%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL066-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 00:42:34 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 0 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(apply(apply(apply(q,u),v),w),apply(v,apply(u,w))),
file('COL066-2.p',unknown),
[] ).
cnf(3,axiom,
equal(apply(apply(w__dfg,u),v),apply(apply(u,v),v)),
file('COL066-2.p',unknown),
[] ).
cnf(4,axiom,
~ equal(apply(apply(apply(apply(apply(apply(q,q),apply(w__dfg,apply(q,apply(q,q)))),x__dfg),y__dfg),y__dfg),z__dfg),apply(apply(x__dfg,y__dfg),apply(apply(x__dfg,y__dfg),z__dfg))),
file('COL066-2.p',unknown),
[] ).
cnf(5,plain,
~ equal(apply(apply(apply(w__dfg,apply(apply(w__dfg,apply(q,apply(q,q))),apply(q,x__dfg))),y__dfg),z__dfg),apply(apply(x__dfg,y__dfg),apply(apply(x__dfg,y__dfg),z__dfg))),
inference(rew,[status(thm),theory(equality)],[3,4,2]),
[iquote('0:Rew:3.0,4.0,2.0,4.0')] ).
cnf(26,plain,
equal(apply(apply(w__dfg,apply(apply(q,u),v)),w),apply(apply(v,apply(u,w)),w)),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(27,plain,
equal(apply(apply(w__dfg,apply(q,u)),v),apply(v,apply(u,v))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(31,plain,
equal(apply(apply(apply(w__dfg,q),u),v),apply(u,apply(u,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(32,plain,
~ equal(apply(apply(apply(w__dfg,apply(apply(q,x__dfg),apply(apply(q,q),apply(q,x__dfg)))),y__dfg),z__dfg),apply(apply(x__dfg,y__dfg),apply(apply(x__dfg,y__dfg),z__dfg))),
inference(rew,[status(thm),theory(equality)],[27,5]),
[iquote('0:Rew:27.0,5.0')] ).
cnf(35,plain,
~ equal(apply(apply(apply(apply(apply(q,q),apply(q,x__dfg)),apply(x__dfg,y__dfg)),y__dfg),z__dfg),apply(apply(x__dfg,y__dfg),apply(apply(x__dfg,y__dfg),z__dfg))),
inference(rew,[status(thm),theory(equality)],[26,32]),
[iquote('0:Rew:26.0,32.0')] ).
cnf(36,plain,
~ equal(apply(apply(apply(w__dfg,q),apply(x__dfg,y__dfg)),z__dfg),apply(apply(x__dfg,y__dfg),apply(apply(x__dfg,y__dfg),z__dfg))),
inference(rew,[status(thm),theory(equality)],[3,35,2]),
[iquote('0:Rew:3.0,35.0,2.0,35.0,2.0,35.0')] ).
cnf(37,plain,
~ equal(apply(apply(x__dfg,y__dfg),apply(apply(x__dfg,y__dfg),z__dfg)),apply(apply(x__dfg,y__dfg),apply(apply(x__dfg,y__dfg),z__dfg))),
inference(rew,[status(thm),theory(equality)],[31,36]),
[iquote('0:Rew:31.0,36.0')] ).
cnf(38,plain,
$false,
inference(obv,[status(thm),theory(equality)],[37]),
[iquote('0:Obv:37.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL066-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 04:19:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 23 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.18/0.40 SPASS allocated 63160 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 1, length 12 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.40 Formulae used in the proof : q_definition w_definition prove_p_combinator
% 0.18/0.40
%------------------------------------------------------------------------------