TSTP Solution File: KLE071+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE071+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 02:28:22 EDT 2022
% Result : Theorem 2.65s 2.91s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 8 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE071+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE071+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE071+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE071+1.p',unknown),
[] ).
cnf(12,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE071+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE071+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE071+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE071+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE071+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE071+1.p',unknown),
[] ).
cnf(19,axiom,
~ equal(multiplication(addition(domain__dfg(skc5),domain__dfg(skc4)),addition(domain__dfg(skc5),domain__dfg(skc3))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
file('KLE071+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(addition(skc4,skc5)),domain__dfg(addition(skc3,skc5))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[9,19,13]),
[iquote('0:Rew:9.0,19.0,13.0,19.0,9.0,19.0,13.0,19.0')] ).
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(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(454,plain,
equal(addition(u,addition(v,w)),addition(w,addition(u,v))),
inference(spr,[status(thm),theory(equality)],[14,9]),
[iquote('0:SpR:14.0,9.0')] ).
cnf(470,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[9,14]),
[iquote('0:SpR:9.0,14.0')] ).
cnf(480,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[14,470]),
[iquote('0:Rew:14.0,470.0')] ).
cnf(590,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[20,18]),
[iquote('0:SpR:20.0,18.0')] ).
cnf(591,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)],[13,18]),
[iquote('0:SpR:13.0,18.0')] ).
cnf(600,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,590]),
[iquote('0:Rew:5.0,590.0')] ).
cnf(602,plain,
equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[600,192]),
[iquote('0:Rew:600.0,192.0')] ).
cnf(617,plain,
~ equal(addition(multiplication(domain__dfg(skc4),domain__dfg(addition(skc3,skc5))),multiplication(domain__dfg(skc5),domain__dfg(addition(skc3,skc5)))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[591,21]),
[iquote('0:Rew:591.0,21.0')] ).
cnf(743,plain,
equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[20,17]),
[iquote('0:SpR:20.0,17.0')] ).
cnf(744,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)],[13,17]),
[iquote('0:SpR:13.0,17.0')] ).
cnf(753,plain,
equal(addition(u,multiplication(u,domain__dfg(v))),u),
inference(rew,[status(thm),theory(equality)],[4,743]),
[iquote('0:Rew:4.0,743.0')] ).
cnf(758,plain,
~ equal(addition(addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),multiplication(domain__dfg(skc4),domain__dfg(skc5))),multiplication(domain__dfg(skc5),domain__dfg(addition(skc3,skc5)))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[744,617]),
[iquote('0:Rew:744.0,617.0')] ).
cnf(766,plain,
~ equal(addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),addition(multiplication(domain__dfg(skc4),domain__dfg(skc5)),multiplication(domain__dfg(skc5),domain__dfg(addition(skc3,skc5))))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[14,758]),
[iquote('0:Rew:14.0,758.0')] ).
cnf(767,plain,
~ equal(addition(domain__dfg(skc5),addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),addition(multiplication(domain__dfg(skc4),domain__dfg(skc5)),multiplication(domain__dfg(skc5),domain__dfg(skc3))))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[480,766,454,602,744]),
[iquote('0:Rew:480.0,766.0,454.0,766.0,602.0,766.0,744.0,766.0')] ).
cnf(928,plain,
equal(addition(u,addition(multiplication(domain__dfg(v),u),w)),addition(u,w)),
inference(spr,[status(thm),theory(equality)],[600,14]),
[iquote('0:SpR:600.0,14.0')] ).
cnf(18533,plain,
equal(addition(u,addition(v,addition(multiplication(domain__dfg(w),u),x))),addition(v,addition(u,x))),
inference(spr,[status(thm),theory(equality)],[928,480]),
[iquote('0:SpR:928.0,480.0')] ).
cnf(18825,plain,
~ equal(addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),addition(domain__dfg(skc5),multiplication(domain__dfg(skc5),domain__dfg(skc3)))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[18533,767]),
[iquote('0:Rew:18533.0,767.0')] ).
cnf(18877,plain,
~ equal(addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
inference(rew,[status(thm),theory(equality)],[9,18825,753]),
[iquote('0:Rew:9.0,18825.0,753.0,18825.0')] ).
cnf(18878,plain,
$false,
inference(obv,[status(thm),theory(equality)],[18877]),
[iquote('0:Obv:18877.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE071+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 12:29:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.65/2.91
% 2.65/2.91 SPASS V 3.9
% 2.65/2.91 SPASS beiseite: Proof found.
% 2.65/2.91 % SZS status Theorem
% 2.65/2.91 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.65/2.91 SPASS derived 13777 clauses, backtracked 0 clauses, performed 0 splits and kept 2179 clauses.
% 2.65/2.91 SPASS allocated 97890 KBytes.
% 2.65/2.91 SPASS spent 0:00:02.48 on the problem.
% 2.65/2.91 0:00:00.04 for the input.
% 2.65/2.91 0:00:00.03 for the FLOTTER CNF translation.
% 2.65/2.91 0:00:00.08 for inferences.
% 2.65/2.91 0:00:00.00 for the backtracking.
% 2.65/2.91 0:00:02.31 for the reduction.
% 2.65/2.91
% 2.65/2.91
% 2.65/2.91 Here is a proof with depth 3, length 35 :
% 2.65/2.91 % SZS output start Refutation
% See solution above
% 2.65/2.91 Formulae used in the proof : multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity domain2 domain5 additive_associativity domain1 right_distributivity left_distributivity goals
% 2.65/2.91
%------------------------------------------------------------------------------