TSTP Solution File: GRP747+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:49:15 EDT 2022
% Result : Theorem 11.79s 12.02s
% Output : Refutation 11.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 59 ( 40 unt; 9 nHn; 59 RR)
% Number of literals : 78 ( 0 equ; 15 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 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,unit),u),
file('GRP747+1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(unit,u),u),
file('GRP747+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP747+1.p',unknown),
[] ).
cnf(4,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP747+1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(rd(u,v),v),u),
file('GRP747+1.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(u,v),v),u),
file('GRP747+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(mult(mult(a,b),c),mult(a,mult(b,c))),
file('GRP747+1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(mult(v,w),v))),
file('GRP747+1.p',unknown),
[] ).
cnf(9,axiom,
( equal(mult(mult(u,v),w),mult(mult(u,w),v))
| skP0(w,v,u) ),
file('GRP747+1.p',unknown),
[] ).
cnf(10,axiom,
( equal(mult(u,mult(v,w)),mult(u,mult(w,v)))
| skP0(w,v,u) ),
file('GRP747+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ skP0(u,v,w)
| equal(mult(mult(w,v),u),mult(w,mult(u,v))) ),
file('GRP747+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ skP0(u,v,w)
| equal(mult(mult(w,u),v),mult(w,mult(v,u))) ),
file('GRP747+1.p',unknown),
[] ).
cnf(66,plain,
equal(mult(u,mult(mult(v,unit),v)),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(67,plain,
equal(mult(u,mult(mult(v,ld(mult(u,v),w)),v)),mult(w,v)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(70,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1,66]),
[iquote('0:Rew:1.0,66.0')] ).
cnf(99,plain,
( equal(mult(mult(rd(u,v),w),v),mult(u,w))
| skP0(v,w,rd(u,v)) ),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(110,plain,
equal(rd(mult(u,mult(v,v)),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[70,6]),
[iquote('0:SpR:70.0,6.0')] ).
cnf(144,plain,
equal(mult(rd(u,mult(v,v)),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[5,110]),
[iquote('0:SpR:5.0,110.0')] ).
cnf(185,plain,
( skP0(u,v,w)
| equal(ld(w,mult(w,mult(u,v))),mult(v,u)) ),
inference(spr,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpR:10.0,4.0')] ).
cnf(247,plain,
( skP0(u,v,w)
| equal(mult(u,v),mult(v,u)) ),
inference(rew,[status(thm),theory(equality)],[4,185]),
[iquote('0:Rew:4.0,185.1')] ).
cnf(283,plain,
equal(rd(rd(u,v),v),rd(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[144,6]),
[iquote('0:SpR:144.0,6.0')] ).
cnf(382,plain,
( ~ skP0(u,v,unit)
| equal(mult(unit,mult(v,u)),mult(u,v)) ),
inference(spr,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpR:2.0,12.1')] ).
cnf(387,plain,
( ~ skP0(u,v,rd(w,u))
| equal(mult(rd(w,u),mult(v,u)),mult(w,v)) ),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.1')] ).
cnf(396,plain,
( ~ skP0(u,v,unit)
| equal(mult(v,u),mult(u,v)) ),
inference(rew,[status(thm),theory(equality)],[2,382]),
[iquote('0:Rew:2.0,382.1')] ).
cnf(397,plain,
equal(mult(u,v),mult(v,u)),
inference(mrr,[status(thm)],[396,247]),
[iquote('0:MRR:396.0,247.0')] ).
cnf(398,plain,
~ equal(mult(c,mult(a,b)),mult(a,mult(b,c))),
inference(rew,[status(thm),theory(equality)],[397,7]),
[iquote('0:Rew:397.0,7.0')] ).
cnf(400,plain,
equal(mult(u,mult(mult(v,u),w)),mult(v,mult(mult(u,w),u))),
inference(rew,[status(thm),theory(equality)],[397,8]),
[iquote('0:Rew:397.0,8.0')] ).
cnf(402,plain,
equal(mult(u,rd(v,u)),v),
inference(rew,[status(thm),theory(equality)],[397,5]),
[iquote('0:Rew:397.0,5.0')] ).
cnf(428,plain,
( equal(mult(u,mult(rd(v,u),w)),mult(v,w))
| skP0(u,w,rd(v,u)) ),
inference(rew,[status(thm),theory(equality)],[397,99]),
[iquote('0:Rew:397.0,99.0')] ).
cnf(438,plain,
equal(mult(u,mult(v,mult(v,ld(mult(u,v),w)))),mult(w,v)),
inference(rew,[status(thm),theory(equality)],[397,67]),
[iquote('0:Rew:397.0,67.0')] ).
cnf(459,plain,
equal(mult(u,mult(mult(v,u),w)),mult(v,mult(u,mult(u,w)))),
inference(rew,[status(thm),theory(equality)],[397,400]),
[iquote('0:Rew:397.0,400.0')] ).
cnf(599,plain,
equal(rd(u,v),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[402,4]),
[iquote('0:SpR:402.0,4.0')] ).
cnf(655,plain,
equal(rd(rd(u,v),v),ld(mult(v,v),u)),
inference(rew,[status(thm),theory(equality)],[599,283]),
[iquote('0:Rew:599.0,283.0')] ).
cnf(657,plain,
( ~ skP0(u,v,ld(u,w))
| equal(mult(rd(w,u),mult(v,u)),mult(w,v)) ),
inference(rew,[status(thm),theory(equality)],[599,387]),
[iquote('0:Rew:599.0,387.0')] ).
cnf(660,plain,
( equal(mult(u,mult(ld(u,v),w)),mult(v,w))
| skP0(u,w,rd(v,u)) ),
inference(rew,[status(thm),theory(equality)],[599,428]),
[iquote('0:Rew:599.0,428.0')] ).
cnf(685,plain,
equal(ld(mult(u,u),v),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[599,655]),
[iquote('0:Rew:599.0,655.0,599.0,655.0')] ).
cnf(699,plain,
( equal(mult(u,mult(ld(u,v),w)),mult(v,w))
| skP0(u,w,ld(u,v)) ),
inference(rew,[status(thm),theory(equality)],[599,660]),
[iquote('0:Rew:599.0,660.1')] ).
cnf(701,plain,
( ~ skP0(u,v,ld(u,w))
| equal(mult(ld(u,w),mult(v,u)),mult(w,v)) ),
inference(rew,[status(thm),theory(equality)],[599,657]),
[iquote('0:Rew:599.0,657.1')] ).
cnf(888,plain,
equal(mult(u,mult(mult(u,v),w)),mult(v,mult(u,mult(u,w)))),
inference(spr,[status(thm),theory(equality)],[397,459]),
[iquote('0:SpR:397.0,459.0')] ).
cnf(897,plain,
equal(mult(u,mult(v,mult(w,u))),mult(w,mult(u,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[397,459]),
[iquote('0:SpR:397.0,459.0')] ).
cnf(910,plain,
equal(mult(u,mult(mult(v,u),ld(u,w))),mult(v,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[3,459]),
[iquote('0:SpR:3.0,459.0')] ).
cnf(1631,plain,
equal(mult(u,mult(mult(v,u),mult(u,ld(mult(u,u),w)))),mult(v,mult(w,u))),
inference(spr,[status(thm),theory(equality)],[438,459]),
[iquote('0:SpR:438.0,459.0')] ).
cnf(1690,plain,
equal(mult(u,mult(mult(v,u),ld(u,w))),mult(v,mult(w,u))),
inference(rew,[status(thm),theory(equality)],[3,1631,685]),
[iquote('0:Rew:3.0,1631.0,685.0,1631.0')] ).
cnf(1691,plain,
equal(mult(u,mult(v,w)),mult(u,mult(w,v))),
inference(rew,[status(thm),theory(equality)],[910,1690]),
[iquote('0:Rew:910.0,1690.0')] ).
cnf(2082,plain,
equal(mult(mult(u,v),w),mult(w,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[1691,397]),
[iquote('0:SpR:1691.0,397.0')] ).
cnf(2239,plain,
( ~ skP0(u,v,w)
| equal(mult(u,mult(v,w)),mult(w,mult(u,v))) ),
inference(spr,[status(thm),theory(equality)],[2082,11]),
[iquote('0:SpR:2082.0,11.1')] ).
cnf(7236,plain,
equal(mult(u,mult(mult(u,v),ld(u,w))),mult(v,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[3,888]),
[iquote('0:SpR:3.0,888.0')] ).
cnf(7769,plain,
equal(mult(u,mult(ld(u,v),mult(w,u))),mult(w,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[3,897]),
[iquote('0:SpR:3.0,897.0')] ).
cnf(8123,plain,
( skP0(u,v,ld(u,w))
| equal(mult(u,mult(v,ld(u,w))),mult(w,v)) ),
inference(spr,[status(thm),theory(equality)],[699,1691]),
[iquote('0:SpR:699.0,1691.0')] ).
cnf(11825,plain,
( ~ skP0(u,v,ld(u,w))
| equal(mult(ld(u,w),mult(u,v)),mult(w,v)) ),
inference(spr,[status(thm),theory(equality)],[701,1691]),
[iquote('0:SpR:701.1,1691.0')] ).
cnf(11923,plain,
( ~ skP0(u,v,ld(u,w))
| equal(mult(u,mult(v,ld(u,w))),mult(w,v)) ),
inference(rew,[status(thm),theory(equality)],[2239,11825]),
[iquote('0:Rew:2239.1,11825.1')] ).
cnf(11924,plain,
equal(mult(u,mult(v,ld(u,w))),mult(w,v)),
inference(mrr,[status(thm)],[11923,8123]),
[iquote('0:MRR:11923.0,8123.0')] ).
cnf(11936,plain,
equal(mult(u,mult(v,w)),mult(w,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[11924,7236]),
[iquote('0:Rew:11924.0,7236.0')] ).
cnf(11946,plain,
~ equal(mult(b,mult(a,c)),mult(a,mult(b,c))),
inference(rew,[status(thm),theory(equality)],[11936,398]),
[iquote('0:Rew:11936.0,398.0')] ).
cnf(11955,plain,
equal(mult(u,mult(u,mult(v,ld(u,w)))),mult(v,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[11936,7769]),
[iquote('0:Rew:11936.0,7769.0')] ).
cnf(11991,plain,
equal(mult(u,mult(v,w)),mult(w,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[11924,11955]),
[iquote('0:Rew:11924.0,11955.0')] ).
cnf(11992,plain,
~ equal(mult(a,mult(c,b)),mult(a,mult(b,c))),
inference(rew,[status(thm),theory(equality)],[11991,11946]),
[iquote('0:Rew:11991.0,11946.0')] ).
cnf(12151,plain,
~ equal(mult(a,mult(b,c)),mult(a,mult(b,c))),
inference(rew,[status(thm),theory(equality)],[397,11992]),
[iquote('0:Rew:397.0,11992.0')] ).
cnf(12152,plain,
$false,
inference(obv,[status(thm),theory(equality)],[12151]),
[iquote('0:Obv:12151.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 07:26:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 11.79/12.02
% 11.79/12.02 SPASS V 3.9
% 11.79/12.02 SPASS beiseite: Proof found.
% 11.79/12.02 % SZS status Theorem
% 11.79/12.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.79/12.02 SPASS derived 8022 clauses, backtracked 0 clauses, performed 0 splits and kept 3475 clauses.
% 11.79/12.02 SPASS allocated 103069 KBytes.
% 11.79/12.02 SPASS spent 0:0:11.57 on the problem.
% 11.79/12.02 0:00:00.03 for the input.
% 11.79/12.02 0:00:00.02 for the FLOTTER CNF translation.
% 11.79/12.02 0:00:00.07 for inferences.
% 11.79/12.02 0:00:00.00 for the backtracking.
% 11.79/12.02 0:0:11.43 for the reduction.
% 11.79/12.02
% 11.79/12.02
% 11.79/12.02 Here is a proof with depth 4, length 59 :
% 11.79/12.02 % SZS output start Refutation
% See solution above
% 11.79/12.02 Formulae used in the proof : f05 f06 f01 f02 f03 f04 goals f07 f08
% 11.79/12.02
%------------------------------------------------------------------------------