%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 00:42:23 EDT 2022
% Result : Unsatisfiable 3.15s 3.33s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 3 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(apply(apply(apply(s,u),v),w),apply(apply(u,w),apply(v,w))),
file('COL006-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(k,u),v),u),
file('COL006-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(f(u),apply(u,f(u))),apply(u,f(u))),
file('COL006-1.p',unknown),
[] ).
cnf(7,plain,
equal(apply(apply(apply(s,apply(apply(s,u),v)),w),x),apply(apply(apply(u,x),apply(v,x)),apply(w,x))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(9,plain,
equal(apply(apply(apply(s,k),u),v),v),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(10,plain,
equal(apply(apply(apply(apply(s,s),u),v),w),apply(apply(v,w),apply(apply(u,v),w))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(14,plain,
equal(apply(apply(apply(s,u),apply(k,v)),w),apply(apply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(15,plain,
equal(apply(apply(apply(s,apply(k,u)),v),w),apply(u,apply(v,w))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(17,plain,
equal(apply(apply(apply(s,apply(s,k)),u),v),apply(u,v)),
inference(spr,[status(thm),theory(equality)],[9,1]),
[iquote('0:SpR:9.0,1.0')] ).
cnf(23,plain,
equal(apply(apply(apply(s,apply(s,apply(s,k))),u),v),apply(v,apply(u,v))),
inference(spr,[status(thm),theory(equality)],[17,1]),
[iquote('0:SpR:17.0,1.0')] ).
cnf(63,plain,
equal(apply(apply(apply(s,apply(s,apply(k,u))),v),w),apply(u,apply(w,apply(v,w)))),
inference(spr,[status(thm),theory(equality)],[15,1]),
[iquote('0:SpR:15.0,1.0')] ).
cnf(112,plain,
equal(apply(apply(apply(apply(s,s),apply(s,k)),u),v),apply(apply(u,v),v)),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(259,plain,
equal(apply(apply(apply(s,apply(apply(s,u),v)),apply(k,w)),x),apply(apply(apply(u,x),apply(v,x)),w)),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(319,plain,
equal(apply(apply(apply(apply(s,u),v),w),x),apply(apply(apply(u,w),apply(v,w)),x)),
inference(rew,[status(thm),theory(equality)],[14,259]),
[iquote('0:Rew:14.0,259.0')] ).
cnf(424,plain,
~ equal(apply(apply(apply(s,apply(s,apply(s,k))),u),f(u)),apply(u,f(u))),
inference(spl,[status(thm),theory(equality)],[23,3]),
[iquote('0:SpL:23.0,3.0')] ).
cnf(789,plain,
equal(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(s,k))),u),apply(u,u)),
inference(spr,[status(thm),theory(equality)],[112,17]),
[iquote('0:SpR:112.0,17.0')] ).
cnf(857,plain,
equal(apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),u),apply(u,u)),
inference(rew,[status(thm),theory(equality)],[1,789]),
[iquote('0:Rew:1.0,789.0')] ).
cnf(2141,plain,
~ equal(apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(s,apply(s,k)))))),u),v),f(apply(v,apply(u,v)))),apply(apply(v,apply(u,v)),f(apply(v,apply(u,v))))),
inference(spl,[status(thm),theory(equality)],[63,424]),
[iquote('0:SpL:63.0,424.0')] ).
cnf(2748,plain,
equal(apply(apply(apply(apply(s,u),u),v),w),apply(apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),apply(u,v)),w)),
inference(spr,[status(thm),theory(equality)],[857,319]),
[iquote('0:SpR:857.0,319.0')] ).
cnf(2788,plain,
$false,
inference(unc,[status(thm)],[2748,2141]),
[iquote('0:UnC:2748.0,2141.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n022.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 12:48:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.15/3.33
% 3.15/3.33 SPASS V 3.9
% 3.15/3.33 SPASS beiseite: Proof found.
% 3.15/3.33 % SZS status Theorem
% 3.15/3.33 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/3.33 SPASS derived 2065 clauses, backtracked 0 clauses, performed 0 splits and kept 1221 clauses.
% 3.15/3.33 SPASS allocated 71440 KBytes.
% 3.15/3.33 SPASS spent 0:00:02.93 on the problem.
% 3.15/3.33 0:00:00.04 for the input.
% 3.15/3.33 0:00:00.00 for the FLOTTER CNF translation.
% 3.15/3.33 0:00:00.04 for inferences.
% 3.15/3.33 0:00:00.00 for the backtracking.
% 3.15/3.33 0:00:02.82 for the reduction.
% 3.15/3.33
% 3.15/3.33
% 3.15/3.33 Here is a proof with depth 5, length 20 :
% 3.15/3.33 % SZS output start Refutation
% See solution above
% 3.15/3.33 Formulae used in the proof : s_definition k_definition prove_fixed_point
% 3.15/3.33
%------------------------------------------------------------------------------