TSTP Solution File: GRP756-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP756-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 1.38s 1.63s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 31 RR)
% Number of literals : 31 ( 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('GRP756-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP756-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP756-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP756-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(u,v),mult(v,w)),mult(u,mult(mult(v,v),w))),
file('GRP756-1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(mult(mult(a,b),c),mult(a,mult(b,c))),
file('GRP756-1.p',unknown),
[] ).
cnf(25,plain,
equal(rd(mult(u,mult(mult(v,v),w)),mult(v,w)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(26,plain,
equal(ld(mult(u,v),mult(u,mult(mult(v,v),w))),mult(v,w)),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(28,plain,
equal(mult(mult(u,mult(v,w)),mult(v,mult(mult(w,w),x))),mult(u,mult(mult(mult(v,w),mult(v,w)),mult(w,x)))),
inference(spr,[status(thm),theory(equality)],[5]),
[iquote('0:SpR:5.0,5.0')] ).
cnf(31,plain,
equal(mult(u,mult(mult(v,v),ld(v,w))),mult(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(32,plain,
equal(mult(rd(u,v),mult(mult(v,v),w)),mult(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(43,plain,
equal(mult(rd(u,mult(mult(v,v),w)),v),rd(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[3,25]),
[iquote('0:SpR:3.0,25.0')] ).
cnf(52,plain,
equal(ld(mult(u,v),mult(u,w)),mult(v,ld(mult(v,v),w))),
inference(spr,[status(thm),theory(equality)],[1,26]),
[iquote('0:SpR:1.0,26.0')] ).
cnf(97,plain,
equal(rd(mult(u,mult(v,w)),mult(mult(v,v),w)),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(109,plain,
equal(mult(u,mult(v,ld(mult(v,v),w))),mult(rd(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,32]),
[iquote('0:SpR:1.0,32.0')] ).
cnf(234,plain,
equal(ld(mult(rd(u,v),w),u),mult(w,ld(mult(w,w),v))),
inference(spr,[status(thm),theory(equality)],[3,52]),
[iquote('0:SpR:3.0,52.0')] ).
cnf(389,plain,
equal(rd(mult(u,mult(v,mult(v,w))),mult(v,mult(mult(v,v),w))),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[5,97]),
[iquote('0:SpR:5.0,97.0')] ).
cnf(585,plain,
equal(mult(u,ld(mult(v,w),mult(v,x))),mult(rd(u,w),x)),
inference(spr,[status(thm),theory(equality)],[52,109]),
[iquote('0:SpR:52.0,109.0')] ).
cnf(1446,plain,
equal(ld(u,u),mult(v,ld(mult(v,v),v))),
inference(spr,[status(thm),theory(equality)],[3,234]),
[iquote('0:SpR:3.0,234.0')] ).
cnf(1547,plain,
equal(mult(u,mult(mult(v,v),mult(w,ld(mult(w,w),w)))),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[1446,31]),
[iquote('0:SpR:1446.0,31.0')] ).
cnf(1594,plain,
equal(ld(u,u),mult(mult(mult(v,v),mult(mult(v,v),v)),ld(mult(mult(v,v),mult(mult(mult(mult(v,v),v),mult(mult(v,v),v)),mult(v,v))),mult(mult(v,v),mult(mult(v,v),v))))),
inference(spr,[status(thm),theory(equality)],[28,1446]),
[iquote('0:SpR:28.0,1446.0')] ).
cnf(1601,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[3,1547,109]),
[iquote('0:Rew:3.0,1547.0,109.0,1547.0')] ).
cnf(1727,plain,
equal(ld(u,u),mult(rd(mult(mult(v,v),mult(v,mult(v,v))),mult(mult(mult(v,mult(v,v)),mult(v,mult(v,v))),mult(v,v))),mult(v,mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[585,1594,1601]),
[iquote('0:Rew:585.0,1594.0,1601.0,1594.0')] ).
cnf(1728,plain,
equal(ld(u,u),rd(mult(v,mult(v,mult(mult(v,v),v))),mult(mult(v,mult(v,v)),mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[43,1727,5]),
[iquote('0:Rew:43.0,1727.0,5.0,1727.0,5.0,1727.0')] ).
cnf(1729,plain,
equal(ld(u,u),rd(v,v)),
inference(rew,[status(thm),theory(equality)],[389,1728,1601]),
[iquote('0:Rew:389.0,1728.0,1601.0,1728.0,1601.0,1728.0')] ).
cnf(2162,plain,
equal(mult(ld(u,u),v),v),
inference(spr,[status(thm),theory(equality)],[1729,3]),
[iquote('0:SpR:1729.0,3.0')] ).
cnf(2164,plain,
equal(mult(ld(u,u),mult(mult(v,v),w)),mult(v,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[1729,32]),
[iquote('0:SpR:1729.0,32.0')] ).
cnf(2189,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[2162,2164]),
[iquote('0:Rew:2162.0,2164.0')] ).
cnf(2192,plain,
equal(mult(u,mult(v,mult(v,ld(v,w)))),mult(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[2189,31]),
[iquote('0:Rew:2189.0,31.0')] ).
cnf(2619,plain,
equal(mult(mult(u,v),w),mult(u,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[1,2192]),
[iquote('0:Rew:1.0,2192.0')] ).
cnf(2620,plain,
$false,
inference(unc,[status(thm)],[2619,6]),
[iquote('0:UnC:2619.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP756-1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n006.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 08:57:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.38/1.63
% 1.38/1.63 SPASS V 3.9
% 1.38/1.63 SPASS beiseite: Proof found.
% 1.38/1.63 % SZS status Theorem
% 1.38/1.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.38/1.63 SPASS derived 1726 clauses, backtracked 0 clauses, performed 0 splits and kept 790 clauses.
% 1.38/1.63 SPASS allocated 71784 KBytes.
% 1.38/1.63 SPASS spent 0:00:01.23 on the problem.
% 1.38/1.63 0:00:00.03 for the input.
% 1.38/1.63 0:00:00.00 for the FLOTTER CNF translation.
% 1.38/1.63 0:00:00.02 for inferences.
% 1.38/1.63 0:00:00.00 for the backtracking.
% 1.38/1.63 0:00:01.15 for the reduction.
% 1.38/1.63
% 1.38/1.63
% 1.38/1.63 Here is a proof with depth 6, length 31 :
% 1.38/1.63 % SZS output start Refutation
% See solution above
% 1.38/1.63 Formulae used in the proof : f01 f02 f03 f04 f05 goals
% 1.38/1.63
%------------------------------------------------------------------------------