%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:48:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 16 ( 0 equ; 3 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP656-10.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP656-10.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP656-10.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(u,mult(v,w)),u),mult(mult(u,v),mult(w,u))),
file('GRP656-10.p',unknown),
[] ).
cnf(6,axiom,
~ equal(tuple(mult(u,x1__dfg(u)),mult(x1_2(u),u)),tuple(x1__dfg(u),x1_2(u))),
file('GRP656-10.p',unknown),
[] ).
cnf(17,plain,
equal(rd(mult(mult(u,v),mult(w,u)),u),mult(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(18,plain,
equal(ld(mult(u,mult(v,w)),mult(mult(u,v),mult(w,u))),u),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(37,plain,
equal(rd(mult(mult(u,v),w),u),mult(u,mult(v,rd(w,u)))),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(125,plain,
equal(mult(u,mult(v,rd(u,u))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[37,4]),
[iquote('0:SpR:37.0,4.0')] ).
cnf(147,plain,
equal(mult(u,rd(v,v)),ld(v,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[125,2]),
[iquote('0:SpR:125.0,2.0')] ).
cnf(162,plain,
equal(mult(u,rd(v,v)),u),
inference(rew,[status(thm),theory(equality)],[2,147]),
[iquote('0:Rew:2.0,147.0')] ).
cnf(243,plain,
equal(ld(mult(u,v),mult(mult(u,v),mult(rd(w,w),u))),u),
inference(spr,[status(thm),theory(equality)],[162,18]),
[iquote('0:SpR:162.0,18.0')] ).
cnf(247,plain,
~ equal(tuple(mult(rd(u,u),x1__dfg(rd(u,u))),x1_2(rd(u,u))),tuple(x1__dfg(rd(u,u)),x1_2(rd(u,u)))),
inference(spl,[status(thm),theory(equality)],[162,6]),
[iquote('0:SpL:162.0,6.0')] ).
cnf(278,plain,
equal(mult(rd(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2,243]),
[iquote('0:Rew:2.0,243.0')] ).
cnf(323,plain,
~ equal(tuple(x1__dfg(rd(u,u)),x1_2(rd(u,u))),tuple(x1__dfg(rd(u,u)),x1_2(rd(u,u)))),
inference(rew,[status(thm),theory(equality)],[278,247]),
[iquote('0:Rew:278.0,247.0')] ).
cnf(324,plain,
$false,
inference(obv,[status(thm),theory(equality)],[323]),
[iquote('0:Obv:323.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP656-10 : TPTP v8.1.0. Released v8.1.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.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 : Mon Jun 13 08:31:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 226 clauses, backtracked 0 clauses, performed 0 splits and kept 122 clauses.
% 0.19/0.49 SPASS allocated 63818 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.00 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.06 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 5, length 16 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : f02 f03 f04 f05 goal
% 0.19/0.49
%------------------------------------------------------------------------------