TSTP Solution File: RNG034-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG034-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 20:41:17 EDT 2022
% Result : Unsatisfiable 0.70s 0.88s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 70 RR)
% Number of literals : 70 ( 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; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG034-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(additive_inverse(associator(cx,cy,cz)),associator(cy,cx,cz)),
file('RNG034-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(additive_identity,u),u),
file('RNG034-1.p',unknown),
[] ).
cnf(6,axiom,
equal(add(additive_inverse(u),u),additive_identity),
file('RNG034-1.p',unknown),
[] ).
cnf(7,axiom,
equal(add(additive_inverse(u),additive_inverse(v)),additive_inverse(add(u,v))),
file('RNG034-1.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG034-1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG034-1.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG034-1.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(multiply(u,u),v),multiply(u,multiply(u,v))),
file('RNG034-1.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
file('RNG034-1.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
file('RNG034-1.p',unknown),
[] ).
cnf(15,axiom,
equal(additive_inverse(additive_identity),additive_identity),
file('RNG034-1.p',unknown),
[] ).
cnf(16,axiom,
equal(add(u,v),add(v,u)),
file('RNG034-1.p',unknown),
[] ).
cnf(17,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG034-1.p',unknown),
[] ).
cnf(20,plain,
equal(add(u,additive_inverse(u)),additive_identity),
inference(rew,[status(thm),theory(equality)],[16,6]),
[iquote('0:Rew:16.0,6.0')] ).
cnf(21,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)],[16,1]),
[iquote('0:Rew:16.0,1.0')] ).
cnf(39,plain,
equal(add(u,additive_identity),u),
inference(spr,[status(thm),theory(equality)],[16,3]),
[iquote('0:SpR:16.0,3.0')] ).
cnf(65,plain,
equal(add(additive_inverse(u),additive_inverse(v)),additive_inverse(add(v,u))),
inference(spr,[status(thm),theory(equality)],[7,16]),
[iquote('0:SpR:7.0,16.0')] ).
cnf(70,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(76,plain,
equal(additive_inverse(add(u,v)),additive_inverse(add(v,u))),
inference(rew,[status(thm),theory(equality)],[7,65]),
[iquote('0:Rew:7.0,65.0')] ).
cnf(79,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)],[70,21]),
[iquote('0:Rew:70.0,21.0')] ).
cnf(83,plain,
equal(add(add(u,v),additive_inverse(add(v,u))),additive_identity),
inference(spr,[status(thm),theory(equality)],[76,20]),
[iquote('0:SpR:76.0,20.0')] ).
cnf(108,plain,
equal(add(u,add(v,additive_inverse(add(v,u)))),additive_identity),
inference(rew,[status(thm),theory(equality)],[17,83]),
[iquote('0:Rew:17.0,83.0')] ).
cnf(118,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[70,16]),
[iquote('0:SpR:70.0,16.0')] ).
cnf(144,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[16,108]),
[iquote('0:SpR:16.0,108.0')] ).
cnf(174,plain,
equal(add(add(u,additive_inverse(v)),w),additive_inverse(add(add(v,additive_inverse(u)),additive_inverse(w)))),
inference(spr,[status(thm),theory(equality)],[118,70]),
[iquote('0:SpR:118.0,70.0')] ).
cnf(224,plain,
equal(add(u,add(additive_inverse(v),w)),additive_inverse(add(v,add(additive_inverse(u),additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[17,174]),
[iquote('0:Rew:17.0,174.0,17.0,174.0')] ).
cnf(225,plain,
equal(add(u,additive_inverse(add(v,additive_inverse(w)))),additive_inverse(add(v,additive_inverse(add(u,w))))),
inference(rew,[status(thm),theory(equality)],[70,224,8]),
[iquote('0:Rew:70.0,224.0,8.0,224.0,70.0,224.0')] ).
cnf(320,plain,
equal(add(u,additive_inverse(add(v,w))),additive_inverse(add(v,add(w,additive_inverse(u))))),
inference(spr,[status(thm),theory(equality)],[17,118]),
[iquote('0:SpR:17.0,118.0')] ).
cnf(324,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[20,17]),
[iquote('0:SpR:20.0,17.0')] ).
cnf(333,plain,
equal(add(u,additive_inverse(add(u,additive_inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[70,324,3]),
[iquote('0:Rew:70.0,324.0,3.0,324.0')] ).
cnf(334,plain,
equal(additive_inverse(add(u,additive_inverse(add(u,v)))),v),
inference(rew,[status(thm),theory(equality)],[225,333]),
[iquote('0:Rew:225.0,333.0')] ).
cnf(346,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[334,8]),
[iquote('0:SpR:334.0,8.0')] ).
cnf(364,plain,
equal(additive_inverse(add(u,additive_inverse(additive_identity))),add(v,additive_inverse(add(u,v)))),
inference(spr,[status(thm),theory(equality)],[144,334]),
[iquote('0:SpR:144.0,334.0')] ).
cnf(389,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(rew,[status(thm),theory(equality)],[39,364,15]),
[iquote('0:Rew:39.0,364.0,15.0,364.0')] ).
cnf(458,plain,
equal(add(u,additive_inverse(add(v,add(w,u)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[17,389]),
[iquote('0:SpR:17.0,389.0')] ).
cnf(841,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)],[79,346]),
[iquote('0:SpR:79.0,346.0')] ).
cnf(854,plain,
equal(additive_inverse(add(multiply(add(u,v),multiply(w,x)),additive_inverse(multiply(add(multiply(u,w),multiply(v,w)),x)))),associator(add(u,v),w,x)),
inference(spr,[status(thm),theory(equality)],[10,79]),
[iquote('0:SpR:10.0,79.0')] ).
cnf(862,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)],[12,79]),
[iquote('0:SpR:12.0,79.0')] ).
cnf(873,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)],[13,79]),
[iquote('0:SpR:13.0,79.0')] ).
cnf(876,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)],[10,79]),
[iquote('0:SpR:10.0,79.0')] ).
cnf(882,plain,
equal(additive_inverse(add(additive_inverse(multiply(u,multiply(v,w))),additive_inverse(multiply(multiply(additive_inverse(u),v),w)))),associator(additive_inverse(u),v,w)),
inference(spr,[status(thm),theory(equality)],[13,79]),
[iquote('0:SpR:13.0,79.0')] ).
cnf(895,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[8,841,16]),
[iquote('0:Rew:8.0,841.0,16.0,841.0')] ).
cnf(908,plain,
equal(associator(u,u,v),additive_identity),
inference(rew,[status(thm),theory(equality)],[15,862,20]),
[iquote('0:Rew:15.0,862.0,20.0,862.0')] ).
cnf(928,plain,
equal(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w))),associator(additive_inverse(u),v,w)),
inference(rew,[status(thm),theory(equality)],[8,882,70,13]),
[iquote('0:Rew:8.0,882.0,70.0,882.0,8.0,882.0,13.0,882.0,13.0,882.0')] ).
cnf(929,plain,
equal(additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),additive_inverse(multiply(u,multiply(v,w)))))),associator(additive_inverse(u),v,w)),
inference(rew,[status(thm),theory(equality)],[320,928,895]),
[iquote('0:Rew:320.0,928.0,895.0,928.0')] ).
cnf(930,plain,
equal(associator(additive_inverse(u),v,w),additive_inverse(associator(u,v,w))),
inference(rew,[status(thm),theory(equality)],[39,929,20]),
[iquote('0:Rew:39.0,929.0,20.0,929.0')] ).
cnf(934,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)],[8,873,70,14,13]),
[iquote('0:Rew:8.0,873.0,70.0,873.0,14.0,873.0,8.0,873.0,13.0,873.0,14.0,873.0')] ).
cnf(935,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)],[320,934,895]),
[iquote('0:Rew:320.0,934.0,895.0,934.0')] ).
cnf(936,plain,
equal(associator(u,additive_inverse(v),w),additive_inverse(associator(u,v,w))),
inference(rew,[status(thm),theory(equality)],[39,935,20]),
[iquote('0:Rew:39.0,935.0,20.0,935.0')] ).
cnf(995,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)],[17,876,9,10]),
[iquote('0:Rew:17.0,876.0,9.0,876.0,10.0,876.0,9.0,876.0')] ).
cnf(996,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)],[458,995,895]),
[iquote('0:Rew:458.0,995.0,895.0,995.0,895.0,995.0')] ).
cnf(997,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)],[17,996]),
[iquote('0:Rew:17.0,996.0')] ).
cnf(998,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)],[225,997]),
[iquote('0:Rew:225.0,997.0')] ).
cnf(999,plain,
equal(add(associator(u,v,w),associator(u,x,w)),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[8,998,346]),
[iquote('0:Rew:8.0,998.0,346.0,998.0')] ).
cnf(1005,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),add(multiply(x,multiply(v,w)),additive_inverse(add(multiply(multiply(u,v),w),multiply(multiply(x,v),w)))))),associator(add(u,x),v,w)),
inference(rew,[status(thm),theory(equality)],[17,854,10]),
[iquote('0:Rew:17.0,854.0,10.0,854.0,10.0,854.0')] ).
cnf(1006,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(add(associator(u,v,w),multiply(u,multiply(v,w))),associator(x,v,w))))),associator(add(u,x),v,w)),
inference(rew,[status(thm),theory(equality)],[458,1005,895]),
[iquote('0:Rew:458.0,1005.0,895.0,1005.0,895.0,1005.0')] ).
cnf(1007,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),associator(x,v,w)))))),associator(add(u,x),v,w)),
inference(rew,[status(thm),theory(equality)],[17,1006]),
[iquote('0:Rew:17.0,1006.0')] ).
cnf(1008,plain,
equal(add(associator(u,v,w),additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(multiply(u,multiply(v,w)),associator(x,v,w)))))),associator(add(u,x),v,w)),
inference(rew,[status(thm),theory(equality)],[225,1007]),
[iquote('0:Rew:225.0,1007.0')] ).
cnf(1009,plain,
equal(add(associator(u,v,w),associator(x,v,w)),associator(add(u,x),v,w)),
inference(rew,[status(thm),theory(equality)],[8,1008,346]),
[iquote('0:Rew:8.0,1008.0,346.0,1008.0')] ).
cnf(2651,plain,
equal(add(associator(u,v,w),additive_identity),associator(u,add(v,u),w)),
inference(spr,[status(thm),theory(equality)],[908,999]),
[iquote('0:SpR:908.0,999.0')] ).
cnf(2691,plain,
equal(associator(u,add(v,u),w),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[39,2651]),
[iquote('0:Rew:39.0,2651.0')] ).
cnf(2983,plain,
equal(add(associator(u,v,w),additive_identity),associator(add(u,v),v,w)),
inference(spr,[status(thm),theory(equality)],[908,1009]),
[iquote('0:SpR:908.0,1009.0')] ).
cnf(2997,plain,
equal(add(additive_identity,associator(u,v,w)),associator(add(v,u),v,w)),
inference(spr,[status(thm),theory(equality)],[908,1009]),
[iquote('0:SpR:908.0,1009.0')] ).
cnf(3026,plain,
equal(associator(add(u,v),v,w),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[39,2983]),
[iquote('0:Rew:39.0,2983.0')] ).
cnf(3031,plain,
equal(associator(add(u,v),u,w),associator(v,u,w)),
inference(rew,[status(thm),theory(equality)],[3,2997]),
[iquote('0:Rew:3.0,2997.0')] ).
cnf(3601,plain,
equal(associator(additive_inverse(add(u,v)),additive_inverse(v),w),associator(additive_inverse(add(u,v)),u,w)),
inference(spr,[status(thm),theory(equality)],[346,2691]),
[iquote('0:SpR:346.0,2691.0')] ).
cnf(3635,plain,
equal(associator(add(u,v),v,w),additive_inverse(associator(add(u,v),u,w))),
inference(rew,[status(thm),theory(equality)],[8,3601,930,936]),
[iquote('0:Rew:8.0,3601.0,930.0,3601.0,936.0,3601.0,930.0,3601.0')] ).
cnf(3636,plain,
equal(associator(u,v,w),additive_inverse(associator(v,u,w))),
inference(rew,[status(thm),theory(equality)],[3026,3635,3031]),
[iquote('0:Rew:3026.0,3635.0,3031.0,3635.0')] ).
cnf(3637,plain,
$false,
inference(unc,[status(thm)],[3636,2]),
[iquote('0:UnC:3636.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG034-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 21:45:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.70/0.88
% 0.70/0.88 SPASS V 3.9
% 0.70/0.88 SPASS beiseite: Proof found.
% 0.70/0.88 % SZS status Theorem
% 0.70/0.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.70/0.88 SPASS derived 2316 clauses, backtracked 0 clauses, performed 0 splits and kept 586 clauses.
% 0.70/0.88 SPASS allocated 66318 KBytes.
% 0.70/0.88 SPASS spent 0:00:00.52 on the problem.
% 0.70/0.88 0:00:00.04 for the input.
% 0.70/0.88 0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.88 0:00:00.03 for inferences.
% 0.70/0.88 0:00:00.00 for the backtracking.
% 0.70/0.88 0:00:00.44 for the reduction.
% 0.70/0.88
% 0.70/0.88
% 0.70/0.88 Here is a proof with depth 5, length 70 :
% 0.70/0.88 % SZS output start Refutation
% See solution above
% 0.70/0.90 Formulae used in the proof : associator prove_skew_symmetry left_additive_identity add_inverse sum_of_inverses additive_inverse_additive_inverse multiply_over_add1 multiply_over_add2 left_alternative inverse_product1 inverse_product2 inverse_additive_identity commutativity_for_addition associativity_for_addition
% 0.70/0.90
%------------------------------------------------------------------------------