TSTP Solution File: COL062-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL062-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 00:42:31 EDT 2022
% Result : Unsatisfiable 12.02s 12.19s
% Output : Refutation 12.02s
% 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 : 11 ( 3 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('COL062-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(t,u),v),apply(v,u)),
file('COL062-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(apply(apply(u,f(u)),g(u)),h(u)),apply(apply(f(u),h(u)),g(u))),
file('COL062-1.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(f(apply(apply(b,u),v)),h(apply(apply(b,u),v))),g(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(f(apply(apply(b,apply(t,v)),u)),h(apply(apply(b,apply(t,v)),u))),g(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(f(apply(apply(b,apply(t,w)),apply(apply(b,u),v))),h(apply(apply(b,apply(t,w)),apply(apply(b,u),v)))),g(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(f(apply(apply(b,apply(t,v)),apply(apply(b,b),u))),h(apply(apply(b,apply(t,v)),apply(apply(b,b),u)))),g(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(510,plain,
~ equal(apply(apply(apply(u,g(apply(apply(b,apply(t,u)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,u)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,u)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,u)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,u)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,u)),apply(apply(b,b),t))))),
inference(spl,[status(thm),theory(equality)],[2,260]),
[iquote('0:SpL:2.0,260.0')] ).
cnf(518,plain,
~ equal(apply(apply(apply(u,apply(v,g(apply(apply(b,apply(t,apply(apply(b,u),v))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,u),v))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,u),v))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,u),v))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,u),v))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,u),v))),apply(apply(b,b),t))))),
inference(spl,[status(thm),theory(equality)],[1,510]),
[iquote('0:SpL:1.0,510.0')] ).
cnf(2179,plain,
~ equal(apply(apply(u,g(apply(apply(b,apply(t,apply(apply(b,b),u))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),u))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),u))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),u))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),u))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),u))),apply(apply(b,b),t))))),
inference(spl,[status(thm),theory(equality)],[1,518]),
[iquote('0:SpL:1.0,518.0')] ).
cnf(2180,plain,
$false,
inference(unc,[status(thm)],[2179,2]),
[iquote('0:UnC:2179.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL062-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue May 31 13:17:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 12.02/12.19
% 12.02/12.19 SPASS V 3.9
% 12.02/12.19 SPASS beiseite: Proof found.
% 12.02/12.19 % SZS status Theorem
% 12.02/12.19 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.02/12.19 SPASS derived 2176 clauses, backtracked 0 clauses, performed 0 splits and kept 1663 clauses.
% 12.02/12.19 SPASS allocated 94832 KBytes.
% 12.02/12.19 SPASS spent 0:0:11.70 on the problem.
% 12.02/12.19 0:00:00.04 for the input.
% 12.02/12.19 0:00:00.00 for the FLOTTER CNF translation.
% 12.02/12.19 0:00:02.10 for inferences.
% 12.02/12.19 0:00:00.00 for the backtracking.
% 12.02/12.19 0:00:09.30 for the reduction.
% 12.02/12.19
% 12.02/12.19
% 12.02/12.19 Here is a proof with depth 7, length 11 :
% 12.02/12.19 % SZS output start Refutation
% See solution above
% 12.02/12.19 Formulae used in the proof : b_definition t_definition prove_c_combinator
% 12.02/12.19
%------------------------------------------------------------------------------