TSTP Solution File: RNG025-5 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG025-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 1.28s 1.50s
% Output : Refutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of clauses : 73 ( 73 unt; 0 nHn; 73 RR)
% Number of literals : 73 ( 0 equ; 3 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 : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
file('RNG025-5.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
file('RNG025-5.p',unknown),
[] ).
cnf(8,axiom,
~ equal(add(associator(x__dfg,y__dfg,z__dfg),associator(x__dfg,z__dfg,y__dfg)),additive_identity),
file('RNG025-5.p',unknown),
[] ).
cnf(9,axiom,
equal(add(additive_identity,u),u),
file('RNG025-5.p',unknown),
[] ).
cnf(10,axiom,
equal(add(u,additive_identity),u),
file('RNG025-5.p',unknown),
[] ).
cnf(14,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG025-5.p',unknown),
[] ).
cnf(15,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG025-5.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG025-5.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG025-5.p',unknown),
[] ).
cnf(18,axiom,
equal(add(u,v),add(v,u)),
file('RNG025-5.p',unknown),
[] ).
cnf(19,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG025-5.p',unknown),
[] ).
cnf(20,axiom,
equal(multiply(multiply(u,v),v),multiply(u,multiply(v,v))),
file('RNG025-5.p',unknown),
[] ).
cnf(22,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG025-5.p',unknown),
[] ).
cnf(23,axiom,
equal(add(multiply(u,v),additive_inverse(multiply(v,u))),commutator(v,u)),
file('RNG025-5.p',unknown),
[] ).
cnf(30,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)],[18,22]),
[iquote('0:Rew:18.0,22.0')] ).
cnf(39,plain,
equal(additive_inverse(additive_identity),additive_identity),
inference(spr,[status(thm),theory(equality)],[14,9]),
[iquote('0:SpR:14.0,9.0')] ).
cnf(104,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[19,14]),
[iquote('0:SpR:19.0,14.0')] ).
cnf(109,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[18,19]),
[iquote('0:SpR:18.0,19.0')] ).
cnf(111,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[14,19]),
[iquote('0:SpR:14.0,19.0')] ).
cnf(115,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[9,111]),
[iquote('0:Rew:9.0,111.0')] ).
cnf(116,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[19,109]),
[iquote('0:Rew:19.0,109.0')] ).
cnf(126,plain,
equal(add(u,add(v,additive_inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[18,115]),
[iquote('0:SpR:18.0,115.0')] ).
cnf(160,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[104,115]),
[iquote('0:SpR:104.0,115.0')] ).
cnf(176,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[10,160]),
[iquote('0:Rew:10.0,160.0')] ).
cnf(192,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[15,176]),
[iquote('0:SpR:15.0,176.0')] ).
cnf(221,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[192,115]),
[iquote('0:SpR:192.0,115.0')] ).
cnf(224,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[18,192]),
[iquote('0:SpR:18.0,192.0')] ).
cnf(230,plain,
equal(add(u,additive_inverse(add(v,add(w,u)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[19,192]),
[iquote('0:SpR:19.0,192.0')] ).
cnf(251,plain,
equal(add(multiply(u,v),commutator(u,v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[23,126]),
[iquote('0:SpR:23.0,126.0')] ).
cnf(269,plain,
equal(add(commutator(u,v),multiply(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[18,251]),
[iquote('0:Rew:18.0,251.0')] ).
cnf(270,plain,
equal(add(commutator(u,multiply(v,u)),multiply(u,multiply(v,u))),multiply(v,multiply(u,u))),
inference(rew,[status(thm),theory(equality)],[269,20]),
[iquote('0:Rew:269.0,20.0')] ).
cnf(410,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[221,18]),
[iquote('0:SpR:221.0,18.0')] ).
cnf(420,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(u,v)),
inference(spr,[status(thm),theory(equality)],[221,23]),
[iquote('0:SpR:221.0,23.0')] ).
cnf(443,plain,
equal(add(u,additive_inverse(add(v,w))),additive_inverse(add(v,add(w,additive_inverse(u))))),
inference(spr,[status(thm),theory(equality)],[19,221]),
[iquote('0:SpR:19.0,221.0')] ).
cnf(462,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)],[410,30]),
[iquote('0:Rew:410.0,30.0')] ).
cnf(481,plain,
equal(additive_inverse(commutator(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[23,420]),
[iquote('0:Rew:23.0,420.0')] ).
cnf(991,plain,
equal(add(u,additive_inverse(add(v,add(u,w)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[116,224]),
[iquote('0:SpR:116.0,224.0')] ).
cnf(1112,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)],[462,224]),
[iquote('0:SpR:462.0,224.0')] ).
cnf(1129,plain,
equal(additive_inverse(add(multiply(u,additive_inverse(multiply(v,w))),additive_inverse(multiply(multiply(u,v),additive_inverse(w))))),associator(u,v,additive_inverse(w))),
inference(spr,[status(thm),theory(equality)],[3,462]),
[iquote('0:SpR:3.0,462.0')] ).
cnf(1130,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)],[16,462]),
[iquote('0:SpR:16.0,462.0')] ).
cnf(1131,plain,
equal(additive_inverse(add(multiply(u,additive_inverse(multiply(v,w))),additive_inverse(multiply(multiply(u,additive_inverse(v)),w)))),associator(u,additive_inverse(v),w)),
inference(spr,[status(thm),theory(equality)],[2,462]),
[iquote('0:SpR:2.0,462.0')] ).
cnf(1133,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)],[17,462]),
[iquote('0:SpR:17.0,462.0')] ).
cnf(1139,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)],[270,462]),
[iquote('0:SpR:270.0,462.0')] ).
cnf(1150,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[15,1112,18]),
[iquote('0:Rew:15.0,1112.0,18.0,1112.0')] ).
cnf(1168,plain,
equal(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w))),associator(u,additive_inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[15,1131,410,3,2]),
[iquote('0:Rew:15.0,1131.0,410.0,1131.0,3.0,1131.0,15.0,1131.0,2.0,1131.0,3.0,1131.0')] ).
cnf(1169,plain,
equal(additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),additive_inverse(multiply(u,multiply(v,w)))))),associator(u,additive_inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[443,1168,1150]),
[iquote('0:Rew:443.0,1168.0,1150.0,1168.0')] ).
cnf(1170,plain,
equal(associator(u,additive_inverse(v),w),additive_inverse(associator(u,v,w))),
inference(rew,[status(thm),theory(equality)],[9,1169,18,14]),
[iquote('0:Rew:9.0,1169.0,18.0,1169.0,14.0,1169.0')] ).
cnf(1171,plain,
equal(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w))),associator(u,v,additive_inverse(w))),
inference(rew,[status(thm),theory(equality)],[15,1129,410,3]),
[iquote('0:Rew:15.0,1129.0,410.0,1129.0,3.0,1129.0,15.0,1129.0,3.0,1129.0')] ).
cnf(1172,plain,
equal(additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),additive_inverse(multiply(u,multiply(v,w)))))),associator(u,v,additive_inverse(w))),
inference(rew,[status(thm),theory(equality)],[443,1171,1150]),
[iquote('0:Rew:443.0,1171.0,1150.0,1171.0')] ).
cnf(1173,plain,
equal(associator(u,v,additive_inverse(w)),additive_inverse(associator(u,v,w))),
inference(rew,[status(thm),theory(equality)],[9,1172,18,14]),
[iquote('0:Rew:9.0,1172.0,18.0,1172.0,14.0,1172.0')] ).
cnf(1213,plain,
equal(associator(u,v,v),additive_identity),
inference(rew,[status(thm),theory(equality)],[39,1139,14,481,23,19]),
[iquote('0:Rew:39.0,1139.0,14.0,1139.0,481.0,1139.0,23.0,1139.0,19.0,1139.0')] ).
cnf(1222,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)],[19,1133,16,17]),
[iquote('0:Rew:19.0,1133.0,16.0,1133.0,17.0,1133.0,16.0,1133.0')] ).
cnf(1223,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)],[230,1222,1150]),
[iquote('0:Rew:230.0,1222.0,1150.0,1222.0,1150.0,1222.0')] ).
cnf(1224,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)],[19,1223]),
[iquote('0:Rew:19.0,1223.0')] ).
cnf(1225,plain,
equal(additive_inverse(additive_inverse(add(associator(u,v,w),associator(u,x,w)))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[991,1224]),
[iquote('0:Rew:991.0,1224.0')] ).
cnf(1226,plain,
equal(add(associator(u,v,w),associator(u,x,w)),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[15,1225]),
[iquote('0:Rew:15.0,1225.0')] ).
cnf(1227,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)],[19,1130,16]),
[iquote('0:Rew:19.0,1130.0,16.0,1130.0,16.0,1130.0')] ).
cnf(1228,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)],[230,1227,1150]),
[iquote('0:Rew:230.0,1227.0,1150.0,1227.0,1150.0,1227.0')] ).
cnf(1229,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)],[19,1228]),
[iquote('0:Rew:19.0,1228.0')] ).
cnf(1230,plain,
equal(additive_inverse(additive_inverse(add(associator(u,v,w),associator(u,v,x)))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[991,1229]),
[iquote('0:Rew:991.0,1229.0')] ).
cnf(1231,plain,
equal(add(associator(u,v,w),associator(u,v,x)),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[15,1230]),
[iquote('0:Rew:15.0,1230.0')] ).
cnf(2380,plain,
equal(add(associator(u,v,w),additive_identity),associator(u,add(v,w),w)),
inference(spr,[status(thm),theory(equality)],[1213,1226]),
[iquote('0:SpR:1213.0,1226.0')] ).
cnf(2394,plain,
equal(associator(u,add(v,w),w),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[9,2380,18]),
[iquote('0:Rew:9.0,2380.0,18.0,2380.0')] ).
cnf(2643,plain,
equal(add(associator(u,v,w),additive_identity),associator(u,v,add(w,v))),
inference(spr,[status(thm),theory(equality)],[1213,1231]),
[iquote('0:SpR:1213.0,1231.0')] ).
cnf(2655,plain,
equal(add(additive_identity,associator(u,v,w)),associator(u,v,add(v,w))),
inference(spr,[status(thm),theory(equality)],[1213,1231]),
[iquote('0:SpR:1213.0,1231.0')] ).
cnf(2662,plain,
equal(associator(u,v,add(w,v)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[9,2643,18]),
[iquote('0:Rew:9.0,2643.0,18.0,2643.0')] ).
cnf(2668,plain,
equal(associator(u,v,add(v,w)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[9,2655]),
[iquote('0:Rew:9.0,2655.0')] ).
cnf(5485,plain,
equal(associator(u,additive_inverse(v),additive_inverse(add(v,w))),associator(u,w,additive_inverse(add(v,w)))),
inference(spr,[status(thm),theory(equality)],[192,2394]),
[iquote('0:SpR:192.0,2394.0')] ).
cnf(5528,plain,
equal(associator(u,v,add(v,w)),additive_inverse(associator(u,w,add(v,w)))),
inference(rew,[status(thm),theory(equality)],[15,5485,1173,1170]),
[iquote('0:Rew:15.0,5485.0,1173.0,5485.0,1170.0,5485.0,1173.0,5485.0')] ).
cnf(5529,plain,
equal(associator(u,v,w),additive_inverse(associator(u,w,v))),
inference(rew,[status(thm),theory(equality)],[2668,5528,2662]),
[iquote('0:Rew:2668.0,5528.0,2662.0,5528.0')] ).
cnf(5531,plain,
~ equal(add(associator(x__dfg,y__dfg,z__dfg),additive_inverse(associator(x__dfg,y__dfg,z__dfg))),additive_identity),
inference(rew,[status(thm),theory(equality)],[5529,8]),
[iquote('0:Rew:5529.0,8.0')] ).
cnf(5544,plain,
~ equal(additive_identity,additive_identity),
inference(rew,[status(thm),theory(equality)],[14,5531]),
[iquote('0:Rew:14.0,5531.0')] ).
cnf(5545,plain,
$false,
inference(obv,[status(thm),theory(equality)],[5544]),
[iquote('0:Obv:5544.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG025-5 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.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 19:09:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.28/1.50
% 1.28/1.50 SPASS V 3.9
% 1.28/1.50 SPASS beiseite: Proof found.
% 1.28/1.50 % SZS status Theorem
% 1.28/1.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.28/1.50 SPASS derived 3133 clauses, backtracked 0 clauses, performed 0 splits and kept 830 clauses.
% 1.28/1.50 SPASS allocated 72113 KBytes.
% 1.28/1.50 SPASS spent 0:00:01.15 on the problem.
% 1.28/1.50 0:00:00.04 for the input.
% 1.28/1.50 0:00:00.00 for the FLOTTER CNF translation.
% 1.28/1.50 0:00:00.03 for inferences.
% 1.28/1.50 0:00:00.00 for the backtracking.
% 1.28/1.50 0:00:01.06 for the reduction.
% 1.28/1.50
% 1.28/1.50
% 1.28/1.50 Here is a proof with depth 5, length 73 :
% 1.28/1.50 % SZS output start Refutation
% See solution above
% 1.35/1.55 Formulae used in the proof : inverse_product1 inverse_product2 prove_equation left_additive_identity right_additive_identity right_additive_inverse additive_inverse_additive_inverse distribute1 distribute2 commutativity_for_addition associativity_for_addition right_alternative associator commutator
% 1.35/1.55
%------------------------------------------------------------------------------