TSTP Solution File: KLE080+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE080+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 02:28:24 EDT 2022
% Result : Theorem 5.33s 5.51s
% Output : Refutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 37 RR)
% Number of literals : 37 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(domain__dfg(zero),zero),
file('KLE080+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE080+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE080+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE080+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE080+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE080+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(antidomain(antidomain(skc1)),domain__dfg(skc1)),
file('KLE080+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(domain__dfg(u),antidomain(u)),one),
file('KLE080+1.p',unknown),
[] ).
cnf(11,axiom,
equal(multiplication(domain__dfg(u),antidomain(u)),zero),
file('KLE080+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE080+1.p',unknown),
[] ).
cnf(15,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE080+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE080+1.p',unknown),
[] ).
cnf(19,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE080+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE080+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE080+1.p',unknown),
[] ).
cnf(22,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[12,8]),
[iquote('0:Rew:12.0,8.0')] ).
cnf(42,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(107,plain,
equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[5,15]),
[iquote('0:SpR:5.0,15.0')] ).
cnf(110,plain,
equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[5,107]),
[iquote('0:Rew:5.0,107.0')] ).
cnf(158,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)],[15,19]),
[iquote('0:SpR:15.0,19.0')] ).
cnf(161,plain,
equal(addition(one,domain__dfg(one)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[4,19]),
[iquote('0:SpR:4.0,19.0')] ).
cnf(163,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[22,161]),
[iquote('0:Rew:22.0,161.0')] ).
cnf(475,plain,
equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[22,21]),
[iquote('0:SpR:22.0,21.0')] ).
cnf(478,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)],[16,21]),
[iquote('0:SpR:16.0,21.0')] ).
cnf(486,plain,
equal(addition(u,multiplication(domain__dfg(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,475]),
[iquote('0:Rew:5.0,475.0')] ).
cnf(489,plain,
equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
inference(rew,[status(thm),theory(equality)],[486,158]),
[iquote('0:Rew:486.0,158.0')] ).
cnf(575,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[10,20]),
[iquote('0:SpR:10.0,20.0')] ).
cnf(587,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[4,575]),
[iquote('0:Rew:4.0,575.0')] ).
cnf(6747,plain,
equal(multiplication(domain__dfg(zero),multiplication(domain__dfg(u),domain__dfg(antidomain(u)))),multiplication(domain__dfg(u),domain__dfg(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[11,489]),
[iquote('0:SpR:11.0,489.0')] ).
cnf(6785,plain,
equal(multiplication(domain__dfg(u),domain__dfg(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[7,6747,1]),
[iquote('0:Rew:7.0,6747.0,1.0,6747.0')] ).
cnf(7321,plain,
equal(addition(zero,multiplication(domain__dfg(u),antidomain(antidomain(u)))),domain__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6785,587]),
[iquote('0:SpR:6785.0,587.0')] ).
cnf(7384,plain,
equal(multiplication(domain__dfg(u),antidomain(antidomain(u))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,7321]),
[iquote('0:Rew:42.0,7321.0')] ).
cnf(7507,plain,
equal(addition(multiplication(domain__dfg(domain__dfg(u)),v),multiplication(domain__dfg(antidomain(u)),v)),multiplication(domain__dfg(one),v)),
inference(spr,[status(thm),theory(equality)],[10,478]),
[iquote('0:SpR:10.0,478.0')] ).
cnf(7550,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[110,7507,5,163]),
[iquote('0:Rew:110.0,7507.0,5.0,7507.0,163.0,7507.0')] ).
cnf(30761,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(antidomain(u))),zero),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[11,7550]),
[iquote('0:SpR:11.0,7550.0')] ).
cnf(30865,plain,
equal(antidomain(antidomain(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,30761,12,7384]),
[iquote('0:Rew:42.0,30761.0,12.0,30761.0,7384.0,30761.0')] ).
cnf(30866,plain,
$false,
inference(unc,[status(thm)],[30865,9]),
[iquote('0:UnC:30865.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE080+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 09:41:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.33/5.51
% 5.33/5.51 SPASS V 3.9
% 5.33/5.51 SPASS beiseite: Proof found.
% 5.33/5.51 % SZS status Theorem
% 5.33/5.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.33/5.51 SPASS derived 21560 clauses, backtracked 0 clauses, performed 0 splits and kept 3366 clauses.
% 5.33/5.51 SPASS allocated 105883 KBytes.
% 5.33/5.51 SPASS spent 0:00:04.98 on the problem.
% 5.33/5.51 0:00:00.03 for the input.
% 5.33/5.51 0:00:00.03 for the FLOTTER CNF translation.
% 5.33/5.51 0:00:00.12 for inferences.
% 5.33/5.51 0:00:00.00 for the backtracking.
% 5.33/5.51 0:00:04.76 for the reduction.
% 5.33/5.51
% 5.33/5.51
% 5.33/5.51 Here is a proof with depth 3, length 37 :
% 5.33/5.51 % SZS output start Refutation
% See solution above
% 5.33/5.51 Formulae used in the proof : domain4 additive_identity multiplicative_right_identity multiplicative_left_identity left_annihilation domain3 goals additive_commutativity domain2 domain5 domain1 right_distributivity left_distributivity
% 5.33/5.51
%------------------------------------------------------------------------------