TSTP Solution File: COL063-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL063-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 00:42:32 EDT 2022
% Result : Unsatisfiable 42.12s 42.30s
% Output : Refutation 42.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 11 ( 0 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 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('COL063-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(t,u),v),apply(v,u)),
file('COL063-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(apply(apply(u,f(u)),g(u)),h(u)),apply(apply(h(u),g(u)),f(u))),
file('COL063-1.p',unknown),
[] ).
cnf(7,plain,
~ equal(apply(apply(apply(u,apply(v,f(apply(apply(b,u),v)))),g(apply(apply(b,u),v))),h(apply(apply(b,u),v))),apply(apply(h(apply(apply(b,u),v)),g(apply(apply(b,u),v))),f(apply(apply(b,u),v)))),
inference(spl,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpL:1.0,3.0')] ).
cnf(19,plain,
~ equal(apply(apply(apply(apply(u,f(apply(apply(b,apply(t,v)),u))),v),g(apply(apply(b,apply(t,v)),u))),h(apply(apply(b,apply(t,v)),u))),apply(apply(h(apply(apply(b,apply(t,v)),u)),g(apply(apply(b,apply(t,v)),u))),f(apply(apply(b,apply(t,v)),u)))),
inference(spl,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpL:2.0,7.0')] ).
cnf(57,plain,
~ equal(apply(apply(apply(apply(u,apply(v,f(apply(apply(b,apply(t,w)),apply(apply(b,u),v))))),w),g(apply(apply(b,apply(t,w)),apply(apply(b,u),v)))),h(apply(apply(b,apply(t,w)),apply(apply(b,u),v)))),apply(apply(h(apply(apply(b,apply(t,w)),apply(apply(b,u),v))),g(apply(apply(b,apply(t,w)),apply(apply(b,u),v)))),f(apply(apply(b,apply(t,w)),apply(apply(b,u),v))))),
inference(spl,[status(thm),theory(equality)],[1,19]),
[iquote('0:SpL:1.0,19.0')] ).
cnf(260,plain,
~ equal(apply(apply(apply(u,f(apply(apply(b,apply(t,v)),apply(apply(b,b),u)))),apply(v,g(apply(apply(b,apply(t,v)),apply(apply(b,b),u))))),h(apply(apply(b,apply(t,v)),apply(apply(b,b),u)))),apply(apply(h(apply(apply(b,apply(t,v)),apply(apply(b,b),u))),g(apply(apply(b,apply(t,v)),apply(apply(b,b),u)))),f(apply(apply(b,apply(t,v)),apply(apply(b,b),u))))),
inference(spl,[status(thm),theory(equality)],[1,57]),
[iquote('0:SpL:1.0,57.0')] ).
cnf(509,plain,
~ equal(apply(apply(apply(u,apply(v,f(apply(apply(b,apply(t,w)),apply(apply(b,b),apply(apply(b,u),v)))))),apply(w,g(apply(apply(b,apply(t,w)),apply(apply(b,b),apply(apply(b,u),v)))))),h(apply(apply(b,apply(t,w)),apply(apply(b,b),apply(apply(b,u),v))))),apply(apply(h(apply(apply(b,apply(t,w)),apply(apply(b,b),apply(apply(b,u),v)))),g(apply(apply(b,apply(t,w)),apply(apply(b,b),apply(apply(b,u),v))))),f(apply(apply(b,apply(t,w)),apply(apply(b,b),apply(apply(b,u),v)))))),
inference(spl,[status(thm),theory(equality)],[1,260]),
[iquote('0:SpL:1.0,260.0')] ).
cnf(3154,plain,
~ equal(apply(apply(u,f(apply(apply(b,apply(t,v)),apply(apply(b,b),apply(apply(b,b),u))))),apply(apply(v,g(apply(apply(b,apply(t,v)),apply(apply(b,b),apply(apply(b,b),u))))),h(apply(apply(b,apply(t,v)),apply(apply(b,b),apply(apply(b,b),u)))))),apply(apply(h(apply(apply(b,apply(t,v)),apply(apply(b,b),apply(apply(b,b),u)))),g(apply(apply(b,apply(t,v)),apply(apply(b,b),apply(apply(b,b),u))))),f(apply(apply(b,apply(t,v)),apply(apply(b,b),apply(apply(b,b),u)))))),
inference(spl,[status(thm),theory(equality)],[1,509]),
[iquote('0:SpL:1.0,509.0')] ).
cnf(3751,plain,
~ equal(apply(apply(u,f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),u))))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),u)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),u)))))),apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),u)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),u))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),u)))))),
inference(spl,[status(thm),theory(equality)],[2,3154]),
[iquote('0:SpL:2.0,3154.0')] ).
cnf(3757,plain,
$false,
inference(unc,[status(thm)],[3751,2]),
[iquote('0:UnC:3751.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COL063-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue May 31 06:19:47 EDT 2022
% 0.14/0.35 % CPUTime :
% 42.12/42.30
% 42.12/42.30 SPASS V 3.9
% 42.12/42.30 SPASS beiseite: Proof found.
% 42.12/42.30 % SZS status Theorem
% 42.12/42.30 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.12/42.30 SPASS derived 3753 clauses, backtracked 0 clauses, performed 0 splits and kept 2869 clauses.
% 42.12/42.30 SPASS allocated 118075 KBytes.
% 42.12/42.30 SPASS spent 0:0:41.60 on the problem.
% 42.12/42.30 0:00:00.04 for the input.
% 42.12/42.30 0:00:00.00 for the FLOTTER CNF translation.
% 42.12/42.30 0:00:06.88 for inferences.
% 42.12/42.30 0:00:00.00 for the backtracking.
% 42.12/42.30 0:0:33.98 for the reduction.
% 42.12/42.30
% 42.12/42.30
% 42.12/42.30 Here is a proof with depth 7, length 11 :
% 42.12/42.30 % SZS output start Refutation
% See solution above
% 42.12/42.30 Formulae used in the proof : b_definition t_definition prove_f_combinator
% 42.12/42.30
%------------------------------------------------------------------------------