TSTP Solution File: GRP685+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:48:58 EDT 2022
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 28 unt; 0 nHn; 30 RR)
% Number of literals : 32 ( 0 equ; 5 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 : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ld(u,mult(u,u)),u),
file('GRP685+1.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP685+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP685+1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP685+1.p',unknown),
[] ).
cnf(5,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP685+1.p',unknown),
[] ).
cnf(6,axiom,
equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
file('GRP685+1.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
file('GRP685+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(rd(mult(skc9,rd(skc10,skc11)),rd(skc10,skc11)),rd(mult(skc9,skc11),skc11))
| ~ equal(rd(mult(skc6,ld(skc7,skc8)),ld(skc7,skc8)),rd(mult(skc6,skc8),skc8)) ),
file('GRP685+1.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)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(19,plain,
equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
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(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)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
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)],[27,7]),
[iquote('0:SpR:27.0,7.0')] ).
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(74,plain,
( ~ equal(rd(mult(skc9,skc11),skc11),rd(mult(skc9,skc11),skc11))
| ~ equal(rd(mult(skc6,ld(skc7,skc8)),ld(skc7,skc8)),rd(mult(skc6,skc8),skc8)) ),
inference(rew,[status(thm),theory(equality)],[73,8]),
[iquote('0:Rew:73.0,8.0')] ).
cnf(85,plain,
~ equal(rd(mult(skc6,ld(skc7,skc8)),ld(skc7,skc8)),rd(mult(skc6,skc8),skc8)),
inference(obv,[status(thm),theory(equality)],[74]),
[iquote('0:Obv:74.0')] ).
cnf(104,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(108,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[104,23]),
[iquote('0:Rew:104.0,23.0')] ).
cnf(141,plain,
equal(rd(mult(u,mult(v,w)),mult(v,w)),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[104,73]),
[iquote('0:SpR:104.0,73.0')] ).
cnf(280,plain,
equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(294,plain,
equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[280,108]),
[iquote('0:Rew:280.0,108.0')] ).
cnf(297,plain,
equal(mult(ld(u,u),v),ld(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[27,294]),
[iquote('0:Rew:27.0,294.0')] ).
cnf(500,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)],[297,141]),
[iquote('0:SpR:297.0,141.0')] ).
cnf(501,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)],[3,141]),
[iquote('0:SpR:3.0,141.0')] ).
cnf(515,plain,
equal(rd(mult(u,ld(v,w)),ld(v,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[500,501]),
[iquote('0:Rew:500.0,501.0')] ).
cnf(516,plain,
$false,
inference(unc,[status(thm)],[515,85]),
[iquote('0:UnC:515.0,85.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 06:14:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.51
% 0.21/0.51 SPASS V 3.9
% 0.21/0.51 SPASS beiseite: Proof found.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 SPASS derived 312 clauses, backtracked 0 clauses, performed 0 splits and kept 149 clauses.
% 0.21/0.51 SPASS allocated 86106 KBytes.
% 0.21/0.51 SPASS spent 0:00:00.15 on the problem.
% 0.21/0.51 0:00:00.04 for the input.
% 0.21/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.51 0:00:00.00 for inferences.
% 0.21/0.51 0:00:00.00 for the backtracking.
% 0.21/0.51 0:00:00.05 for the reduction.
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 Here is a proof with depth 5, length 30 :
% 0.21/0.51 % SZS output start Refutation
% See solution above
% 0.21/0.51 Formulae used in the proof : f01 f02 f03 f04 f07 f05 f06 goals
% 0.21/0.51
%------------------------------------------------------------------------------