%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWV052-1.002.001 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 19:15:36 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 12 unt; 6 nHn; 18 RR)
% Number of literals : 24 ( 0 equ; 1 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( equal(u,i)
| equal(u,o) ),
file('HWV052-1.002.001.p',unknown),
[] ).
cnf(2,axiom,
~ equal(inv(u),u),
file('HWV052-1.002.001.p',unknown),
[] ).
cnf(3,axiom,
equal(unpack1(u,v,pack1(u,v)),u),
file('HWV052-1.002.001.p',unknown),
[] ).
cnf(4,axiom,
equal(unpack1(inv(u),v,pack1(u,v)),u),
file('HWV052-1.002.001.p',unknown),
[] ).
cnf(7,axiom,
equal(unpack2(u,v,pack1(u,v)),v),
file('HWV052-1.002.001.p',unknown),
[] ).
cnf(9,axiom,
equal(unpack2(u,inv(v),pack1(u,v)),v),
file('HWV052-1.002.001.p',unknown),
[] ).
cnf(10,axiom,
equal(unpack2(u,v,inv(pack1(u,v))),v),
file('HWV052-1.002.001.p',unknown),
[] ).
cnf(21,plain,
( equal(pack1(u,v),o)
| equal(unpack2(u,v,i),v) ),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(151,plain,
( equal(pack1(u,v),o)
| equal(unpack2(u,inv(v),i),v) ),
inference(spr,[status(thm),theory(equality)],[1,9]),
[iquote('0:SpR:1.0,9.0')] ).
cnf(180,plain,
( equal(inv(pack1(u,v)),o)
| equal(unpack2(u,v,i),v) ),
inference(spr,[status(thm),theory(equality)],[1,10]),
[iquote('0:SpR:1.0,10.0')] ).
cnf(184,plain,
( equal(inv(o),o)
| equal(unpack2(u,v,i),v) ),
inference(rew,[status(thm),theory(equality)],[21,180]),
[iquote('0:Rew:21.0,180.0')] ).
cnf(185,plain,
equal(unpack2(u,v,i),v),
inference(mrr,[status(thm)],[184,2]),
[iquote('0:MRR:184.0,2.0')] ).
cnf(186,plain,
( equal(pack1(u,v),o)
| equal(inv(v),v) ),
inference(rew,[status(thm),theory(equality)],[185,151]),
[iquote('0:Rew:185.0,151.1')] ).
cnf(187,plain,
equal(pack1(u,v),o),
inference(mrr,[status(thm)],[186,2]),
[iquote('0:MRR:186.1,2.0')] ).
cnf(189,plain,
equal(unpack1(u,v,o),u),
inference(rew,[status(thm),theory(equality)],[187,3]),
[iquote('0:Rew:187.0,3.0')] ).
cnf(191,plain,
equal(unpack1(inv(u),v,o),u),
inference(rew,[status(thm),theory(equality)],[187,4]),
[iquote('0:Rew:187.0,4.0')] ).
cnf(218,plain,
equal(inv(u),u),
inference(rew,[status(thm),theory(equality)],[189,191]),
[iquote('0:Rew:189.0,191.0')] ).
cnf(219,plain,
$false,
inference(mrr,[status(thm)],[218,2]),
[iquote('0:MRR:218.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : HWV052-1.002.001 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 17 06:24:12 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 171 clauses, backtracked 0 clauses, performed 0 splits and kept 76 clauses.
% 0.20/0.43 SPASS allocated 63268 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.04 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.02 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 1, length 18 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : bit_domain bit_inverse unpack1 unpack1_01 unpack2 unpack2_05 unpack2_06
% 0.20/0.43
%------------------------------------------------------------------------------