%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Fri Jul 15 00:07:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 6 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(domain__dfg(domain__dfg(a)),domain__dfg(a)),
file('CAT011-1.p',unknown),
[] ).
cnf(11,axiom,
identity_map(domain__dfg(u)),
file('CAT011-1.p',unknown),
[] ).
cnf(13,axiom,
defined(u,domain__dfg(u)),
file('CAT011-1.p',unknown),
[] ).
cnf(15,axiom,
product(u,domain__dfg(u),u),
file('CAT011-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ identity_map(u)
| ~ defined(u,v)
| product(u,v,v) ),
file('CAT011-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT011-1.p',unknown),
[] ).
cnf(38,plain,
( ~ product(u,domain__dfg(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[15,19]),
[iquote('0:Res:15.0,19.0')] ).
cnf(180,plain,
( ~ identity_map(u)
| ~ defined(u,domain__dfg(u))
| equal(domain__dfg(u),u) ),
inference(res,[status(thm),theory(equality)],[17,38]),
[iquote('0:Res:17.2,38.0')] ).
cnf(183,plain,
( ~ identity_map(u)
| equal(domain__dfg(u),u) ),
inference(mrr,[status(thm)],[180,13]),
[iquote('0:MRR:180.1,13.0')] ).
cnf(238,plain,
( ~ identity_map(domain__dfg(a))
| ~ equal(domain__dfg(a),domain__dfg(a)) ),
inference(spl,[status(thm),theory(equality)],[183,1]),
[iquote('0:SpL:183.1,1.0')] ).
cnf(245,plain,
~ identity_map(domain__dfg(a)),
inference(obv,[status(thm),theory(equality)],[238]),
[iquote('0:Obv:238.1')] ).
cnf(246,plain,
$false,
inference(ssi,[status(thm)],[245,11]),
[iquote('0:SSi:245.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CAT011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 21:43:24 EDT 2022
% 0.13/0.34 % 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 194 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses.
% 0.20/0.43 SPASS allocated 75803 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 0:00:00.01 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 3, length 12 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : prove_domain_is_idempotent domain_is_an_identity_map mapping_from_x_to_its_domain product_on_domain identity1 composition_is_well_defined
% 0.20/0.43
%------------------------------------------------------------------------------