TSTP Solution File: KLE068+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE068+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 02:28:21 EDT 2022
% Result : Theorem 108.03s 108.22s
% Output : Refutation 108.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 46 RR)
% Number of literals : 46 ( 0 equ; 2 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('KLE068+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE068+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE068+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE068+1.p',unknown),
[] ).
cnf(12,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE068+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE068+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE068+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(domain__dfg(multiplication(domain__dfg(skc3),domain__dfg(skc2))),multiplication(domain__dfg(skc3),domain__dfg(skc2))),
file('KLE068+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE068+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE068+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(21,plain,
~ equal(multiplication(domain__dfg(skc3),domain__dfg(skc2)),domain__dfg(multiplication(domain__dfg(skc3),skc2))),
inference(rew,[status(thm),theory(equality)],[12,17]),
[iquote('0:Rew:12.0,17.0')] ).
cnf(91,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(94,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,91]),
[iquote('0:Rew:5.0,91.0')] ).
cnf(100,plain,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(domain__dfg(u),v))),
inference(spr,[status(thm),theory(equality)],[94,13]),
[iquote('0:SpR:94.0,13.0')] ).
cnf(109,plain,
equal(domain__dfg(addition(domain__dfg(u),v)),domain__dfg(addition(u,v))),
inference(rew,[status(thm),theory(equality)],[13,100]),
[iquote('0:Rew:13.0,100.0')] ).
cnf(191,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(192,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)],[94,16]),
[iquote('0:SpR:94.0,16.0')] ).
cnf(194,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(196,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[20,194]),
[iquote('0:Rew:20.0,194.0')] ).
cnf(202,plain,
equal(addition(one,domain__dfg(u)),domain__dfg(addition(one,u))),
inference(spr,[status(thm),theory(equality)],[196,13]),
[iquote('0:SpR:196.0,13.0')] ).
cnf(209,plain,
equal(domain__dfg(addition(one,u)),one),
inference(rew,[status(thm),theory(equality)],[20,202]),
[iquote('0:Rew:20.0,202.0')] ).
cnf(221,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(multiplication(u,one))),
inference(spr,[status(thm),theory(equality)],[209,12]),
[iquote('0:SpR:209.0,12.0')] ).
cnf(235,plain,
equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,221]),
[iquote('0:Rew:4.0,221.0')] ).
cnf(236,plain,
equal(domain__dfg(addition(multiplication(u,one),multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[18,235]),
[iquote('0:Rew:18.0,235.0')] ).
cnf(237,plain,
equal(domain__dfg(addition(u,multiplication(u,v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[4,236]),
[iquote('0:Rew:4.0,236.0')] ).
cnf(622,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(623,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(632,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,622]),
[iquote('0:Rew:5.0,622.0')] ).
cnf(634,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[632,191]),
[iquote('0:Rew:632.0,191.0')] ).
cnf(635,plain,
equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[632,192]),
[iquote('0:Rew:632.0,192.0')] ).
cnf(825,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(826,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(835,plain,
equal(addition(u,multiplication(u,domain__dfg(v))),u),
inference(rew,[status(thm),theory(equality)],[4,825]),
[iquote('0:Rew:4.0,825.0')] ).
cnf(945,plain,
equal(addition(multiplication(u,v),multiplication(u,multiplication(domain__dfg(w),v))),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[632,18]),
[iquote('0:SpR:632.0,18.0')] ).
cnf(6024,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)],[632,826]),
[iquote('0:SpR:632.0,826.0')] ).
cnf(8169,plain,
equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[109,237]),
[iquote('0:SpR:109.0,237.0')] ).
cnf(8263,plain,
equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[94,8169]),
[iquote('0:Rew:94.0,8169.0')] ).
cnf(18658,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)],[8263,623]),
[iquote('0:SpR:8263.0,623.0')] ).
cnf(56082,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)],[634,945]),
[iquote('0:SpR:634.0,945.0')] ).
cnf(56257,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)],[9,56082]),
[iquote('0:Rew:9.0,56082.0')] ).
cnf(56258,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)],[18658,56257]),
[iquote('0:Rew:18658.0,56257.0')] ).
cnf(128018,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)],[635,6024]),
[iquote('0:SpR:635.0,6024.0')] ).
cnf(128358,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)],[835,128018,9]),
[iquote('0:Rew:835.0,128018.0,9.0,128018.0')] ).
cnf(128359,plain,
equal(multiplication(domain__dfg(u),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[56258,128358]),
[iquote('0:Rew:56258.0,128358.0')] ).
cnf(128360,plain,
$false,
inference(unc,[status(thm)],[128359,21]),
[iquote('0:UnC:128359.0,21.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE068+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 11:44:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 108.03/108.22
% 108.03/108.22 SPASS V 3.9
% 108.03/108.22 SPASS beiseite: Proof found.
% 108.03/108.22 % SZS status Theorem
% 108.03/108.22 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 108.03/108.22 SPASS derived 88867 clauses, backtracked 0 clauses, performed 0 splits and kept 14906 clauses.
% 108.03/108.22 SPASS allocated 165531 KBytes.
% 108.03/108.22 SPASS spent 0:1:45.00 on the problem.
% 108.03/108.22 0:00:00.04 for the input.
% 108.03/108.22 0:00:00.03 for the FLOTTER CNF translation.
% 108.03/108.22 0:00:00.58 for inferences.
% 108.03/108.22 0:00:00.00 for the backtracking.
% 108.03/108.22 0:1:44.22 for the reduction.
% 108.03/108.22
% 108.03/108.22
% 108.03/108.22 Here is a proof with depth 5, length 46 :
% 108.03/108.22 % SZS output start Refutation
% See solution above
% 108.03/108.22 Formulae used in the proof : multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity domain2 domain5 domain1 goals right_distributivity left_distributivity
% 108.03/108.22
%------------------------------------------------------------------------------