TSTP Solution File: SEU293+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Tue Jul 19 14:35:55 EDT 2022
% Result : Theorem 0.47s 0.64s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of clauses : 44 ( 19 unt; 3 nHn; 44 RR)
% Number of literals : 97 ( 0 equ; 57 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
function(skc15),
file('SEU293+1.p',unknown),
[] ).
cnf(33,axiom,
relation_of2_as_subset(skc15,skc17,skc16),
file('SEU293+1.p',unknown),
[] ).
cnf(34,axiom,
quasi_total(skc15,skc17,skc16),
file('SEU293+1.p',unknown),
[] ).
cnf(35,axiom,
~ equal(skc16,empty_set),
file('SEU293+1.p',unknown),
[] ).
cnf(46,axiom,
( skP0(u,v)
| equal(v,empty_set) ),
file('SEU293+1.p',unknown),
[] ).
cnf(59,axiom,
( in(skc19,skc17)
| in(skc19,relation_inverse_image(skc15,skc18)) ),
file('SEU293+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ element(u,powerset(cartesian_product2(v,w)))
| relation(u) ),
file('SEU293+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ relation_of2_as_subset(u,v,w)
| relation_of2(u,v,w) ),
file('SEU293+1.p',unknown),
[] ).
cnf(70,axiom,
( in(skc19,relation_inverse_image(skc15,skc18))
| in(apply(skc15,skc19),skc18) ),
file('SEU293+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ relation_of2_as_subset(u,v,w)
| element(u,powerset(cartesian_product2(v,w))) ),
file('SEU293+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ relation_of2(u,v,w)
| equal(relation_dom_as_subset(v,w,u),relation_dom(u)) ),
file('SEU293+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ in(skc19,skc17)
| ~ in(skc19,relation_inverse_image(skc15,skc18))
| ~ in(apply(skc15,skc19),skc18) ),
file('SEU293+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ skP0(u,v)
| ~ relation_of2_as_subset(w,u,v)
| ~ quasi_total(w,u,v)
| equal(relation_dom_as_subset(u,v,w),u) ),
file('SEU293+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_inverse_image(u,x))
| in(v,relation_dom(u)) ),
file('SEU293+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_inverse_image(u,x))
| in(apply(u,v),x) ),
file('SEU293+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,relation_inverse_image(u,x))
| ~ in(apply(u,v),x)
| in(v,w) ),
file('SEU293+1.p',unknown),
[] ).
cnf(94,plain,
( ~ relation(skc15)
| ~ in(u,v)
| ~ equal(v,relation_inverse_image(skc15,w))
| in(u,relation_dom(skc15)) ),
inference(res,[status(thm),theory(equality)],[1,82]),
[iquote('0:Res:1.0,82.1')] ).
cnf(96,plain,
skP0(u,skc16),
inference(res,[status(thm),theory(equality)],[46,35]),
[iquote('0:Res:46.0,35.0')] ).
cnf(102,plain,
( ~ skP0(skc17,skc16)
| ~ relation_of2_as_subset(skc15,skc17,skc16)
| equal(relation_dom_as_subset(skc17,skc16,skc15),skc17) ),
inference(res,[status(thm),theory(equality)],[34,81]),
[iquote('0:Res:34.0,81.0')] ).
cnf(106,plain,
element(skc15,powerset(cartesian_product2(skc17,skc16))),
inference(res,[status(thm),theory(equality)],[33,72]),
[iquote('0:Res:33.0,72.0')] ).
cnf(107,plain,
relation_of2(skc15,skc17,skc16),
inference(res,[status(thm),theory(equality)],[33,66]),
[iquote('0:Res:33.0,66.0')] ).
cnf(110,plain,
equal(relation_dom_as_subset(skc17,skc16,skc15),skc17),
inference(mrr,[status(thm)],[102,96,33]),
[iquote('0:MRR:102.0,102.1,96.0,33.0')] ).
cnf(113,plain,
in(skc19,relation_inverse_image(skc15,skc18)),
inference(spt,[spt(split,[position(s1)])],[59]),
[iquote('1:Spt:59.1')] ).
cnf(114,plain,
( ~ in(skc19,skc17)
| ~ in(apply(skc15,skc19),skc18) ),
inference(mrr,[status(thm)],[77,113]),
[iquote('1:MRR:77.1,113.0')] ).
cnf(156,plain,
relation(skc15),
inference(res,[status(thm),theory(equality)],[106,63]),
[iquote('0:Res:106.0,63.0')] ).
cnf(159,plain,
( ~ in(u,v)
| ~ equal(v,relation_inverse_image(skc15,w))
| in(u,relation_dom(skc15)) ),
inference(mrr,[status(thm)],[94,156]),
[iquote('0:MRR:94.0,156.0')] ).
cnf(266,plain,
( ~ relation_of2(skc15,skc17,skc16)
| equal(relation_dom(skc15),skc17) ),
inference(spr,[status(thm),theory(equality)],[74,110]),
[iquote('0:SpR:74.1,110.0')] ).
cnf(268,plain,
equal(relation_dom(skc15),skc17),
inference(mrr,[status(thm)],[266,107]),
[iquote('0:MRR:266.0,107.0')] ).
cnf(276,plain,
( ~ in(u,v)
| ~ equal(v,relation_inverse_image(skc15,w))
| in(u,skc17) ),
inference(rew,[status(thm),theory(equality)],[268,159]),
[iquote('0:Rew:268.0,159.2')] ).
cnf(361,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_inverse_image(u,w))
| in(apply(u,v),w) ),
inference(eqr,[status(thm),theory(equality)],[83]),
[iquote('0:EqR:83.3')] ).
cnf(456,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ in(apply(u,v),w)
| in(v,relation_inverse_image(u,w)) ),
inference(eqr,[status(thm),theory(equality)],[87]),
[iquote('0:EqR:87.3')] ).
cnf(812,plain,
( ~ in(u,relation_inverse_image(skc15,v))
| in(u,skc17) ),
inference(eqr,[status(thm),theory(equality)],[276]),
[iquote('0:EqR:276.1')] ).
cnf(838,plain,
in(skc19,skc17),
inference(res,[status(thm),theory(equality)],[113,812]),
[iquote('1:Res:113.0,812.0')] ).
cnf(846,plain,
~ in(apply(skc15,skc19),skc18),
inference(mrr,[status(thm)],[114,838]),
[iquote('1:MRR:114.0,838.0')] ).
cnf(1127,plain,
( ~ function(skc15)
| ~ relation(skc15)
| ~ in(skc19,relation_inverse_image(skc15,skc18)) ),
inference(res,[status(thm),theory(equality)],[361,846]),
[iquote('1:Res:361.3,846.0')] ).
cnf(1130,plain,
~ in(skc19,relation_inverse_image(skc15,skc18)),
inference(ssi,[status(thm)],[1127,1,156]),
[iquote('1:SSi:1127.1,1127.0,1.0,156.0,1.0,156.0')] ).
cnf(1131,plain,
$false,
inference(mrr,[status(thm)],[1130,113]),
[iquote('1:MRR:1130.0,113.0')] ).
cnf(1133,plain,
~ in(skc19,relation_inverse_image(skc15,skc18)),
inference(spt,[spt(split,[position(sa)])],[1131,113]),
[iquote('1:Spt:1131.0,59.1,113.0')] ).
cnf(1134,plain,
in(skc19,skc17),
inference(spt,[spt(split,[position(s2)])],[59]),
[iquote('1:Spt:1131.0,59.0')] ).
cnf(1136,plain,
in(apply(skc15,skc19),skc18),
inference(mrr,[status(thm)],[70,1133]),
[iquote('1:MRR:70.0,1133.0')] ).
cnf(1618,plain,
( ~ function(skc15)
| ~ relation(skc15)
| ~ in(skc19,relation_dom(skc15))
| in(skc19,relation_inverse_image(skc15,skc18)) ),
inference(res,[status(thm),theory(equality)],[1136,456]),
[iquote('1:Res:1136.0,456.3')] ).
cnf(1620,plain,
( ~ function(skc15)
| ~ relation(skc15)
| ~ in(skc19,skc17)
| in(skc19,relation_inverse_image(skc15,skc18)) ),
inference(rew,[status(thm),theory(equality)],[268,1618]),
[iquote('1:Rew:268.0,1618.2')] ).
cnf(1621,plain,
( ~ in(skc19,skc17)
| in(skc19,relation_inverse_image(skc15,skc18)) ),
inference(ssi,[status(thm)],[1620,1,156]),
[iquote('1:SSi:1620.1,1620.0,1.0,156.0,1.0,156.0')] ).
cnf(1622,plain,
$false,
inference(mrr,[status(thm)],[1621,1134,1133]),
[iquote('1:MRR:1621.0,1621.1,1134.0,1133.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 13:25:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 1237 clauses, backtracked 8 clauses, performed 1 splits and kept 721 clauses.
% 0.47/0.64 SPASS allocated 99115 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.27 on the problem.
% 0.47/0.64 0:00:00.04 for the input.
% 0.47/0.64 0:00:00.04 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.02 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.15 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 3, length 44 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.64 Formulae used in the proof : t46_funct_2 d1_funct_2 cc1_relset_1 redefinition_m2_relset_1 dt_m2_relset_1 redefinition_k4_relset_1 d13_funct_1 antisymmetry_r2_hidden
% 0.47/0.64
%------------------------------------------------------------------------------