%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 00:42:20 EDT 2022
% Result : Unsatisfiable 0.71s 0.86s
% Output : Refutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 9 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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(apply(s,u),v),w),apply(apply(u,w),apply(v,w))),
file('COL001-1.p',unknown),
[] ).
cnf(2,axiom,
equal(apply(apply(k,u),v),u),
file('COL001-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(apply(combinator,u),u),
file('COL001-1.p',unknown),
[] ).
cnf(8,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(9,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,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(138,plain,
equal(apply(apply(apply(apply(s,s),apply(s,k)),u),v),apply(apply(u,v),v)),
inference(spr,[status(thm),theory(equality)],[8,9]),
[iquote('0:SpR:8.0,9.0')] ).
cnf(780,plain,
equal(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,u))),v),apply(u,apply(v,v))),
inference(spr,[status(thm),theory(equality)],[138,14]),
[iquote('0:SpR:138.0,14.0')] ).
cnf(842,plain,
$false,
inference(unc,[status(thm)],[780,3]),
[iquote('0:UnC:780.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 16:08:11 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.71/0.86
% 0.71/0.86 SPASS V 3.9
% 0.71/0.86 SPASS beiseite: Proof found.
% 0.71/0.86 % SZS status Theorem
% 0.71/0.86 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.71/0.86 SPASS derived 650 clauses, backtracked 0 clauses, performed 0 splits and kept 427 clauses.
% 0.71/0.86 SPASS allocated 65835 KBytes.
% 0.71/0.86 SPASS spent 0:00:00.48 on the problem.
% 0.71/0.86 0:00:00.03 for the input.
% 0.71/0.86 0:00:00.00 for the FLOTTER CNF translation.
% 0.71/0.86 0:00:00.01 for inferences.
% 0.71/0.86 0:00:00.00 for the backtracking.
% 0.71/0.86 0:00:00.42 for the reduction.
% 0.71/0.86
% 0.71/0.86
% 0.71/0.86 Here is a proof with depth 3, length 9 :
% 0.71/0.86 % SZS output start Refutation
% See solution above
% 0.71/0.86 Formulae used in the proof : s_definition k_definition prove_fixed_point
% 0.71/0.86
%------------------------------------------------------------------------------