TSTP Solution File: GRP682-11 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP682-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:48:56 EDT 2022
% Result : Unsatisfiable 0.55s 0.72s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 47 RR)
% Number of literals : 47 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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(ld(u,mult(u,u)),u),
file('GRP682-11.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP682-11.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP682-11.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP682-11.p',unknown),
[] ).
cnf(5,axiom,
equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
file('GRP682-11.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
file('GRP682-11.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP682-11.p',unknown),
[] ).
cnf(8,axiom,
~ equal(ld(rd(x0__dfg,x1__dfg),mult(rd(x0__dfg,x1__dfg),x2__dfg)),ld(x0__dfg,mult(x0__dfg,x2__dfg))),
file('GRP682-11.p',unknown),
[] ).
cnf(17,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(rd(u,u),v),v),v)),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(19,plain,
equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(20,plain,
equal(rd(u,u),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[2,19,1,3]),
[iquote('0:Rew:2.0,19.0,1.0,19.0,3.0,19.0')] ).
cnf(21,plain,
equal(rd(mult(ld(u,u),v),v),ld(u,mult(u,ld(v,v)))),
inference(rew,[status(thm),theory(equality)],[20,7]),
[iquote('0:Rew:20.0,7.0')] ).
cnf(23,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(ld(u,u),v),v),v)),
inference(rew,[status(thm),theory(equality)],[20,17]),
[iquote('0:Rew:20.0,17.0')] ).
cnf(25,plain,
equal(mult(ld(u,u),u),rd(mult(u,u),u)),
inference(spr,[status(thm),theory(equality)],[20,4]),
[iquote('0:SpR:20.0,4.0')] ).
cnf(27,plain,
equal(mult(ld(u,u),u),u),
inference(rew,[status(thm),theory(equality)],[2,25]),
[iquote('0:Rew:2.0,25.0')] ).
cnf(53,plain,
equal(mult(u,rd(mult(v,w),w)),rd(mult(mult(u,v),w),w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(65,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),mult(ld(u,u),rd(mult(u,w),w))),
inference(spr,[status(thm),theory(equality)],[27,6]),
[iquote('0:SpR:27.0,6.0')] ).
cnf(72,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(mult(ld(u,u),u),w),w)),
inference(rew,[status(thm),theory(equality)],[53,65]),
[iquote('0:Rew:53.0,65.0')] ).
cnf(73,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[27,72]),
[iquote('0:Rew:27.0,72.0')] ).
cnf(102,plain,
equal(rd(mult(mult(u,v),v),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[2,53]),
[iquote('0:SpR:2.0,53.0')] ).
cnf(105,plain,
equal(mult(u,ld(v,mult(v,ld(w,w)))),rd(mult(mult(u,ld(v,v)),w),w)),
inference(spr,[status(thm),theory(equality)],[21,53]),
[iquote('0:SpR:21.0,53.0')] ).
cnf(106,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[102,23]),
[iquote('0:Rew:102.0,23.0')] ).
cnf(130,plain,
equal(rd(mult(rd(u,v),v),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[73,2]),
[iquote('0:SpR:73.0,2.0')] ).
cnf(139,plain,
equal(rd(mult(u,mult(v,w)),mult(v,w)),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[102,73]),
[iquote('0:SpR:102.0,73.0')] ).
cnf(148,plain,
equal(rd(rd(mult(u,v),v),v),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[4,130]),
[iquote('0:Rew:4.0,130.0')] ).
cnf(177,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),mult(ld(u,mult(u,ld(w,w))),w)),
inference(spr,[status(thm),theory(equality)],[27,5]),
[iquote('0:SpR:27.0,5.0')] ).
cnf(178,plain,
equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(191,plain,
equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[178,106]),
[iquote('0:Rew:178.0,106.0')] ).
cnf(192,plain,
equal(mult(ld(u,u),v),ld(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[27,191]),
[iquote('0:Rew:27.0,191.0')] ).
cnf(198,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,ld(w,mult(w,w))))),
inference(rew,[status(thm),theory(equality)],[192,177,178]),
[iquote('0:Rew:192.0,177.0,178.0,177.0')] ).
cnf(199,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1,198]),
[iquote('0:Rew:1.0,198.0')] ).
cnf(398,plain,
equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[192,139]),
[iquote('0:SpR:192.0,139.0')] ).
cnf(399,plain,
equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,ld(v,w)),ld(v,w))),
inference(spr,[status(thm),theory(equality)],[3,139]),
[iquote('0:SpR:3.0,139.0')] ).
cnf(412,plain,
equal(rd(mult(u,ld(v,w)),ld(v,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[398,399]),
[iquote('0:Rew:398.0,399.0')] ).
cnf(470,plain,
equal(ld(u,mult(u,mult(u,v))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[1,178]),
[iquote('0:SpR:1.0,178.0')] ).
cnf(796,plain,
equal(ld(mult(u,v),mult(mult(u,v),w)),ld(u,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[470,199]),
[iquote('0:SpR:470.0,199.0')] ).
cnf(1243,plain,
equal(rd(rd(mult(u,v),v),ld(w,v)),rd(u,ld(w,v))),
inference(spr,[status(thm),theory(equality)],[412,148]),
[iquote('0:SpR:412.0,148.0')] ).
cnf(1454,plain,
equal(rd(mult(mult(u,ld(u,u)),v),v),ld(u,mult(u,mult(u,ld(v,v))))),
inference(spr,[status(thm),theory(equality)],[105,3]),
[iquote('0:SpR:105.0,3.0')] ).
cnf(1486,plain,
equal(mult(u,ld(v,v)),rd(mult(u,v),v)),
inference(rew,[status(thm),theory(equality)],[1,1454,3,470]),
[iquote('0:Rew:1.0,1454.0,3.0,1454.0,470.0,1454.0')] ).
cnf(1616,plain,
equal(rd(rd(mult(u,v),v),ld(v,v)),rd(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[1486,412]),
[iquote('0:SpR:1486.0,412.0')] ).
cnf(1644,plain,
equal(rd(mult(u,v),v),rd(u,ld(v,v))),
inference(rew,[status(thm),theory(equality)],[1243,1616]),
[iquote('0:Rew:1243.0,1616.0')] ).
cnf(1657,plain,
equal(mult(rd(u,v),v),rd(u,ld(v,v))),
inference(rew,[status(thm),theory(equality)],[1644,4]),
[iquote('0:Rew:1644.0,4.0')] ).
cnf(1664,plain,
equal(mult(u,ld(v,v)),rd(u,ld(v,v))),
inference(rew,[status(thm),theory(equality)],[1644,1486]),
[iquote('0:Rew:1644.0,1486.0')] ).
cnf(2116,plain,
equal(ld(rd(u,ld(v,v)),mult(rd(u,ld(v,v)),w)),ld(u,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[1664,796]),
[iquote('0:SpR:1664.0,796.0')] ).
cnf(2129,plain,
equal(ld(rd(u,ld(v,v)),mult(rd(u,ld(v,v)),w)),ld(rd(u,v),mult(rd(u,v),w))),
inference(spr,[status(thm),theory(equality)],[1657,796]),
[iquote('0:SpR:1657.0,796.0')] ).
cnf(2138,plain,
equal(ld(rd(u,v),mult(rd(u,v),w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[2116,2129]),
[iquote('0:Rew:2116.0,2129.0')] ).
cnf(2139,plain,
$false,
inference(unc,[status(thm)],[2138,8]),
[iquote('0:UnC:2138.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP682-11 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.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 : Tue Jun 14 07:41:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.72
% 0.55/0.72 SPASS V 3.9
% 0.55/0.72 SPASS beiseite: Proof found.
% 0.55/0.72 % SZS status Theorem
% 0.55/0.72 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.72 SPASS derived 1299 clauses, backtracked 0 clauses, performed 0 splits and kept 506 clauses.
% 0.55/0.72 SPASS allocated 66544 KBytes.
% 0.55/0.72 SPASS spent 0:00:00.35 on the problem.
% 0.55/0.72 0:00:00.04 for the input.
% 0.55/0.72 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.72 0:00:00.01 for inferences.
% 0.55/0.72 0:00:00.00 for the backtracking.
% 0.55/0.72 0:00:00.28 for the reduction.
% 0.55/0.72
% 0.55/0.72
% 0.55/0.72 Here is a proof with depth 6, length 47 :
% 0.55/0.72 % SZS output start Refutation
% See solution above
% 0.55/0.72 Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 goal
% 0.55/0.72
%------------------------------------------------------------------------------