TSTP Solution File: RNG025-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG025-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 20:41:14 EDT 2022
% Result : Unsatisfiable 0.16s 0.53s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% 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 : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(associator(x__dfg,y__dfg,x__dfg),additive_identity),
file('RNG025-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG025-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG025-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG025-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG025-6.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG025-6.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG025-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG025-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG025-6.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(multiply(u,v),v),multiply(u,multiply(v,v))),
file('RNG025-6.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(multiply(u,u),v),multiply(u,multiply(u,v))),
file('RNG025-6.p',unknown),
[] ).
cnf(15,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG025-6.p',unknown),
[] ).
cnf(16,axiom,
equal(add(multiply(u,v),additive_inverse(multiply(v,u))),commutator(v,u)),
file('RNG025-6.p',unknown),
[] ).
cnf(18,plain,
equal(add(additive_inverse(multiply(u,multiply(v,w))),multiply(multiply(u,v),w)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[11,15]),
[iquote('0:Rew:11.0,15.0')] ).
cnf(27,plain,
equal(additive_inverse(additive_identity),additive_identity),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(64,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.0,7.0')] ).
cnf(71,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(75,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[2,71]),
[iquote('0:Rew:2.0,71.0')] ).
cnf(86,plain,
equal(add(u,add(v,additive_inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[11,75]),
[iquote('0:SpR:11.0,75.0')] ).
cnf(118,plain,
equal(add(multiply(u,v),commutator(u,v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[16,86]),
[iquote('0:SpR:16.0,86.0')] ).
cnf(132,plain,
equal(add(commutator(u,v),multiply(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[11,118]),
[iquote('0:Rew:11.0,118.0')] ).
cnf(133,plain,
equal(add(commutator(u,multiply(v,u)),multiply(u,multiply(v,u))),multiply(v,multiply(u,u))),
inference(rew,[status(thm),theory(equality)],[132,13]),
[iquote('0:Rew:132.0,13.0')] ).
cnf(149,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[64,75]),
[iquote('0:SpR:64.0,75.0')] ).
cnf(166,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[3,149]),
[iquote('0:Rew:3.0,149.0')] ).
cnf(219,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[8,166]),
[iquote('0:SpR:8.0,166.0')] ).
cnf(248,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[219,75]),
[iquote('0:SpR:219.0,75.0')] ).
cnf(252,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[11,219]),
[iquote('0:SpR:11.0,219.0')] ).
cnf(258,plain,
equal(add(u,additive_inverse(add(v,add(w,u)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[12,219]),
[iquote('0:SpR:12.0,219.0')] ).
cnf(396,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[248,11]),
[iquote('0:SpR:248.0,11.0')] ).
cnf(399,plain,
equal(add(additive_inverse(add(u,additive_inverse(v))),w),add(v,add(additive_inverse(u),w))),
inference(spr,[status(thm),theory(equality)],[248,12]),
[iquote('0:SpR:248.0,12.0')] ).
cnf(407,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(u,v)),
inference(spr,[status(thm),theory(equality)],[248,16]),
[iquote('0:SpR:248.0,16.0')] ).
cnf(446,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w)))),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[396,18]),
[iquote('0:Rew:396.0,18.0')] ).
cnf(465,plain,
equal(additive_inverse(commutator(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[16,407]),
[iquote('0:Rew:16.0,407.0')] ).
cnf(474,plain,
equal(additive_inverse(add(add(u,additive_inverse(v)),additive_inverse(w))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[396,399]),
[iquote('0:Rew:396.0,399.0,396.0,399.0')] ).
cnf(475,plain,
equal(additive_inverse(add(u,add(additive_inverse(v),additive_inverse(w)))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[12,474]),
[iquote('0:Rew:12.0,474.0')] ).
cnf(476,plain,
equal(additive_inverse(add(u,additive_inverse(add(v,additive_inverse(additive_inverse(w)))))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[396,475]),
[iquote('0:Rew:396.0,475.0')] ).
cnf(477,plain,
equal(additive_inverse(add(u,additive_inverse(add(v,w)))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[8,476]),
[iquote('0:Rew:8.0,476.0')] ).
cnf(854,plain,
equal(additive_inverse(additive_inverse(multiply(multiply(u,v),w))),add(multiply(u,multiply(v,w)),associator(u,v,w))),
inference(spr,[status(thm),theory(equality)],[446,252]),
[iquote('0:SpR:446.0,252.0')] ).
cnf(867,plain,
equal(additive_inverse(add(multiply(u,multiply(u,v)),additive_inverse(multiply(u,multiply(u,v))))),associator(u,u,v)),
inference(spr,[status(thm),theory(equality)],[14,446]),
[iquote('0:SpR:14.0,446.0')] ).
cnf(871,plain,
equal(additive_inverse(add(multiply(u,add(multiply(v,w),multiply(v,x))),additive_inverse(multiply(multiply(u,v),add(w,x))))),associator(u,v,add(w,x))),
inference(spr,[status(thm),theory(equality)],[9,446]),
[iquote('0:SpR:9.0,446.0')] ).
cnf(875,plain,
equal(additive_inverse(add(multiply(u,add(multiply(v,w),multiply(x,w))),additive_inverse(multiply(multiply(u,add(v,x)),w)))),associator(u,add(v,x),w)),
inference(spr,[status(thm),theory(equality)],[10,446]),
[iquote('0:SpR:10.0,446.0')] ).
cnf(881,plain,
equal(additive_inverse(add(add(commutator(u,multiply(v,u)),multiply(u,multiply(v,u))),additive_inverse(multiply(multiply(v,u),u)))),associator(v,u,u)),
inference(spr,[status(thm),theory(equality)],[133,446]),
[iquote('0:SpR:133.0,446.0')] ).
cnf(892,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[8,854,11]),
[iquote('0:Rew:8.0,854.0,11.0,854.0')] ).
cnf(901,plain,
equal(associator(u,u,v),additive_identity),
inference(rew,[status(thm),theory(equality)],[27,867,7]),
[iquote('0:Rew:27.0,867.0,7.0,867.0')] ).
cnf(948,plain,
equal(associator(u,v,v),additive_identity),
inference(rew,[status(thm),theory(equality)],[27,881,7,465,16,12]),
[iquote('0:Rew:27.0,881.0,7.0,881.0,465.0,881.0,16.0,881.0,12.0,881.0')] ).
cnf(957,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),add(multiply(u,multiply(x,w)),additive_inverse(add(multiply(multiply(u,v),w),multiply(multiply(u,x),w)))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[12,875,9,10]),
[iquote('0:Rew:12.0,875.0,9.0,875.0,10.0,875.0,9.0,875.0')] ).
cnf(958,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(add(associator(u,v,w),multiply(u,multiply(v,w))),associator(u,x,w))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[258,957,892]),
[iquote('0:Rew:258.0,957.0,892.0,957.0,892.0,957.0')] ).
cnf(959,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),associator(u,x,w)))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[12,958]),
[iquote('0:Rew:12.0,958.0')] ).
cnf(960,plain,
equal(add(associator(u,v,w),additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(multiply(u,multiply(v,w)),associator(u,x,w)))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[477,959]),
[iquote('0:Rew:477.0,959.0')] ).
cnf(961,plain,
equal(add(associator(u,v,w),associator(u,x,w)),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[8,960,252]),
[iquote('0:Rew:8.0,960.0,252.0,960.0')] ).
cnf(962,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),add(multiply(u,multiply(v,x)),additive_inverse(add(multiply(multiply(u,v),w),multiply(multiply(u,v),x)))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[12,871,9]),
[iquote('0:Rew:12.0,871.0,9.0,871.0,9.0,871.0')] ).
cnf(963,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(add(associator(u,v,w),multiply(u,multiply(v,w))),associator(u,v,x))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[258,962,892]),
[iquote('0:Rew:258.0,962.0,892.0,962.0,892.0,962.0')] ).
cnf(964,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),associator(u,v,x)))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[12,963]),
[iquote('0:Rew:12.0,963.0')] ).
cnf(965,plain,
equal(add(associator(u,v,w),additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(multiply(u,multiply(v,w)),associator(u,v,x)))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[477,964]),
[iquote('0:Rew:477.0,964.0')] ).
cnf(966,plain,
equal(add(associator(u,v,w),associator(u,v,x)),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[8,965,252]),
[iquote('0:Rew:8.0,965.0,252.0,965.0')] ).
cnf(1539,plain,
equal(add(associator(u,v,w),additive_identity),associator(u,add(v,u),w)),
inference(spr,[status(thm),theory(equality)],[901,961]),
[iquote('0:SpR:901.0,961.0')] ).
cnf(1552,plain,
equal(associator(u,add(v,u),w),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[2,1539,11]),
[iquote('0:Rew:2.0,1539.0,11.0,1539.0')] ).
cnf(2025,plain,
equal(add(additive_identity,associator(u,v,w)),associator(u,v,add(v,w))),
inference(spr,[status(thm),theory(equality)],[948,966]),
[iquote('0:SpR:948.0,966.0')] ).
cnf(2036,plain,
equal(associator(u,v,add(v,w)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[2,2025]),
[iquote('0:Rew:2.0,2025.0')] ).
cnf(2060,plain,
equal(associator(u,v,add(v,u)),additive_identity),
inference(spr,[status(thm),theory(equality)],[1552,948]),
[iquote('0:SpR:1552.0,948.0')] ).
cnf(2089,plain,
equal(associator(u,v,u),additive_identity),
inference(rew,[status(thm),theory(equality)],[2036,2060]),
[iquote('0:Rew:2036.0,2060.0')] ).
cnf(2090,plain,
$false,
inference(unc,[status(thm)],[2089,1]),
[iquote('0:UnC:2089.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : RNG025-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon May 30 16:59:57 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.53
% 0.16/0.53 SPASS V 3.9
% 0.16/0.53 SPASS beiseite: Proof found.
% 0.16/0.53 % SZS status Theorem
% 0.16/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.53 SPASS derived 1150 clauses, backtracked 0 clauses, performed 0 splits and kept 287 clauses.
% 0.16/0.53 SPASS allocated 65931 KBytes.
% 0.16/0.53 SPASS spent 0:00:00.21 on the problem.
% 0.16/0.53 0:00:00.03 for the input.
% 0.16/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.16/0.53 0:00:00.01 for inferences.
% 0.16/0.53 0:00:00.00 for the backtracking.
% 0.16/0.53 0:00:00.15 for the reduction.
% 0.16/0.53
% 0.16/0.53
% 0.16/0.53 Here is a proof with depth 5, length 62 :
% 0.16/0.53 % SZS output start Refutation
% See solution above
% 0.16/0.53 Formulae used in the proof : prove_flexible_law left_additive_identity right_additive_identity right_additive_inverse additive_inverse_additive_inverse distribute1 distribute2 commutativity_for_addition associativity_for_addition right_alternative left_alternative associator commutator
% 0.16/0.54
%------------------------------------------------------------------------------