),
[iquote('0:Rew:2.0,1297.0')] ).
cnf(1302,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1301]),
[iquote('0:Obv:1301.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 12:25:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 768 clauses, backtracked 0 clauses, performed 0 splits and kept 123 clauses.
% 0.20/0.53 SPASS allocated 64392 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.53 0:00:00.04 for the input.
% 0.20/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.01 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.11 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 3, length 40 :
% 0.20/0.53 % SZS output start Refutation
% See solution above
% 0.20/0.53 Formulae used in the proof : boolean_ring a_times_b_is_c prove_commutativity left_identity left_additive_inverse distribute1 distribute2 additive_inverse_additive_inverse multiply_additive_inverse1 multiply_additive_inverse2 associative_addition commutative_addition associative_multiplication
% 0.20/0.53
%------------------------------------------------------------------------------