%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 00:42:24 EDT 2022
% Result : Unsatisfiable 29.66s 29.86s
% Output : Refutation 29.66s
% 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; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(apply(apply(o,u),v),apply(v,apply(u,v))),
file('COL011-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(apply(q1,u),v),w),apply(u,apply(w,v))),
file('COL011-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(combinator,u),u),
file('COL011-1.p',unknown),
[] ).
cnf(6,plain,
equal(apply(apply(u,v),apply(apply(o,u),v)),apply(apply(o,v),apply(u,v))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(9,plain,
equal(apply(u,apply(apply(v,apply(apply(q1,u),w)),w)),apply(apply(o,v),apply(apply(q1,u),w))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(672,plain,
equal(apply(u,apply(v,apply(w,apply(apply(q1,u),w)))),apply(apply(o,apply(q1,v)),apply(apply(q1,u),w))),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(674,plain,
~ equal(apply(apply(u,apply(apply(q1,combinator),v)),v),apply(apply(o,u),apply(apply(q1,combinator),v))),
inference(spl,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpL:9.0,3.0')] ).
cnf(2616,plain,
~ equal(apply(u,apply(v,apply(apply(q1,combinator),v))),apply(apply(o,apply(q1,u)),apply(apply(q1,combinator),v))),
inference(spl,[status(thm),theory(equality)],[2,674]),
[iquote('0:SpL:2.0,674.0')] ).
cnf(10442,plain,
~ equal(apply(apply(o,apply(q1,u)),apply(apply(q1,combinator),v)),apply(u,apply(apply(o,apply(q1,combinator)),v))),
inference(spl,[status(thm),theory(equality)],[1,2616]),
[iquote('0:SpL:1.0,2616.0')] ).
cnf(14307,plain,
equal(apply(apply(apply(o,apply(q1,u)),apply(apply(q1,v),w)),apply(apply(o,v),apply(u,apply(w,apply(apply(q1,v),w))))),apply(apply(o,apply(u,apply(w,apply(apply(q1,v),w)))),apply(apply(o,apply(q1,u)),apply(apply(q1,v),w)))),
inference(spr,[status(thm),theory(equality)],[672,6]),
[iquote('0:SpR:672.0,6.0')] ).
cnf(14602,plain,
~ equal(apply(apply(o,apply(q1,u)),apply(apply(o,apply(q1,v)),apply(apply(q1,apply(q1,combinator)),w))),apply(u,apply(apply(o,apply(q1,combinator)),apply(v,apply(w,apply(apply(q1,apply(q1,combinator)),w)))))),
inference(spl,[status(thm),theory(equality)],[672,10442]),
[iquote('0:SpL:672.0,10442.0')] ).
cnf(14937,plain,
$false,
inference(unc,[status(thm)],[14307,14602]),
[iquote('0:UnC:14307.0,14602.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 08:35:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 29.66/29.86
% 29.66/29.86 SPASS V 3.9
% 29.66/29.86 SPASS beiseite: Proof found.
% 29.66/29.86 % SZS status Theorem
% 29.66/29.86 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.66/29.86 SPASS derived 8710 clauses, backtracked 0 clauses, performed 0 splits and kept 3109 clauses.
% 29.66/29.86 SPASS allocated 104795 KBytes.
% 29.66/29.86 SPASS spent 0:0:29.20 on the problem.
% 29.66/29.86 0:00:00.03 for the input.
% 29.66/29.86 0:00:00.00 for the FLOTTER CNF translation.
% 29.66/29.86 0:00:00.22 for inferences.
% 29.66/29.86 0:00:00.00 for the backtracking.
% 29.66/29.86 0:0:28.91 for the reduction.
% 29.66/29.86
% 29.66/29.86
% 29.66/29.86 Here is a proof with depth 5, length 12 :
% 29.66/29.86 % SZS output start Refutation
% See solution above
% 29.66/29.86 Formulae used in the proof : o_definition q1_definition prove_fixed_point
% 29.66/29.86
%------------------------------------------------------------------------------