%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL075-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 00:42:35 EDT 2022
% Result : Unsatisfiable 1.46s 1.70s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 7 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(apply(apply(k,u),v),u),
file('COL075-1.p',unknown),
[] ).
cnf(6,axiom,
equal(apply(apply(u,apply(k,v)),apply(w,v)),apply(apply(apply(abstraction,u),w),v)),
file('COL075-1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(apply(apply(u,b(u)),c(u)),apply(b(u),b(u))),
file('COL075-1.p',unknown),
[] ).
cnf(220,plain,
equal(apply(apply(apply(abstraction,u),apply(k,v)),w),apply(apply(u,apply(k,w)),v)),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(3783,plain,
equal(apply(apply(apply(apply(abstraction,abstraction),k),u),v),apply(apply(apply(k,u),apply(k,v)),u)),
inference(spr,[status(thm),theory(equality)],[6,220]),
[iquote('0:SpR:6.0,220.0')] ).
cnf(3800,plain,
equal(apply(apply(apply(apply(abstraction,abstraction),k),u),v),apply(u,u)),
inference(rew,[status(thm),theory(equality)],[1,3783]),
[iquote('0:Rew:1.0,3783.0')] ).
cnf(3801,plain,
$false,
inference(unc,[status(thm)],[3800,11]),
[iquote('0:UnC:3800.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL075-1 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 12:17:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.46/1.70
% 1.46/1.70 SPASS V 3.9
% 1.46/1.70 SPASS beiseite: Proof found.
% 1.46/1.70 % SZS status Theorem
% 1.46/1.70 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.46/1.70 SPASS derived 2656 clauses, backtracked 0 clauses, performed 0 splits and kept 1156 clauses.
% 1.46/1.70 SPASS allocated 68865 KBytes.
% 1.46/1.70 SPASS spent 0:00:01.32 on the problem.
% 1.46/1.70 0:00:00.04 for the input.
% 1.46/1.70 0:00:00.00 for the FLOTTER CNF translation.
% 1.46/1.70 0:00:00.04 for inferences.
% 1.46/1.70 0:00:00.00 for the backtracking.
% 1.46/1.70 0:00:01.23 for the reduction.
% 1.46/1.70
% 1.46/1.70
% 1.46/1.70 Here is a proof with depth 2, length 7 :
% 1.46/1.70 % SZS output start Refutation
% See solution above
% 1.46/1.70 Formulae used in the proof : k_definition abstraction prove_diagonal_combinator
% 1.46/1.70
%------------------------------------------------------------------------------