%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL003-19 : 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 00:42:22 EDT 2022
% Result : Unsatisfiable 86.55s 86.72s
% Output : Refutation 86.55s
% 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 : 7 ( 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('COL003-19.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(w__dfg,u),v),apply(apply(u,v),v)),
file('COL003-19.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(apply(b,apply(apply(b,apply(w__dfg,w__dfg)),apply(apply(b,apply(b,w__dfg)),b))),b),strong_fixed_point),
file('COL003-19.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
file('COL003-19.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(34,plain,
equal(apply(apply(apply(b,apply(w__dfg,w__dfg)),apply(apply(b,apply(b,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(apply(b,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(309,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(435,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)],[309,2]),
[iquote('0:SpR:309.0,2.0')] ).
cnf(489,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(3777,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)],[6,489]),
[iquote('0:SpR:6.0,489.0')] ).
cnf(35781,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)],[435,3777]),
[iquote('0:SpR:435.0,3777.0')] ).
cnf(35862,plain,
equal(apply(u,apply(strong_fixed_point,u)),apply(strong_fixed_point,u)),
inference(rew,[status(thm),theory(equality)],[36,35781]),
[iquote('0:Rew:36.0,35781.0')] ).
cnf(35863,plain,
$false,
inference(unc,[status(thm)],[35862,4]),
[iquote('0:UnC:35862.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL003-19 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 15:48:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 86.55/86.72
% 86.55/86.72 SPASS V 3.9
% 86.55/86.72 SPASS beiseite: Proof found.
% 86.55/86.72 % SZS status Theorem
% 86.55/86.72 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 86.55/86.72 SPASS derived 19003 clauses, backtracked 0 clauses, performed 0 splits and kept 5698 clauses.
% 86.55/86.72 SPASS allocated 125185 KBytes.
% 86.55/86.72 SPASS spent 0:1:25.86 on the problem.
% 86.55/86.72 0:00:00.03 for the input.
% 86.55/86.72 0:00:00.00 for the FLOTTER CNF translation.
% 86.55/86.72 0:00:00.36 for inferences.
% 86.55/86.72 0:00:00.00 for the backtracking.
% 86.55/86.72 0:1:25.44 for the reduction.
% 86.55/86.72
% 86.55/86.72
% 86.55/86.72 Here is a proof with depth 5, length 19 :
% 86.55/86.72 % SZS output start Refutation
% See solution above
% 86.55/86.72 Formulae used in the proof : b_definition w_definition strong_fixed_point prove_strong_fixed_point
% 86.55/86.72
%------------------------------------------------------------------------------