TSTP Solution File: GRP402-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:47:12 EDT 2022
% Result : Unsatisfiable 1.16s 1.38s
% Output : Refutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 37 ( 26 unt; 0 nHn; 37 RR)
% Number of literals : 48 ( 0 equ; 13 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(v,commutator(v,u))),multiply(v,u)),
file('GRP402-1.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(commutator(u,v),w),multiply(w,commutator(u,v))),
file('GRP402-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(commutator(commutator(a,b),c),commutator(a,commutator(b,c))),
file('GRP402-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP402-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(u,v),multiply(w,v))
| equal(u,w) ),
file('GRP402-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(multiply(u,v),multiply(u,w))
| equal(v,w) ),
file('GRP402-1.p',unknown),
[] ).
cnf(19,plain,
equal(multiply(commutator(u,v),multiply(w,x)),multiply(w,multiply(x,commutator(u,v)))),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(21,plain,
equal(multiply(u,multiply(multiply(v,commutator(v,u)),w)),multiply(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(22,plain,
equal(multiply(multiply(commutator(u,v),w),x),multiply(w,multiply(commutator(u,v),x))),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(25,plain,
equal(multiply(u,multiply(v,multiply(commutator(v,u),w))),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[4,21]),
[iquote('0:Rew:4.0,21.0,4.0,21.0')] ).
cnf(26,plain,
equal(multiply(commutator(u,v),multiply(w,x)),multiply(w,multiply(commutator(u,v),x))),
inference(rew,[status(thm),theory(equality)],[4,22]),
[iquote('0:Rew:4.0,22.0')] ).
cnf(30,plain,
( ~ equal(multiply(u,v),multiply(v,w))
| equal(multiply(u,commutator(u,v)),w) ),
inference(spl,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpL:1.0,6.0')] ).
cnf(33,plain,
( ~ equal(multiply(u,multiply(v,w)),multiply(multiply(u,v),x))
| equal(w,x) ),
inference(spl,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpL:4.0,6.0')] ).
cnf(38,plain,
( ~ equal(multiply(u,multiply(v,w)),multiply(u,multiply(v,x)))
| equal(w,x) ),
inference(rew,[status(thm),theory(equality)],[4,33]),
[iquote('0:Rew:4.0,33.0')] ).
cnf(43,plain,
( ~ equal(multiply(u,commutator(v,w)),multiply(x,u))
| equal(commutator(v,w),x) ),
inference(spl,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpL:2.0,5.0')] ).
cnf(49,plain,
equal(multiply(u,multiply(commutator(u,commutator(v,w)),commutator(v,w))),multiply(u,commutator(v,w))),
inference(spr,[status(thm),theory(equality)],[19,1]),
[iquote('0:SpR:19.0,1.0')] ).
cnf(76,plain,
equal(multiply(u,multiply(commutator(v,w),commutator(u,commutator(v,w)))),multiply(u,commutator(v,w))),
inference(rew,[status(thm),theory(equality)],[2,49]),
[iquote('0:Rew:2.0,49.0')] ).
cnf(146,plain,
equal(multiply(commutator(u,v),multiply(w,commutator(commutator(u,v),w))),multiply(commutator(u,v),w)),
inference(spr,[status(thm),theory(equality)],[26,1]),
[iquote('0:SpR:26.0,1.0')] ).
cnf(194,plain,
equal(multiply(u,commutator(u,u)),u),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.0')] ).
cnf(224,plain,
equal(multiply(u,multiply(commutator(u,u),v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[194,4]),
[iquote('0:SpR:194.0,4.0')] ).
cnf(230,plain,
equal(multiply(commutator(u,u),multiply(v,u)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[194,19]),
[iquote('0:SpR:194.0,19.0')] ).
cnf(342,plain,
equal(multiply(u,multiply(commutator(commutator(v,v),u),v)),multiply(commutator(v,v),multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[230,25]),
[iquote('0:SpR:230.0,25.0')] ).
cnf(388,plain,
equal(multiply(u,multiply(v,commutator(commutator(v,v),u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[2,342,230]),
[iquote('0:Rew:2.0,342.0,230.0,342.0')] ).
cnf(885,plain,
( ~ equal(multiply(u,v),v)
| equal(commutator(v,v),u) ),
inference(spl,[status(thm),theory(equality)],[194,43]),
[iquote('0:SpL:194.0,43.0')] ).
cnf(937,plain,
( ~ equal(multiply(u,v),multiply(u,v))
| equal(commutator(multiply(u,v),multiply(u,v)),commutator(v,v)) ),
inference(spl,[status(thm),theory(equality)],[230,885]),
[iquote('0:SpL:230.0,885.0')] ).
cnf(940,plain,
equal(commutator(multiply(u,v),multiply(u,v)),commutator(v,v)),
inference(obv,[status(thm),theory(equality)],[937]),
[iquote('0:Obv:937.0')] ).
cnf(1008,plain,
equal(commutator(multiply(u,commutator(v,w)),multiply(u,commutator(v,w))),commutator(u,u)),
inference(spr,[status(thm),theory(equality)],[2,940]),
[iquote('0:SpR:2.0,940.0')] ).
cnf(1041,plain,
equal(commutator(commutator(u,v),commutator(u,v)),commutator(w,w)),
inference(rew,[status(thm),theory(equality)],[940,1008]),
[iquote('0:Rew:940.0,1008.0')] ).
cnf(1179,plain,
equal(multiply(commutator(u,u),multiply(u,commutator(v,v))),multiply(commutator(u,u),u)),
inference(spr,[status(thm),theory(equality)],[1041,388]),
[iquote('0:SpR:1041.0,388.0')] ).
cnf(1255,plain,
equal(multiply(u,commutator(v,v)),u),
inference(rew,[status(thm),theory(equality)],[224,1179,26,194,2]),
[iquote('0:Rew:224.0,1179.0,26.0,1179.0,194.0,1179.0,2.0,1179.0')] ).
cnf(1469,plain,
( ~ equal(multiply(u,multiply(v,w)),multiply(u,v))
| equal(commutator(x,x),w) ),
inference(spl,[status(thm),theory(equality)],[1255,38]),
[iquote('0:SpL:1255.0,38.0')] ).
cnf(3295,plain,
( ~ equal(multiply(u,commutator(v,w)),multiply(u,commutator(v,w)))
| equal(commutator(x,x),commutator(u,commutator(v,w))) ),
inference(spl,[status(thm),theory(equality)],[76,1469]),
[iquote('0:SpL:76.0,1469.0')] ).
cnf(3320,plain,
equal(commutator(u,u),commutator(v,commutator(w,x))),
inference(obv,[status(thm),theory(equality)],[3295]),
[iquote('0:Obv:3295.0')] ).
cnf(4008,plain,
( ~ equal(multiply(commutator(u,v),w),multiply(commutator(u,v),w))
| equal(commutator(x,x),commutator(commutator(u,v),w)) ),
inference(spl,[status(thm),theory(equality)],[146,1469]),
[iquote('0:SpL:146.0,1469.0')] ).
cnf(4041,plain,
equal(commutator(u,u),commutator(commutator(v,w),x)),
inference(obv,[status(thm),theory(equality)],[4008]),
[iquote('0:Obv:4008.0')] ).
cnf(4146,plain,
~ equal(commutator(u,u),commutator(a,commutator(b,c))),
inference(spl,[status(thm),theory(equality)],[4041,3]),
[iquote('0:SpL:4041.0,3.0')] ).
cnf(4189,plain,
$false,
inference(unc,[status(thm)],[4146,3320]),
[iquote('0:UnC:4146.0,3320.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n007.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jun 13 11:41:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.16/1.38
% 1.16/1.38 SPASS V 3.9
% 1.16/1.38 SPASS beiseite: Proof found.
% 1.16/1.38 % SZS status Theorem
% 1.16/1.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.16/1.38 SPASS derived 2909 clauses, backtracked 0 clauses, performed 0 splits and kept 808 clauses.
% 1.16/1.38 SPASS allocated 67668 KBytes.
% 1.16/1.38 SPASS spent 0:00:01.02 on the problem.
% 1.16/1.38 0:00:00.04 for the input.
% 1.16/1.38 0:00:00.00 for the FLOTTER CNF translation.
% 1.16/1.38 0:00:00.03 for inferences.
% 1.16/1.38 0:00:00.00 for the backtracking.
% 1.16/1.38 0:00:00.92 for the reduction.
% 1.16/1.38
% 1.16/1.38
% 1.16/1.38 Here is a proof with depth 9, length 37 :
% 1.16/1.38 % SZS output start Refutation
% See solution above
% 1.16/1.38 Formulae used in the proof : commutator nilpotency prove_commutator_is_associative associativity_of_multiply right_cancellation left_cancellation
% 1.16/1.38
%------------------------------------------------------------------------------