%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL003-16 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 00:42:21 EDT 2022
% Result : Unsatisfiable 3.05s 3.23s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 14 RR)
% Number of literals : 14 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(apply(apply(apply(b,u),v),w),apply(u,apply(v,w))),
file('COL003-16.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(w__dfg,u),v),apply(apply(u,v),v)),
file('COL003-16.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(apply(b,apply(apply(b,apply(apply(b,apply(w__dfg,w__dfg)),w__dfg)),b)),b),strong_fixed_point),
file('COL003-16.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
file('COL003-16.p',unknown),
[] ).
cnf(6,plain,
equal(apply(apply(w__dfg,w__dfg),u),apply(apply(u,u),u)),
inference(spr,[status(thm),theory(equality)],[2]),
[iquote('0:SpR:2.0,2.0')] ).
cnf(26,plain,
equal(apply(apply(w__dfg,apply(b,u)),v),apply(u,apply(v,v))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(34,plain,
equal(apply(apply(apply(b,apply(apply(b,apply(w__dfg,w__dfg)),w__dfg)),b),apply(b,u)),apply(strong_fixed_point,u)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(36,plain,
equal(apply(apply(w__dfg,w__dfg),apply(w__dfg,apply(b,apply(b,u)))),apply(strong_fixed_point,u)),
inference(rew,[status(thm),theory(equality)],[1,34]),
[iquote('0:Rew:1.0,34.0,1.0,34.0')] ).
cnf(40,plain,
equal(apply(apply(w__dfg,apply(w__dfg,apply(b,u))),v),apply(apply(u,apply(v,v)),v)),
inference(spr,[status(thm),theory(equality)],[26,2]),
[iquote('0:SpR:26.0,2.0')] ).
cnf(488,plain,
equal(apply(apply(w__dfg,apply(w__dfg,apply(b,apply(b,u)))),v),apply(u,apply(apply(v,v),v))),
inference(spr,[status(thm),theory(equality)],[40,1]),
[iquote('0:SpR:40.0,1.0')] ).
cnf(3778,plain,
equal(apply(apply(w__dfg,apply(w__dfg,apply(b,apply(b,u)))),v),apply(u,apply(apply(w__dfg,w__dfg),v))),
inference(spr,[status(thm),theory(equality)],[6,488]),
[iquote('0:SpR:6.0,488.0')] ).
cnf(5494,plain,
equal(apply(u,apply(apply(w__dfg,w__dfg),apply(w__dfg,apply(b,apply(b,u))))),apply(apply(w__dfg,w__dfg),apply(w__dfg,apply(b,apply(b,u))))),
inference(spr,[status(thm),theory(equality)],[3778,2]),
[iquote('0:SpR:3778.0,2.0')] ).
cnf(5545,plain,
equal(apply(u,apply(strong_fixed_point,u)),apply(strong_fixed_point,u)),
inference(rew,[status(thm),theory(equality)],[36,5494]),
[iquote('0:Rew:36.0,5494.0')] ).
cnf(5546,plain,
$false,
inference(unc,[status(thm)],[5545,4]),
[iquote('0:UnC:5545.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL003-16 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 14:46:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.05/3.23
% 3.05/3.23 SPASS V 3.9
% 3.05/3.23 SPASS beiseite: Proof found.
% 3.05/3.23 % SZS status Theorem
% 3.05/3.23 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.05/3.23 SPASS derived 3021 clauses, backtracked 0 clauses, performed 0 splits and kept 1121 clauses.
% 3.05/3.23 SPASS allocated 73769 KBytes.
% 3.05/3.23 SPASS spent 0:00:02.84 on the problem.
% 3.05/3.23 0:00:00.04 for the input.
% 3.05/3.23 0:00:00.00 for the FLOTTER CNF translation.
% 3.05/3.23 0:00:00.07 for inferences.
% 3.05/3.23 0:00:00.00 for the backtracking.
% 3.05/3.23 0:00:02.71 for the reduction.
% 3.05/3.23
% 3.05/3.23
% 3.05/3.23 Here is a proof with depth 5, length 14 :
% 3.05/3.23 % SZS output start Refutation
% See solution above
% 3.05/3.23 Formulae used in the proof : b_definition w_definition strong_fixed_point prove_strong_fixed_point
% 3.05/3.23
%------------------------------------------------------------------------------