%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL003-18 : TPTP v8.1.0. Released v2.1.0.
% 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 : Fri Jul 15 00:42:21 EDT 2022
% Result : Unsatisfiable 90.89s 91.09s
% Output : Refutation 90.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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('COL003-18.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(w__dfg,u),v),apply(apply(u,v),v)),
file('COL003-18.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(apply(b,apply(apply(b,apply(w__dfg,w__dfg)),apply(b,w__dfg))),apply(apply(b,b),b)),strong_fixed_point),
file('COL003-18.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
file('COL003-18.p',unknown),
[] ).
cnf(5,plain,
equal(apply(apply(apply(u,v),v),v),apply(apply(w__dfg,apply(w__dfg,u)),v)),
inference(spr,[status(thm),theory(equality)],[2]),
[iquote('0:SpR:2.0,2.0')] ).
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(11,plain,
equal(apply(apply(w__dfg,apply(u,v)),v),apply(apply(w__dfg,apply(w__dfg,u)),v)),
inference(rew,[status(thm),theory(equality)],[2,5]),
[iquote('0:Rew:2.0,5.0')] ).
cnf(25,plain,
equal(apply(apply(w__dfg,apply(apply(b,u),v)),w),apply(apply(u,apply(v,w)),w)),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
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(35,plain,
equal(apply(apply(apply(b,apply(w__dfg,w__dfg)),apply(b,w__dfg)),apply(apply(apply(b,b),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(apply(b,w__dfg),apply(b,apply(b,u)))),apply(strong_fixed_point,u)),
inference(rew,[status(thm),theory(equality)],[1,35]),
[iquote('0:Rew:1.0,35.0,1.0,35.0')] ).
cnf(38,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(304,plain,
equal(apply(apply(w__dfg,apply(apply(b,w__dfg),u)),v),apply(apply(w__dfg,apply(w__dfg,u)),v)),
inference(spr,[status(thm),theory(equality)],[25,11]),
[iquote('0:SpR:25.0,11.0')] ).
cnf(431,plain,
equal(apply(apply(w__dfg,apply(w__dfg,u)),apply(apply(b,w__dfg),u)),apply(apply(w__dfg,w__dfg),apply(apply(b,w__dfg),u))),
inference(spr,[status(thm),theory(equality)],[304,2]),
[iquote('0:SpR:304.0,2.0')] ).
cnf(485,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)],[38,1]),
[iquote('0:SpR:38.0,1.0')] ).
cnf(3788,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)],[6,485]),
[iquote('0:SpR:6.0,485.0')] ).
cnf(35827,plain,
equal(apply(u,apply(apply(w__dfg,w__dfg),apply(apply(b,w__dfg),apply(b,apply(b,u))))),apply(apply(w__dfg,w__dfg),apply(apply(b,w__dfg),apply(b,apply(b,u))))),
inference(spr,[status(thm),theory(equality)],[431,3788]),
[iquote('0:SpR:431.0,3788.0')] ).
cnf(35908,plain,
equal(apply(u,apply(strong_fixed_point,u)),apply(strong_fixed_point,u)),
inference(rew,[status(thm),theory(equality)],[36,35827]),
[iquote('0:Rew:36.0,35827.0')] ).
cnf(35909,plain,
$false,
inference(unc,[status(thm)],[35908,4]),
[iquote('0:UnC:35908.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL003-18 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n019.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 May 31 09:46:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 90.89/91.09
% 90.89/91.09 SPASS V 3.9
% 90.89/91.09 SPASS beiseite: Proof found.
% 90.89/91.09 % SZS status Theorem
% 90.89/91.09 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 90.89/91.09 SPASS derived 19011 clauses, backtracked 0 clauses, performed 0 splits and kept 5704 clauses.
% 90.89/91.09 SPASS allocated 124601 KBytes.
% 90.89/91.09 SPASS spent 0:1:30.21 on the problem.
% 90.89/91.09 0:00:00.03 for the input.
% 90.89/91.09 0:00:00.00 for the FLOTTER CNF translation.
% 90.89/91.09 0:00:00.38 for inferences.
% 90.89/91.09 0:00:00.00 for the backtracking.
% 90.89/91.09 0:1:29.76 for the reduction.
% 90.89/91.09
% 90.89/91.09
% 90.89/91.09 Here is a proof with depth 5, length 19 :
% 90.89/91.09 % SZS output start Refutation
% See solution above
% 90.89/91.09 Formulae used in the proof : b_definition w_definition strong_fixed_point prove_strong_fixed_point
% 90.89/91.09
%------------------------------------------------------------------------------