TSTP Solution File: KLE078+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE078+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 5.92s 6.14s
% Output : Refutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of clauses : 63 ( 57 unt; 0 nHn; 63 RR)
% Number of literals : 70 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 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('KLE078+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE078+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE078+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE078+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE078+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE078+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE078+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(domain__dfg(antidomain(skc1)),antidomain(skc1)),
file('KLE078+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(domain__dfg(u),antidomain(u)),one),
file('KLE078+1.p',unknown),
[] ).
cnf(11,axiom,
equal(multiplication(domain__dfg(u),antidomain(u)),zero),
file('KLE078+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE078+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE078+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE078+1.p',unknown),
[] ).
cnf(15,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
file('KLE078+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE078+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE078+1.p',unknown),
[] ).
cnf(19,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE078+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE078+1.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE078+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(58,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.1,12.0')] ).
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(116,plain,
equal(multiplication(domain__dfg(u),antidomain(domain__dfg(u))),zero),
inference(spr,[status(thm),theory(equality)],[110,11]),
[iquote('0:SpR:110.0,11.0')] ).
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(317,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
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(476,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[10,21]),
[iquote('0:SpR:10.0,21.0')] ).
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(487,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[486,19]),
[iquote('0:Rew:486.0,19.0')] ).
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(494,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),v),
inference(rew,[status(thm),theory(equality)],[5,476]),
[iquote('0:Rew:5.0,476.0')] ).
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(888,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[58,13]),
[iquote('0:SpR:58.1,13.1')] ).
cnf(982,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[317,14]),
[iquote('0:SpL:317.0,14.0')] ).
cnf(989,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[982]),
[iquote('0:Obv:982.0')] ).
cnf(997,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,989]),
[iquote('0:SpR:12.0,989.0')] ).
cnf(1877,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(domain__dfg(u)))),antidomain(domain__dfg(u))),
inference(spr,[status(thm),theory(equality)],[116,494]),
[iquote('0:SpR:116.0,494.0')] ).
cnf(1896,plain,
equal(multiplication(antidomain(u),antidomain(domain__dfg(u))),antidomain(domain__dfg(u))),
inference(rew,[status(thm),theory(equality)],[42,1877]),
[iquote('0:Rew:42.0,1877.0')] ).
cnf(2003,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[587,997]),
[iquote('0:SpR:587.0,997.0')] ).
cnf(2082,plain,
leq(antidomain(u),domain__dfg(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[487,2003]),
[iquote('0:SpR:487.0,2003.0')] ).
cnf(6549,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(6585,plain,
equal(multiplication(domain__dfg(u),domain__dfg(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[7,6549,1]),
[iquote('0:Rew:7.0,6549.0,1.0,6549.0')] ).
cnf(6671,plain,
equal(addition(zero,multiplication(domain__dfg(u),antidomain(antidomain(u)))),domain__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6585,587]),
[iquote('0:SpR:6585.0,587.0')] ).
cnf(6728,plain,
equal(multiplication(domain__dfg(u),antidomain(antidomain(u))),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,6671]),
[iquote('0:Rew:42.0,6671.0')] ).
cnf(7500,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(7543,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[110,7500,5,163]),
[iquote('0:Rew:110.0,7500.0,5.0,7500.0,163.0,7500.0')] ).
cnf(18031,plain,
( ~ leq(domain__dfg(antidomain(u)),antidomain(u))
| equal(domain__dfg(antidomain(u)),antidomain(u)) ),
inference(res,[status(thm),theory(equality)],[2082,888]),
[iquote('0:Res:2082.0,888.0')] ).
cnf(27740,plain,
leq(antidomain(domain__dfg(u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1896,2003]),
[iquote('0:SpR:1896.0,2003.0')] ).
cnf(30830,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(antidomain(u))),zero),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[11,7543]),
[iquote('0:SpR:11.0,7543.0')] ).
cnf(30832,plain,
equal(addition(multiplication(domain__dfg(u),antidomain(antidomain(antidomain(u)))),domain__dfg(antidomain(u))),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[6728,7543]),
[iquote('0:SpR:6728.0,7543.0')] ).
cnf(30934,plain,
equal(antidomain(antidomain(u)),domain__dfg(u)),
inference(rew,[status(thm),theory(equality)],[42,30830,12,6728]),
[iquote('0:Rew:42.0,30830.0,12.0,30830.0,6728.0,30830.0')] ).
cnf(31228,plain,
equal(addition(domain__dfg(antidomain(u)),multiplication(domain__dfg(u),antidomain(antidomain(antidomain(u))))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[12,30832]),
[iquote('0:Rew:12.0,30832.0')] ).
cnf(31229,plain,
equal(addition(domain__dfg(antidomain(u)),multiplication(domain__dfg(u),antidomain(domain__dfg(u)))),antidomain(domain__dfg(u))),
inference(rew,[status(thm),theory(equality)],[30934,31228]),
[iquote('0:Rew:30934.0,31228.0')] ).
cnf(31230,plain,
equal(antidomain(domain__dfg(u)),domain__dfg(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[42,31229,12,116]),
[iquote('0:Rew:42.0,31229.0,12.0,31229.0,116.0,31229.0')] ).
cnf(31251,plain,
leq(domain__dfg(antidomain(u)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[31230,27740]),
[iquote('0:Rew:31230.0,27740.0')] ).
cnf(31562,plain,
equal(domain__dfg(antidomain(u)),antidomain(u)),
inference(mrr,[status(thm)],[18031,31251]),
[iquote('0:MRR:18031.0,31251.0')] ).
cnf(31563,plain,
$false,
inference(unc,[status(thm)],[31562,9]),
[iquote('0:UnC:31562.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : KLE078+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n027.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 10:43:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 5.92/6.14
% 5.92/6.14 SPASS V 3.9
% 5.92/6.14 SPASS beiseite: Proof found.
% 5.92/6.14 % SZS status Theorem
% 5.92/6.14 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.92/6.14 SPASS derived 22106 clauses, backtracked 0 clauses, performed 0 splits and kept 3623 clauses.
% 5.92/6.14 SPASS allocated 106451 KBytes.
% 5.92/6.14 SPASS spent 0:00:05.60 on the problem.
% 5.92/6.14 0:00:00.04 for the input.
% 5.92/6.14 0:00:00.03 for the FLOTTER CNF translation.
% 5.92/6.14 0:00:00.12 for inferences.
% 5.92/6.14 0:00:00.00 for the backtracking.
% 5.92/6.14 0:00:05.38 for the reduction.
% 5.92/6.14
% 5.92/6.14
% 5.92/6.14 Here is a proof with depth 6, length 63 :
% 5.92/6.14 % SZS output start Refutation
% See solution above
% 5.92/6.14 Formulae used in the proof : domain4 additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation domain3 goals additive_commutativity order domain2 domain5 additive_associativity domain1 right_distributivity left_distributivity
% 5.92/6.14
%------------------------------------------------------------------------------