%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 02:28:39 EDT 2022
% Result : Theorem 16.04s 16.26s
% Output : Refutation 16.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of clauses : 59 ( 52 unt; 0 nHn; 59 RR)
% Number of literals : 66 ( 0 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(divergence(skc1),zero),
file('KLE129+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE129+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE129+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE129+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE129+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE129+1.p',unknown),
[] ).
cnf(9,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE129+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE129+1.p',unknown),
[] ).
cnf(14,axiom,
equal(forward_diamond(u,divergence(u)),divergence(u)),
file('KLE129+1.p',unknown),
[] ).
cnf(15,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE129+1.p',unknown),
[] ).
cnf(20,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE129+1.p',unknown),
[] ).
cnf(24,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE129+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE129+1.p',unknown),
[] ).
cnf(27,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE129+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ equal(addition(domain__dfg(u),forward_diamond(skc1,domain__dfg(u))),forward_diamond(skc1,domain__dfg(u)))
| equal(domain__dfg(u),zero) ),
file('KLE129+1.p',unknown),
[] ).
cnf(29,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE129+1.p',unknown),
[] ).
cnf(34,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[13,15]),
[iquote('0:Rew:13.0,15.0')] ).
cnf(39,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[9,20]),
[iquote('0:Rew:9.0,20.0,9.0,20.0')] ).
cnf(41,plain,
( ~ equal(addition(antidomain(antidomain(u)),forward_diamond(skc1,antidomain(antidomain(u)))),forward_diamond(skc1,antidomain(antidomain(u))))
| equal(antidomain(antidomain(u)),zero) ),
inference(rew,[status(thm),theory(equality)],[9,28]),
[iquote('0:Rew:9.0,28.1,9.0,28.0')] ).
cnf(56,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(68,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.0,2.0')] ).
cnf(91,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[56,34]),
[iquote('0:SpR:56.0,34.0')] ).
cnf(93,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[68,91]),
[iquote('0:Rew:68.0,91.0')] ).
cnf(248,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,24]),
[iquote('0:SpR:3.0,24.0')] ).
cnf(329,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[34,248]),
[iquote('0:SpR:34.0,248.0')] ).
cnf(335,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[13,329]),
[iquote('0:Rew:13.0,329.0')] ).
cnf(371,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[34,27]),
[iquote('0:SpR:34.0,27.0')] ).
cnf(382,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[5,371]),
[iquote('0:Rew:5.0,371.0')] ).
cnf(418,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[34,26]),
[iquote('0:SpR:34.0,26.0')] ).
cnf(430,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[4,418]),
[iquote('0:Rew:4.0,418.0')] ).
cnf(492,plain,
equal(addition(one,forward_diamond(u,v)),one),
inference(spr,[status(thm),theory(equality)],[39,335]),
[iquote('0:SpR:39.0,335.0')] ).
cnf(508,plain,
equal(addition(one,divergence(u)),one),
inference(spr,[status(thm),theory(equality)],[14,492]),
[iquote('0:SpR:14.0,492.0')] ).
cnf(527,plain,
equal(addition(multiplication(u,one),multiplication(u,divergence(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[508,26]),
[iquote('0:SpR:508.0,26.0')] ).
cnf(534,plain,
equal(addition(u,multiplication(u,divergence(v))),u),
inference(rew,[status(thm),theory(equality)],[4,527]),
[iquote('0:Rew:4.0,527.0')] ).
cnf(674,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)],[8,29]),
[iquote('0:SpR:8.0,29.0')] ).
cnf(696,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[335,674,93]),
[iquote('0:Rew:335.0,674.0,93.0,674.0')] ).
cnf(1183,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[696,8]),
[iquote('0:SpR:696.0,8.0')] ).
cnf(1226,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[5,1183]),
[iquote('0:Rew:5.0,1183.0')] ).
cnf(4061,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1226,382]),
[iquote('0:SpR:1226.0,382.0')] ).
cnf(4067,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[8,382]),
[iquote('0:SpR:8.0,382.0')] ).
cnf(4084,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[68,4067]),
[iquote('0:Rew:68.0,4067.0')] ).
cnf(4102,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[68,4061,13]),
[iquote('0:Rew:68.0,4061.0,13.0,4061.0')] ).
cnf(4143,plain,
equal(addition(antidomain(antidomain(divergence(u))),divergence(u)),antidomain(antidomain(divergence(u)))),
inference(spr,[status(thm),theory(equality)],[4084,534]),
[iquote('0:SpR:4084.0,534.0')] ).
cnf(4171,plain,
equal(addition(divergence(u),antidomain(antidomain(divergence(u)))),antidomain(antidomain(divergence(u)))),
inference(rew,[status(thm),theory(equality)],[13,4143]),
[iquote('0:Rew:13.0,4143.0')] ).
cnf(4507,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1226,430]),
[iquote('0:SpR:1226.0,430.0')] ).
cnf(4530,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[68,4507]),
[iquote('0:Rew:68.0,4507.0')] ).
cnf(4531,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4102,4530]),
[iquote('0:Rew:4102.0,4530.0')] ).
cnf(4648,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4531,39]),
[iquote('0:SpR:4531.0,39.0')] ).
cnf(4671,plain,
equal(antidomain(antidomain(forward_diamond(u,v))),forward_diamond(u,v)),
inference(spr,[status(thm),theory(equality)],[39,4531]),
[iquote('0:SpR:39.0,4531.0')] ).
cnf(4713,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[4648,39]),
[iquote('0:Rew:4648.0,39.0')] ).
cnf(4717,plain,
( ~ equal(addition(antidomain(antidomain(u)),forward_diamond(skc1,u)),forward_diamond(skc1,u))
| equal(antidomain(antidomain(u)),zero) ),
inference(rew,[status(thm),theory(equality)],[4713,41]),
[iquote('0:Rew:4713.0,41.0')] ).
cnf(5564,plain,
( ~ equal(addition(antidomain(antidomain(divergence(skc1))),divergence(skc1)),divergence(skc1))
| equal(antidomain(antidomain(divergence(skc1))),zero) ),
inference(spl,[status(thm),theory(equality)],[14,4717]),
[iquote('0:SpL:14.0,4717.0')] ).
cnf(5581,plain,
( ~ equal(addition(divergence(skc1),antidomain(antidomain(divergence(skc1)))),divergence(skc1))
| equal(antidomain(antidomain(divergence(skc1))),zero) ),
inference(rew,[status(thm),theory(equality)],[13,5564]),
[iquote('0:Rew:13.0,5564.0')] ).
cnf(5582,plain,
( ~ equal(antidomain(antidomain(divergence(skc1))),divergence(skc1))
| equal(antidomain(antidomain(divergence(skc1))),zero) ),
inference(rew,[status(thm),theory(equality)],[4171,5581]),
[iquote('0:Rew:4171.0,5581.0')] ).
cnf(48250,plain,
equal(antidomain(antidomain(divergence(u))),divergence(u)),
inference(spr,[status(thm),theory(equality)],[14,4671]),
[iquote('0:SpR:14.0,4671.0')] ).
cnf(48385,plain,
( ~ equal(divergence(skc1),divergence(skc1))
| equal(antidomain(antidomain(divergence(skc1))),zero) ),
inference(rew,[status(thm),theory(equality)],[48250,5582]),
[iquote('0:Rew:48250.0,5582.0')] ).
cnf(48504,plain,
equal(antidomain(antidomain(divergence(skc1))),zero),
inference(obv,[status(thm),theory(equality)],[48385]),
[iquote('0:Obv:48385.0')] ).
cnf(48505,plain,
equal(divergence(skc1),zero),
inference(rew,[status(thm),theory(equality)],[48250,48504]),
[iquote('0:Rew:48250.0,48504.0')] ).
cnf(48506,plain,
$false,
inference(mrr,[status(thm)],[48505,1]),
[iquote('0:MRR:48505.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 09:51:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 16.04/16.26
% 16.04/16.26 SPASS V 3.9
% 16.04/16.26 SPASS beiseite: Proof found.
% 16.04/16.26 % SZS status Theorem
% 16.04/16.26 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.04/16.26 SPASS derived 31642 clauses, backtracked 0 clauses, performed 0 splits and kept 5537 clauses.
% 16.04/16.26 SPASS allocated 129611 KBytes.
% 16.04/16.26 SPASS spent 0:0:15.48 on the problem.
% 16.04/16.26 0:00:00.04 for the input.
% 16.04/16.26 0:00:00.03 for the FLOTTER CNF translation.
% 16.04/16.26 0:00:00.21 for inferences.
% 16.04/16.26 0:00:00.00 for the backtracking.
% 16.04/16.26 0:0:15.13 for the reduction.
% 16.04/16.26
% 16.04/16.26
% 16.04/16.26 Here is a proof with depth 6, length 59 :
% 16.04/16.26 % SZS output start Refutation
% See solution above
% 16.04/16.26 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 domain4 additive_commutativity divergence1 domain3 forward_diamond additive_associativity right_distributivity left_distributivity domain2
% 16.04/16.26
%------------------------------------------------------------------------------