%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE063+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:28:20 EDT 2022
% Result : Theorem 0.22s 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 27 RR)
% Number of literals : 27 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE063+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE063+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE063+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE063+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(addition(domain__dfg(skc2),domain__dfg(skc3)),domain__dfg(skc3)),
file('KLE063+1.p',unknown),
[] ).
cnf(13,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE063+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE063+1.p',unknown),
[] ).
cnf(15,axiom,
equal(addition(skc2,multiplication(domain__dfg(skc3),skc2)),multiplication(domain__dfg(skc3),skc2)),
file('KLE063+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE063+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE063+1.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[9,8]),
[iquote('0:Rew:9.0,8.0')] ).
cnf(22,plain,
~ equal(domain__dfg(addition(skc2,skc3)),domain__dfg(skc3)),
inference(rew,[status(thm),theory(equality)],[14,10]),
[iquote('0:Rew:14.0,10.0')] ).
cnf(145,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,13]),
[iquote('0:SpR:5.0,13.0')] ).
cnf(148,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,145]),
[iquote('0:Rew:5.0,145.0')] ).
cnf(164,plain,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,domain__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[148,14]),
[iquote('0:SpR:148.0,14.0')] ).
cnf(175,plain,
equal(domain__dfg(addition(u,domain__dfg(v))),domain__dfg(addition(u,v))),
inference(rew,[status(thm),theory(equality)],[14,164]),
[iquote('0:Rew:14.0,164.0')] ).
cnf(284,plain,
equal(domain__dfg(addition(one,u)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[21,175]),
[iquote('0:SpR:21.0,175.0')] ).
cnf(324,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(multiplication(u,domain__dfg(one)))),
inference(spr,[status(thm),theory(equality)],[284,13]),
[iquote('0:SpR:284.0,13.0')] ).
cnf(342,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,324,13]),
[iquote('0:Rew:4.0,324.0,13.0,324.0')] ).
cnf(343,plain,
equal(domain__dfg(addition(multiplication(u,one),multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[19,342]),
[iquote('0:Rew:19.0,342.0')] ).
cnf(344,plain,
equal(domain__dfg(addition(u,multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,343]),
[iquote('0:Rew:4.0,343.0')] ).
cnf(841,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[21,20]),
[iquote('0:SpR:21.0,20.0')] ).
cnf(852,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,841]),
[iquote('0:Rew:5.0,841.0')] ).
cnf(853,plain,
equal(multiplication(domain__dfg(skc3),skc2),skc2),
inference(rew,[status(thm),theory(equality)],[852,15]),
[iquote('0:Rew:852.0,15.0')] ).
cnf(906,plain,
equal(domain__dfg(addition(domain__dfg(skc3),skc2)),domain__dfg(domain__dfg(skc3))),
inference(spr,[status(thm),theory(equality)],[853,344]),
[iquote('0:SpR:853.0,344.0')] ).
cnf(909,plain,
equal(domain__dfg(addition(skc2,skc3)),domain__dfg(skc3)),
inference(rew,[status(thm),theory(equality)],[175,906,9,148]),
[iquote('0:Rew:175.0,906.0,9.0,906.0,148.0,906.0')] ).
cnf(910,plain,
$false,
inference(mrr,[status(thm)],[909,22]),
[iquote('0:MRR:909.0,22.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE063+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 11:26:32 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.51
% 0.22/0.51 SPASS V 3.9
% 0.22/0.51 SPASS beiseite: Proof found.
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.51 SPASS derived 601 clauses, backtracked 0 clauses, performed 0 splits and kept 151 clauses.
% 0.22/0.51 SPASS allocated 85836 KBytes.
% 0.22/0.51 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.51 0:00:00.04 for the input.
% 0.22/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.51 0:00:00.01 for inferences.
% 0.22/0.51 0:00:00.00 for the backtracking.
% 0.22/0.51 0:00:00.04 for the reduction.
% 0.22/0.51
% 0.22/0.51
% 0.22/0.51 Here is a proof with depth 5, length 27 :
% 0.22/0.51 % SZS output start Refutation
% See solution above
% 0.22/0.51 Formulae used in the proof : multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity goals domain2 domain5 right_distributivity left_distributivity
% 0.22/0.51
%------------------------------------------------------------------------------