TSTP Solution File: KLE133+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE133+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 02:28:40 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 49 ( 46 unt; 0 nHn; 49 RR)
% Number of literals : 52 ( 0 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE133+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE133+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE133+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,zero),zero),
file('KLE133+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(zero,u),zero),
file('KLE133+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE133+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE133+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE133+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE133+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE133+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE133+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE133+1.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE133+1.p',unknown),
[] ).
cnf(23,axiom,
equal(forward_diamond(skc2,forward_diamond(skc2,domain__dfg(u))),forward_diamond(skc2,domain__dfg(u))),
file('KLE133+1.p',unknown),
[] ).
cnf(30,axiom,
equal(addition(domain__dfg(u),forward_diamond(star(skc2),domain_difference(domain__dfg(u),forward_diamond(skc2,domain__dfg(u))))),forward_diamond(star(skc2),domain_difference(domain__dfg(u),forward_diamond(skc2,domain__dfg(u))))),
file('KLE133+1.p',unknown),
[] ).
cnf(31,axiom,
~ equal(addition(forward_diamond(skc2,domain__dfg(skc3)),forward_diamond(star(skc2),domain_difference(domain__dfg(skc3),forward_diamond(skc2,domain__dfg(skc3))))),forward_diamond(star(skc2),domain_difference(domain__dfg(skc3),forward_diamond(skc2,domain__dfg(skc3))))),
file('KLE133+1.p',unknown),
[] ).
cnf(35,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,14]),
[iquote('0:Rew:12.0,14.0')] ).
cnf(40,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[8,19]),
[iquote('0:Rew:8.0,19.0,8.0,19.0')] ).
cnf(41,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[8,18]),
[iquote('0:Rew:8.0,18.0')] ).
cnf(42,plain,
equal(forward_diamond(skc2,forward_diamond(skc2,antidomain(antidomain(u)))),forward_diamond(skc2,antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[8,23]),
[iquote('0:Rew:8.0,23.0')] ).
cnf(43,plain,
equal(addition(antidomain(antidomain(u)),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(u)),forward_diamond(skc2,antidomain(antidomain(u)))))),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(u)),forward_diamond(skc2,antidomain(antidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[8,30]),
[iquote('0:Rew:8.0,30.0')] ).
cnf(44,plain,
~ equal(addition(forward_diamond(skc2,antidomain(antidomain(skc3))),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(skc3)),forward_diamond(skc2,antidomain(antidomain(skc3)))))),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(skc3)),forward_diamond(skc2,antidomain(antidomain(skc3)))))),
inference(rew,[status(thm),theory(equality)],[8,31]),
[iquote('0:Rew:8.0,31.0')] ).
cnf(47,plain,
~ leq(forward_diamond(skc2,antidomain(antidomain(skc3))),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(skc3)),forward_diamond(skc2,antidomain(antidomain(skc3)))))),
inference(res,[status(thm),theory(equality)],[16,44]),
[iquote('0:Res:16.1,44.0')] ).
cnf(61,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(73,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(96,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[61,35]),
[iquote('0:SpR:61.0,35.0')] ).
cnf(98,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[73,96]),
[iquote('0:Rew:73.0,96.0')] ).
cnf(117,plain,
( ~ equal(u,u)
| leq(zero,u) ),
inference(spl,[status(thm),theory(equality)],[73,17]),
[iquote('0:SpL:73.0,17.0')] ).
cnf(121,plain,
leq(zero,u),
inference(obv,[status(thm),theory(equality)],[117]),
[iquote('0:Obv:117.0')] ).
cnf(123,plain,
equal(domain_difference(u,u),zero),
inference(spr,[status(thm),theory(equality)],[41,7]),
[iquote('0:SpR:41.0,7.0')] ).
cnf(126,plain,
equal(multiplication(antidomain(antidomain(u)),one),domain_difference(u,zero)),
inference(spr,[status(thm),theory(equality)],[98,41]),
[iquote('0:SpR:98.0,41.0')] ).
cnf(130,plain,
equal(domain_difference(u,zero),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[3,126]),
[iquote('0:Rew:3.0,126.0')] ).
cnf(162,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(zero)))),forward_diamond(u,one)),
inference(spr,[status(thm),theory(equality)],[61,40]),
[iquote('0:SpR:61.0,40.0')] ).
cnf(163,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(one)))),forward_diamond(u,zero)),
inference(spr,[status(thm),theory(equality)],[98,40]),
[iquote('0:SpR:98.0,40.0')] ).
cnf(164,plain,
equal(forward_diamond(zero,u),antidomain(antidomain(zero))),
inference(spr,[status(thm),theory(equality)],[6,40]),
[iquote('0:SpR:6.0,40.0')] ).
cnf(168,plain,
equal(forward_diamond(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[61,164,98]),
[iquote('0:Rew:61.0,164.0,98.0,164.0')] ).
cnf(169,plain,
equal(forward_diamond(u,one),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[3,162,98]),
[iquote('0:Rew:3.0,162.0,98.0,162.0')] ).
cnf(170,plain,
equal(forward_diamond(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[61,163,98,5]),
[iquote('0:Rew:61.0,163.0,98.0,163.0,5.0,163.0,61.0,163.0')] ).
cnf(306,plain,
equal(forward_diamond(skc2,forward_diamond(skc2,antidomain(zero))),forward_diamond(skc2,antidomain(zero))),
inference(spr,[status(thm),theory(equality)],[61,42]),
[iquote('0:SpR:61.0,42.0')] ).
cnf(312,plain,
equal(forward_diamond(skc2,antidomain(antidomain(skc2))),antidomain(antidomain(skc2))),
inference(rew,[status(thm),theory(equality)],[169,306,98]),
[iquote('0:Rew:169.0,306.0,98.0,306.0')] ).
cnf(883,plain,
equal(addition(antidomain(antidomain(skc2)),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(skc2)),antidomain(antidomain(skc2))))),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(skc2)),antidomain(antidomain(skc2))))),
inference(spr,[status(thm),theory(equality)],[312,43]),
[iquote('0:SpR:312.0,43.0')] ).
cnf(904,plain,
equal(antidomain(antidomain(skc2)),zero),
inference(rew,[status(thm),theory(equality)],[73,883,12,170,123]),
[iquote('0:Rew:73.0,883.0,12.0,883.0,170.0,883.0,123.0,883.0')] ).
cnf(921,plain,
equal(addition(antidomain(skc2),zero),one),
inference(spr,[status(thm),theory(equality)],[904,35]),
[iquote('0:SpR:904.0,35.0')] ).
cnf(933,plain,
equal(antidomain(skc2),one),
inference(rew,[status(thm),theory(equality)],[73,921,12]),
[iquote('0:Rew:73.0,921.0,12.0,921.0')] ).
cnf(955,plain,
equal(multiplication(one,skc2),zero),
inference(spr,[status(thm),theory(equality)],[933,7]),
[iquote('0:SpR:933.0,7.0')] ).
cnf(970,plain,
equal(skc2,zero),
inference(rew,[status(thm),theory(equality)],[4,955]),
[iquote('0:Rew:4.0,955.0')] ).
cnf(981,plain,
~ leq(forward_diamond(zero,antidomain(antidomain(skc3))),forward_diamond(star(zero),domain_difference(antidomain(antidomain(skc3)),forward_diamond(zero,antidomain(antidomain(skc3)))))),
inference(rew,[status(thm),theory(equality)],[970,47]),
[iquote('0:Rew:970.0,47.0')] ).
cnf(1014,plain,
~ leq(zero,forward_diamond(star(zero),antidomain(antidomain(antidomain(antidomain(skc3)))))),
inference(rew,[status(thm),theory(equality)],[130,981,168]),
[iquote('0:Rew:130.0,981.0,168.0,981.0')] ).
cnf(1015,plain,
$false,
inference(mrr,[status(thm)],[1014,121]),
[iquote('0:MRR:1014.0,121.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE133+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.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 09:57:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 764 clauses, backtracked 0 clauses, performed 0 splits and kept 280 clauses.
% 0.19/0.53 SPASS allocated 86140 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.53 0:00:00.04 for the input.
% 0.19/0.53 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.07 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 5, length 49 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : additive_identity multiplicative_right_identity multiplicative_left_identity right_annihilation left_annihilation domain1 domain4 additive_commutativity domain3 order domain_difference forward_diamond goals
% 0.19/0.53
%------------------------------------------------------------------------------