TSTP Solution File: KLE060+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE060+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 02:28:19 EDT 2022
% Result : Theorem 117.48s 117.63s
% Output : Refutation 117.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 45 RR)
% Number of literals : 45 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE060+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE060+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE060+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE060+1.p',unknown),
[] ).
cnf(12,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE060+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE060+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE060+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(multiplication(domain__dfg(skc3),domain__dfg(skc2)),domain__dfg(multiplication(domain__dfg(skc3),skc2))),
file('KLE060+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE060+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE060+1.p',unknown),
[] ).
cnf(20,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[9,8]),
[iquote('0:Rew:9.0,8.0')] ).
cnf(90,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(93,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,90]),
[iquote('0:Rew:5.0,90.0')] ).
cnf(99,plain,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(domain__dfg(u),v))),
inference(spr,[status(thm),theory(equality)],[93,13]),
[iquote('0:SpR:93.0,13.0')] ).
cnf(108,plain,
equal(domain__dfg(addition(domain__dfg(u),v)),domain__dfg(addition(u,v))),
inference(rew,[status(thm),theory(equality)],[13,99]),
[iquote('0:Rew:13.0,99.0')] ).
cnf(190,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[12,16]),
[iquote('0:SpR:12.0,16.0')] ).
cnf(191,plain,
equal(addition(domain__dfg(u),multiplication(domain__dfg(u),domain__dfg(u))),multiplication(domain__dfg(u),domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[93,16]),
[iquote('0:SpR:93.0,16.0')] ).
cnf(193,plain,
equal(addition(one,domain__dfg(one)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[4,16]),
[iquote('0:SpR:4.0,16.0')] ).
cnf(195,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[20,193]),
[iquote('0:Rew:20.0,193.0')] ).
cnf(201,plain,
equal(addition(one,domain__dfg(u)),domain__dfg(addition(one,u))),
inference(spr,[status(thm),theory(equality)],[195,13]),
[iquote('0:SpR:195.0,13.0')] ).
cnf(208,plain,
equal(domain__dfg(addition(one,u)),one),
inference(rew,[status(thm),theory(equality)],[20,201]),
[iquote('0:Rew:20.0,201.0')] ).
cnf(220,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(multiplication(u,one))),
inference(spr,[status(thm),theory(equality)],[208,12]),
[iquote('0:SpR:208.0,12.0')] ).
cnf(234,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,220]),
[iquote('0:Rew:4.0,220.0')] ).
cnf(235,plain,
equal(domain__dfg(addition(multiplication(u,one),multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[18,234]),
[iquote('0:Rew:18.0,234.0')] ).
cnf(236,plain,
equal(domain__dfg(addition(u,multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,235]),
[iquote('0:Rew:4.0,235.0')] ).
cnf(621,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[20,19]),
[iquote('0:SpR:20.0,19.0')] ).
cnf(622,plain,
equal(multiplication(domain__dfg(addition(u,v)),w),addition(multiplication(domain__dfg(u),w),multiplication(domain__dfg(v),w))),
inference(spr,[status(thm),theory(equality)],[13,19]),
[iquote('0:SpR:13.0,19.0')] ).
cnf(631,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,621]),
[iquote('0:Rew:5.0,621.0')] ).
cnf(633,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[631,190]),
[iquote('0:Rew:631.0,190.0')] ).
cnf(634,plain,
equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[631,191]),
[iquote('0:Rew:631.0,191.0')] ).
cnf(824,plain,
equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[20,18]),
[iquote('0:SpR:20.0,18.0')] ).
cnf(825,plain,
equal(multiplication(u,domain__dfg(addition(v,w))),addition(multiplication(u,domain__dfg(v)),multiplication(u,domain__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[13,18]),
[iquote('0:SpR:13.0,18.0')] ).
cnf(834,plain,
equal(addition(u,multiplication(u,domain__dfg(v))),u),
inference(rew,[status(thm),theory(equality)],[4,824]),
[iquote('0:Rew:4.0,824.0')] ).
cnf(944,plain,
equal(addition(multiplication(u,v),multiplication(u,multiplication(domain__dfg(w),v))),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[631,18]),
[iquote('0:SpR:631.0,18.0')] ).
cnf(6023,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,domain__dfg(multiplication(domain__dfg(w),v)))),multiplication(u,domain__dfg(v))),
inference(spr,[status(thm),theory(equality)],[631,825]),
[iquote('0:SpR:631.0,825.0')] ).
cnf(8168,plain,
equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[108,236]),
[iquote('0:SpR:108.0,236.0')] ).
cnf(8262,plain,
equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[93,8168]),
[iquote('0:Rew:93.0,8168.0')] ).
cnf(18657,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(multiplication(domain__dfg(u),w)),v)),multiplication(domain__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[8262,622]),
[iquote('0:SpR:8262.0,622.0')] ).
cnf(56081,plain,
equal(addition(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),multiplication(domain__dfg(u),domain__dfg(v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
inference(spr,[status(thm),theory(equality)],[633,944]),
[iquote('0:SpR:633.0,944.0')] ).
cnf(56256,plain,
equal(addition(multiplication(domain__dfg(u),domain__dfg(v)),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[9,56081]),
[iquote('0:Rew:9.0,56081.0')] ).
cnf(56257,plain,
equal(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),multiplication(domain__dfg(u),domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[18657,56256]),
[iquote('0:Rew:18657.0,56256.0')] ).
cnf(128017,plain,
equal(addition(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
inference(spr,[status(thm),theory(equality)],[634,6023]),
[iquote('0:SpR:634.0,6023.0')] ).
cnf(128357,plain,
equal(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[834,128017,9]),
[iquote('0:Rew:834.0,128017.0,9.0,128017.0')] ).
cnf(128358,plain,
equal(multiplication(domain__dfg(u),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[56257,128357]),
[iquote('0:Rew:56257.0,128357.0')] ).
cnf(128359,plain,
$false,
inference(unc,[status(thm)],[128358,17]),
[iquote('0:UnC:128358.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE060+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n003.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 : Thu Jun 16 07:43:26 EDT 2022
% 0.14/0.36 % CPUTime :
% 117.48/117.63
% 117.48/117.63 SPASS V 3.9
% 117.48/117.63 SPASS beiseite: Proof found.
% 117.48/117.63 % SZS status Theorem
% 117.48/117.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 117.48/117.63 SPASS derived 88867 clauses, backtracked 0 clauses, performed 0 splits and kept 14906 clauses.
% 117.48/117.63 SPASS allocated 165541 KBytes.
% 117.48/117.63 SPASS spent 0:1:53.81 on the problem.
% 117.48/117.63 0:00:00.03 for the input.
% 117.48/117.63 0:00:00.03 for the FLOTTER CNF translation.
% 117.48/117.63 0:00:00.62 for inferences.
% 117.48/117.63 0:00:00.00 for the backtracking.
% 117.48/117.63 0:1:52.98 for the reduction.
% 117.48/117.63
% 117.48/117.63
% 117.48/117.63 Here is a proof with depth 5, length 45 :
% 117.48/117.63 % SZS output start Refutation
% See solution above
% 117.48/117.63 Formulae used in the proof : multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity domain2 domain5 domain1 goals right_distributivity left_distributivity
% 117.48/117.63
%------------------------------------------------------------------------------