TSTP Solution File: KLE100+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE100+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 02:28:31 EDT 2022
% Result : Theorem 11.45s 11.70s
% Output : Refutation 11.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 63 unt; 0 nHn; 68 RR)
% Number of literals : 73 ( 0 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE100+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE100+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE100+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE100+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE100+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE100+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE100+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE100+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(antidomain(skc5),multiplication(skc3,domain__dfg(skc4))),zero),
file('KLE100+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE100+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE100+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE100+1.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE100+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(addition(forward_diamond(skc3,domain__dfg(skc4)),domain__dfg(skc5)),domain__dfg(skc5)),
file('KLE100+1.p',unknown),
[] ).
cnf(24,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE100+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE100+1.p',unknown),
[] ).
cnf(27,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE100+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE100+1.p',unknown),
[] ).
cnf(32,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,13]),
[iquote('0:Rew:12.0,13.0')] ).
cnf(37,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(38,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(39,plain,
equal(multiplication(antidomain(skc5),multiplication(skc3,antidomain(antidomain(skc4)))),zero),
inference(rew,[status(thm),theory(equality)],[8,15]),
[iquote('0:Rew:8.0,15.0')] ).
cnf(40,plain,
~ equal(addition(antidomain(antidomain(skc5)),forward_diamond(skc3,antidomain(antidomain(skc4)))),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[12,23,8]),
[iquote('0:Rew:12.0,23.0,8.0,23.0,8.0,23.0')] ).
cnf(54,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(65,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(88,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[54,32]),
[iquote('0:SpR:54.0,32.0')] ).
cnf(90,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[65,88]),
[iquote('0:Rew:65.0,88.0')] ).
cnf(98,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[16,12]),
[iquote('0:SpR:16.1,12.0')] ).
cnf(197,plain,
equal(multiplication(antidomain(antidomain(u)),forward_diamond(v,w)),domain_difference(u,antidomain(multiplication(v,antidomain(antidomain(w)))))),
inference(spr,[status(thm),theory(equality)],[37,38]),
[iquote('0:SpR:37.0,38.0')] ).
cnf(316,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,24]),
[iquote('0:SpR:2.0,24.0')] ).
cnf(346,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[32,316]),
[iquote('0:SpR:32.0,316.0')] ).
cnf(348,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[316,17]),
[iquote('0:SpL:316.0,17.0')] ).
cnf(351,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,346]),
[iquote('0:Rew:12.0,346.0')] ).
cnf(354,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[348]),
[iquote('0:Obv:348.0')] ).
cnf(360,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,354]),
[iquote('0:SpR:12.0,354.0')] ).
cnf(433,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[32,27]),
[iquote('0:SpR:32.0,27.0')] ).
cnf(446,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,433]),
[iquote('0:Rew:4.0,433.0')] ).
cnf(529,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[32,26]),
[iquote('0:SpR:32.0,26.0')] ).
cnf(530,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[351,26]),
[iquote('0:SpR:351.0,26.0')] ).
cnf(539,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,530]),
[iquote('0:Rew:3.0,530.0')] ).
cnf(545,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,529]),
[iquote('0:Rew:3.0,529.0')] ).
cnf(604,plain,
( ~ leq(forward_diamond(skc3,antidomain(antidomain(skc4))),antidomain(antidomain(skc5)))
| ~ equal(antidomain(antidomain(skc5)),antidomain(antidomain(skc5))) ),
inference(spl,[status(thm),theory(equality)],[98,40]),
[iquote('0:SpL:98.1,40.0')] ).
cnf(605,plain,
~ leq(forward_diamond(skc3,antidomain(antidomain(skc4))),antidomain(antidomain(skc5))),
inference(obv,[status(thm),theory(equality)],[604]),
[iquote('0:Obv:604.1')] ).
cnf(909,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(915,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(skc5),antidomain(antidomain(multiplication(skc3,antidomain(antidomain(skc4)))))))),antidomain(multiplication(antidomain(skc5),antidomain(antidomain(multiplication(skc3,antidomain(antidomain(skc4)))))))),
inference(spr,[status(thm),theory(equality)],[39,28]),
[iquote('0:SpR:39.0,28.0')] ).
cnf(933,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[351,909,90]),
[iquote('0:Rew:351.0,909.0,90.0,909.0')] ).
cnf(945,plain,
equal(antidomain(multiplication(antidomain(skc5),forward_diamond(skc3,skc4))),one),
inference(rew,[status(thm),theory(equality)],[351,915,90,37]),
[iquote('0:Rew:351.0,915.0,90.0,915.0,37.0,915.0')] ).
cnf(1023,plain,
equal(multiplication(one,multiplication(antidomain(skc5),forward_diamond(skc3,skc4))),zero),
inference(spr,[status(thm),theory(equality)],[945,7]),
[iquote('0:SpR:945.0,7.0')] ).
cnf(1047,plain,
equal(multiplication(antidomain(skc5),forward_diamond(skc3,skc4)),zero),
inference(rew,[status(thm),theory(equality)],[4,1023]),
[iquote('0:Rew:4.0,1023.0')] ).
cnf(1216,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[539,360]),
[iquote('0:SpR:539.0,360.0')] ).
cnf(1252,plain,
leq(domain_difference(u,v),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[38,1216]),
[iquote('0:SpR:38.0,1216.0')] ).
cnf(1391,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[933,7]),
[iquote('0:SpR:933.0,7.0')] ).
cnf(1439,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1391]),
[iquote('0:Rew:4.0,1391.0')] ).
cnf(4411,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1439,446]),
[iquote('0:SpR:1439.0,446.0')] ).
cnf(4430,plain,
equal(addition(zero,multiplication(antidomain(antidomain(skc5)),forward_diamond(skc3,skc4))),forward_diamond(skc3,skc4)),
inference(spr,[status(thm),theory(equality)],[1047,446]),
[iquote('0:SpR:1047.0,446.0')] ).
cnf(4454,plain,
equal(multiplication(antidomain(antidomain(skc5)),forward_diamond(skc3,skc4)),forward_diamond(skc3,skc4)),
inference(rew,[status(thm),theory(equality)],[65,4430]),
[iquote('0:Rew:65.0,4430.0')] ).
cnf(4455,plain,
equal(domain_difference(skc5,antidomain(multiplication(skc3,antidomain(antidomain(skc4))))),forward_diamond(skc3,skc4)),
inference(rew,[status(thm),theory(equality)],[197,4454]),
[iquote('0:Rew:197.0,4454.0')] ).
cnf(4458,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[65,4411,12]),
[iquote('0:Rew:65.0,4411.0,12.0,4411.0')] ).
cnf(4910,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1439,545]),
[iquote('0:SpR:1439.0,545.0')] ).
cnf(4932,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[65,4910]),
[iquote('0:Rew:65.0,4910.0')] ).
cnf(4933,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4458,4932]),
[iquote('0:Rew:4458.0,4932.0')] ).
cnf(5070,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4933,37]),
[iquote('0:SpR:4933.0,37.0')] ).
cnf(5107,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(forward_diamond(u,v))),
inference(spr,[status(thm),theory(equality)],[37,4933]),
[iquote('0:SpR:37.0,4933.0')] ).
cnf(5164,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[5070,37]),
[iquote('0:Rew:5070.0,37.0')] ).
cnf(5169,plain,
~ leq(forward_diamond(skc3,skc4),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[5164,605]),
[iquote('0:Rew:5164.0,605.0')] ).
cnf(5174,plain,
equal(domain_difference(skc5,antidomain(forward_diamond(skc3,skc4))),forward_diamond(skc3,skc4)),
inference(rew,[status(thm),theory(equality)],[5107,4455]),
[iquote('0:Rew:5107.0,4455.0')] ).
cnf(43901,plain,
leq(forward_diamond(skc3,skc4),antidomain(antidomain(skc5))),
inference(spr,[status(thm),theory(equality)],[5174,1252]),
[iquote('0:SpR:5174.0,1252.0')] ).
cnf(43953,plain,
$false,
inference(mrr,[status(thm)],[43901,5169]),
[iquote('0:MRR:43901.0,5169.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE100+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.11 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n004.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Thu Jun 16 07:55:38 EDT 2022
% 0.11/0.32 % CPUTime :
% 11.45/11.70
% 11.45/11.70 SPASS V 3.9
% 11.45/11.70 SPASS beiseite: Proof found.
% 11.45/11.70 % SZS status Theorem
% 11.45/11.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.45/11.70 SPASS derived 29417 clauses, backtracked 0 clauses, performed 0 splits and kept 4701 clauses.
% 11.45/11.70 SPASS allocated 121943 KBytes.
% 11.45/11.70 SPASS spent 0:0:11.05 on the problem.
% 11.45/11.70 0:00:00.04 for the input.
% 11.45/11.70 0:00:00.03 for the FLOTTER CNF translation.
% 11.45/11.70 0:00:00.19 for inferences.
% 11.45/11.70 0:00:00.00 for the backtracking.
% 11.45/11.70 0:0:10.73 for the reduction.
% 11.45/11.70
% 11.45/11.70
% 11.45/11.70 Here is a proof with depth 6, length 68 :
% 11.45/11.70 % SZS output start Refutation
% See solution above
% 11.45/11.70 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 domain4 additive_commutativity domain3 goals order domain_difference forward_diamond additive_associativity right_distributivity left_distributivity domain2
% 11.45/11.70
%------------------------------------------------------------------------------