%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE113+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Sun Jul 17 02:28:35 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE113+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE113+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,zero),zero),
file('KLE113+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(forward_diamond(skc1,zero),zero),
file('KLE113+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE113+1.p',unknown),
[] ).
cnf(9,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE113+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE113+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE113+1.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE113+1.p',unknown),
[] ).
cnf(31,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(36,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[9,19]),
[iquote('0:Rew:9.0,19.0,9.0,19.0')] ).
cnf(51,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,3]),
[iquote('0:SpR:8.0,3.0')] ).
cnf(62,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(85,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[51,31]),
[iquote('0:SpR:51.0,31.0')] ).
cnf(87,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[62,85]),
[iquote('0:Rew:62.0,85.0')] ).
cnf(152,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(one)))),forward_diamond(u,zero)),
inference(spr,[status(thm),theory(equality)],[87,36]),
[iquote('0:SpR:87.0,36.0')] ).
cnf(159,plain,
equal(forward_diamond(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[51,152,87,5]),
[iquote('0:Rew:51.0,152.0,87.0,152.0,5.0,152.0,51.0,152.0')] ).
cnf(160,plain,
$false,
inference(unc,[status(thm)],[159,7]),
[iquote('0:UnC:159.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE113+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 11:16:26 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.46
% 0.21/0.46 SPASS V 3.9
% 0.21/0.46 SPASS beiseite: Proof found.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.46 SPASS derived 107 clauses, backtracked 0 clauses, performed 0 splits and kept 65 clauses.
% 0.21/0.46 SPASS allocated 85225 KBytes.
% 0.21/0.46 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.46 0:00:00.03 for the input.
% 0.21/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.46 0:00:00.00 for inferences.
% 0.21/0.46 0:00:00.00 for the backtracking.
% 0.21/0.46 0:00:00.01 for the reduction.
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 Here is a proof with depth 3, length 18 :
% 0.21/0.46 % SZS output start Refutation
% See solution above
% 0.21/0.46 Formulae used in the proof : additive_identity multiplicative_right_identity right_annihilation goals domain1 domain4 additive_commutativity domain3 forward_diamond
% 0.21/0.46
%------------------------------------------------------------------------------