TSTP Solution File: GRP754-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP754-1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sat Jul 16 11:49:17 EDT 2022
% Result : Unsatisfiable 62.87s 63.11s
% Output : Refutation 62.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 36 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP754-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP754-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP754-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP754-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(rd(u,u),v),mult(u,w)),mult(u,mult(v,w))),
file('GRP754-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(mult(u,v),mult(w,ld(v,v))),mult(mult(u,w),v)),
file('GRP754-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(mult(mult(a,b),mult(a,c)),mult(mult(a,a),mult(b,c))),
file('GRP754-1.p',unknown),
[] ).
cnf(18,plain,
equal(rd(mult(u,mult(v,w)),mult(u,w)),mult(rd(u,u),v)),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(19,plain,
equal(ld(mult(rd(u,u),v),mult(u,mult(v,w))),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(23,plain,
equal(mult(mult(rd(u,u),v),w),mult(u,mult(v,ld(u,w)))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(39,plain,
equal(ld(mult(u,v),mult(mult(u,w),v)),mult(w,ld(v,v))),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(42,plain,
equal(mult(mult(u,rd(v,ld(w,w))),w),mult(mult(u,w),v)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(53,plain,
equal(rd(mult(u,v),mult(u,w)),mult(rd(u,u),rd(v,w))),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(71,plain,
equal(ld(mult(rd(u,u),v),mult(u,w)),mult(u,ld(v,w))),
inference(spr,[status(thm),theory(equality)],[1,19]),
[iquote('0:SpR:1.0,19.0')] ).
cnf(155,plain,
equal(ld(mult(rd(u,v),w),mult(u,w)),mult(v,ld(w,w))),
inference(spr,[status(thm),theory(equality)],[3,39]),
[iquote('0:SpR:3.0,39.0')] ).
cnf(161,plain,
equal(ld(mult(rd(u,u),v),mult(u,mult(w,ld(u,v)))),mult(w,ld(v,v))),
inference(spr,[status(thm),theory(equality)],[23,39]),
[iquote('0:SpR:23.0,39.0')] ).
cnf(163,plain,
equal(mult(u,ld(ld(v,w),ld(v,w))),ld(w,mult(mult(v,u),ld(v,w)))),
inference(spr,[status(thm),theory(equality)],[1,39]),
[iquote('0:SpR:1.0,39.0')] ).
cnf(169,plain,
equal(mult(u,ld(v,mult(w,ld(u,v)))),mult(w,ld(v,v))),
inference(rew,[status(thm),theory(equality)],[71,161]),
[iquote('0:Rew:71.0,161.0')] ).
cnf(176,plain,
equal(rd(mult(mult(u,v),w),v),mult(u,rd(w,ld(v,v)))),
inference(spr,[status(thm),theory(equality)],[42,4]),
[iquote('0:SpR:42.0,4.0')] ).
cnf(177,plain,
equal(ld(mult(u,rd(v,ld(w,w))),mult(mult(u,w),v)),w),
inference(spr,[status(thm),theory(equality)],[42,2]),
[iquote('0:SpR:42.0,2.0')] ).
cnf(354,plain,
equal(mult(u,ld(v,ld(u,w))),ld(mult(rd(u,u),v),w)),
inference(spr,[status(thm),theory(equality)],[1,71]),
[iquote('0:SpR:1.0,71.0')] ).
cnf(504,plain,
equal(mult(u,ld(ld(v,w),ld(v,w))),ld(mult(rd(v,u),ld(v,w)),w)),
inference(spr,[status(thm),theory(equality)],[1,155]),
[iquote('0:SpR:1.0,155.0')] ).
cnf(520,plain,
equal(ld(mult(rd(u,v),ld(u,w)),w),ld(w,mult(mult(u,v),ld(u,w)))),
inference(rew,[status(thm),theory(equality)],[163,504]),
[iquote('0:Rew:163.0,504.0')] ).
cnf(556,plain,
equal(ld(u,mult(v,ld(w,w))),ld(w,mult(v,ld(u,w)))),
inference(spr,[status(thm),theory(equality)],[169,2]),
[iquote('0:SpR:169.0,2.0')] ).
cnf(559,plain,
equal(mult(rd(u,u),rd(ld(v,mult(w,ld(u,v))),x)),rd(mult(w,ld(v,v)),mult(u,x))),
inference(spr,[status(thm),theory(equality)],[169,53]),
[iquote('0:SpR:169.0,53.0')] ).
cnf(648,plain,
equal(mult(u,rd(ld(v,mult(w,ld(mult(u,x),v))),ld(x,x))),rd(mult(w,ld(v,v)),x)),
inference(spr,[status(thm),theory(equality)],[169,176]),
[iquote('0:SpR:169.0,176.0')] ).
cnf(676,plain,
equal(ld(mult(u,rd(ld(v,mult(w,ld(mult(u,x),v))),ld(x,x))),mult(w,ld(v,v))),x),
inference(spr,[status(thm),theory(equality)],[169,177]),
[iquote('0:SpR:169.0,177.0')] ).
cnf(701,plain,
equal(ld(u,mult(v,ld(rd(mult(v,ld(u,u)),w),u))),w),
inference(rew,[status(thm),theory(equality)],[556,676,648]),
[iquote('0:Rew:556.0,676.0,648.0,676.0')] ).
cnf(2569,plain,
equal(mult(u,ld(rd(mult(u,ld(v,v)),w),v)),mult(v,w)),
inference(spr,[status(thm),theory(equality)],[701,1]),
[iquote('0:SpR:701.0,1.0')] ).
cnf(7029,plain,
equal(ld(rd(mult(u,ld(v,v)),w),v),ld(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[2569,2]),
[iquote('0:SpR:2569.0,2.0')] ).
cnf(7091,plain,
equal(mult(u,ld(rd(ld(mult(rd(u,u),ld(u,v)),v),w),ld(u,v))),mult(ld(u,v),w)),
inference(spr,[status(thm),theory(equality)],[354,2569]),
[iquote('0:SpR:354.0,2569.0')] ).
cnf(7132,plain,
equal(ld(mult(rd(u,u),rd(ld(mult(rd(u,u),ld(u,v)),v),w)),v),mult(ld(u,v),w)),
inference(rew,[status(thm),theory(equality)],[354,7091]),
[iquote('0:Rew:354.0,7091.0')] ).
cnf(7133,plain,
equal(ld(mult(u,u),mult(v,mult(u,w))),mult(ld(u,v),w)),
inference(rew,[status(thm),theory(equality)],[7029,7132,559,520]),
[iquote('0:Rew:7029.0,7132.0,559.0,7132.0,520.0,7132.0')] ).
cnf(16357,plain,
equal(mult(mult(u,u),mult(ld(u,v),w)),mult(v,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[7133,1]),
[iquote('0:SpR:7133.0,1.0')] ).
cnf(23473,plain,
equal(mult(mult(u,u),mult(v,w)),mult(mult(u,v),mult(u,w))),
inference(spr,[status(thm),theory(equality)],[2,16357]),
[iquote('0:SpR:2.0,16357.0')] ).
cnf(23527,plain,
$false,
inference(unc,[status(thm)],[23473,7]),
[iquote('0:UnC:23473.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP754-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 09:31:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 62.87/63.11
% 62.87/63.11 SPASS V 3.9
% 62.87/63.11 SPASS beiseite: Proof found.
% 62.87/63.11 % SZS status Theorem
% 62.87/63.11 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.87/63.11 SPASS derived 12460 clauses, backtracked 0 clauses, performed 0 splits and kept 6816 clauses.
% 62.87/63.11 SPASS allocated 135246 KBytes.
% 62.87/63.11 SPASS spent 0:01:02.12 on the problem.
% 62.87/63.11 0:00:00.03 for the input.
% 62.87/63.11 0:00:00.00 for the FLOTTER CNF translation.
% 62.87/63.11 0:00:00.13 for inferences.
% 62.87/63.11 0:00:00.00 for the backtracking.
% 62.87/63.11 0:01:01.92 for the reduction.
% 62.87/63.11
% 62.87/63.11
% 62.87/63.11 Here is a proof with depth 7, length 36 :
% 62.87/63.11 % SZS output start Refutation
% See solution above
% 62.87/63.11 Formulae used in the proof : f01 f02 f03 f04 f05 f06 goals
% 62.87/63.11
%------------------------------------------------------------------------------