TSTP Solution File: SEU078+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU078+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:33:51 EDT 2022
% Result : Theorem 1.93s 2.17s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 34
% Syntax : Number of clauses : 114 ( 32 unt; 30 nHn; 114 RR)
% Number of literals : 270 ( 0 equ; 139 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc10),
file('SEU078+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc10),
file('SEU078+1.p',unknown),
[] ).
cnf(7,axiom,
empty(empty_set),
file('SEU078+1.p',unknown),
[] ).
cnf(24,axiom,
empty(skf20(u)),
file('SEU078+1.p',unknown),
[] ).
cnf(26,axiom,
subset(u,u),
file('SEU078+1.p',unknown),
[] ).
cnf(28,axiom,
element(skf18(u),u),
file('SEU078+1.p',unknown),
[] ).
cnf(30,axiom,
~ empty(singleton(u)),
file('SEU078+1.p',unknown),
[] ).
cnf(33,axiom,
element(skf19(u),powerset(u)),
file('SEU078+1.p',unknown),
[] ).
cnf(34,axiom,
element(skf20(u),powerset(u)),
file('SEU078+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ empty(skf19(u))
| empty(u) ),
file('SEU078+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU078+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ disjoint(u,v)
| disjoint(v,u) ),
file('SEU078+1.p',unknown),
[] ).
cnf(43,axiom,
( in(u,v)
| disjoint(singleton(u),v) ),
file('SEU078+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU078+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ equal(u,empty_set)
| subset(u,singleton(v)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ element(u,powerset(v))
| subset(u,v) ),
file('SEU078+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU078+1.p',unknown),
[] ).
cnf(54,axiom,
( one_to_one(skc10)
| subset(relation_inverse_image(skc10,singleton(u)),singleton(skf11(u))) ),
file('SEU078+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ one_to_one(skc10)
| ~ subset(relation_inverse_image(skc10,singleton(skc11)),singleton(u)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU078+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SEU078+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ subset(u,singleton(v))
| equal(u,empty_set)
| equal(u,singleton(v)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf22(u),relation_rng(u)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ relation(u)
| ~ disjoint(relation_rng(u),v)
| equal(relation_inverse_image(u,v),empty_set) ),
file('SEU078+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_inverse_image(u,singleton(skf22(u))),singleton(v))
| one_to_one(u) ),
file('SEU078+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(skf14(u,x),relation_dom(u)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_inverse_image(u,x))
| in(apply(u,v),x) ),
file('SEU078+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| equal(apply(u,skf14(u,v)),v) ),
file('SEU078+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(u)
| ~ in(v,relation_rng(u))
| equal(relation_inverse_image(u,singleton(v)),singleton(skf23(v,u))) ),
file('SEU078+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ function(u)
| ~ relation(u)
| equal(v,relation_inverse_image(u,w))
| in(skf12(w,u,v),v)
| in(skf12(w,u,v),relation_dom(u)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ in(apply(u,skf12(v,u,w)),v)
| ~ in(skf12(v,u,w),w)
| ~ in(skf12(v,u,w),relation_dom(u)) ),
file('SEU078+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ function(u)
| ~ relation(u)
| equal(v,relation_inverse_image(u,w))
| in(apply(u,skf12(w,u,v)),w)
| in(skf12(w,u,v),v) ),
file('SEU078+1.p',unknown),
[] ).
cnf(80,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('SEU078+1.p',unknown),
[] ).
cnf(88,plain,
( ~ relation(skc10)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc10))
| equal(apply(skc10,skf14(skc10,u)),u) ),
inference(res,[status(thm),theory(equality)],[2,73]),
[iquote('0:Res:2.0,73.1')] ).
cnf(89,plain,
( ~ relation(skc10)
| ~ in(u,v)
| ~ equal(v,relation_inverse_image(skc10,w))
| in(apply(skc10,u),w) ),
inference(res,[status(thm),theory(equality)],[2,72]),
[iquote('0:Res:2.0,72.1')] ).
cnf(90,plain,
( ~ relation(skc10)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc10))
| in(skf14(skc10,w),relation_dom(skc10)) ),
inference(res,[status(thm),theory(equality)],[2,71]),
[iquote('0:Res:2.0,71.1')] ).
cnf(93,plain,
( ~ relation(skc10)
| ~ equal(relation_inverse_image(skc10,singleton(skf22(skc10))),singleton(u))
| one_to_one(skc10) ),
inference(res,[status(thm),theory(equality)],[2,67]),
[iquote('0:Res:2.0,67.1')] ).
cnf(94,plain,
( ~ relation(skc10)
| in(skf22(skc10),relation_rng(skc10))
| one_to_one(skc10) ),
inference(res,[status(thm),theory(equality)],[2,63]),
[iquote('0:Res:2.0,63.1')] ).
cnf(96,plain,
( ~ function(skc10)
| in(apply(skc10,skf12(u,skc10,v)),u)
| in(skf12(u,skc10,v),v)
| equal(v,relation_inverse_image(skc10,u)) ),
inference(res,[status(thm),theory(equality)],[1,79]),
[iquote('0:Res:1.0,79.0')] ).
cnf(98,plain,
( ~ function(skc10)
| in(skf12(u,skc10,v),relation_dom(skc10))
| in(skf12(u,skc10,v),v)
| equal(v,relation_inverse_image(skc10,u)) ),
inference(res,[status(thm),theory(equality)],[1,76]),
[iquote('0:Res:1.0,76.0')] ).
cnf(109,plain,
( ~ disjoint(relation_rng(skc10),u)
| equal(relation_inverse_image(skc10,u),empty_set) ),
inference(res,[status(thm),theory(equality)],[1,65]),
[iquote('0:Res:1.0,65.0')] ).
cnf(112,plain,
( one_to_one(skc10)
| in(skf22(skc10),relation_rng(skc10)) ),
inference(mrr,[status(thm)],[94,1]),
[iquote('0:MRR:94.0,1.0')] ).
cnf(113,plain,
( ~ equal(relation_inverse_image(skc10,singleton(skf22(skc10))),singleton(u))
| one_to_one(skc10) ),
inference(mrr,[status(thm)],[93,1]),
[iquote('0:MRR:93.0,1.0')] ).
cnf(115,plain,
( ~ in(u,v)
| ~ equal(v,relation_inverse_image(skc10,w))
| in(apply(skc10,u),w) ),
inference(mrr,[status(thm)],[89,1]),
[iquote('0:MRR:89.0,1.0')] ).
cnf(116,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc10))
| in(skf14(skc10,w),relation_dom(skc10)) ),
inference(mrr,[status(thm)],[90,1]),
[iquote('0:MRR:90.0,1.0')] ).
cnf(118,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc10))
| equal(apply(skc10,skf14(skc10,u)),u) ),
inference(mrr,[status(thm)],[88,1]),
[iquote('0:MRR:88.0,1.0')] ).
cnf(121,plain,
( equal(u,relation_inverse_image(skc10,v))
| in(skf12(v,skc10,u),u)
| in(skf12(v,skc10,u),relation_dom(skc10)) ),
inference(mrr,[status(thm)],[98,2]),
[iquote('0:MRR:98.0,2.0')] ).
cnf(123,plain,
( equal(u,relation_inverse_image(skc10,v))
| in(apply(skc10,skf12(v,skc10,u)),v)
| in(skf12(v,skc10,u),u) ),
inference(mrr,[status(thm)],[96,2]),
[iquote('0:MRR:96.0,2.0')] ).
cnf(125,plain,
one_to_one(skc10),
inference(spt,[spt(split,[position(s1)])],[112]),
[iquote('1:Spt:112.0')] ).
cnf(126,plain,
~ subset(relation_inverse_image(skc10,singleton(skc11)),singleton(u)),
inference(mrr,[status(thm)],[55,125]),
[iquote('1:MRR:55.0,125.0')] ).
cnf(129,plain,
equal(skf20(u),empty_set),
inference(ems,[status(thm)],[40,24]),
[iquote('0:EmS:40.0,24.0')] ).
cnf(141,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[129,34]),
[iquote('0:Rew:129.0,34.0')] ).
cnf(224,plain,
( in(u,v)
| disjoint(v,singleton(u)) ),
inference(res,[status(thm),theory(equality)],[43,41]),
[iquote('0:Res:43.1,41.0')] ).
cnf(250,plain,
subset(skf19(u),u),
inference(res,[status(thm),theory(equality)],[33,47]),
[iquote('0:Res:33.0,47.0')] ).
cnf(273,plain,
( empty(u)
| in(skf18(u),u) ),
inference(res,[status(thm),theory(equality)],[28,51]),
[iquote('0:Res:28.0,51.0')] ).
cnf(294,plain,
( equal(skf19(singleton(u)),empty_set)
| equal(skf19(singleton(u)),singleton(u)) ),
inference(res,[status(thm),theory(equality)],[250,60]),
[iquote('0:Res:250.0,60.0')] ).
cnf(312,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[141,62]),
[iquote('0:Res:141.0,62.2')] ).
cnf(315,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[312,7]),
[iquote('0:EmS:312.0,7.0')] ).
cnf(393,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[59]),
[iquote('0:EqR:59.1')] ).
cnf(411,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[58]),
[iquote('0:EqR:58.1')] ).
cnf(412,plain,
( ~ empty(singleton(u))
| ~ equal(v,u) ),
inference(res,[status(thm),theory(equality)],[393,44]),
[iquote('0:Res:393.1,44.1')] ).
cnf(415,plain,
~ empty(singleton(u)),
inference(aed,[status(thm),theory(equality)],[412]),
[iquote('0:AED:412.1')] ).
cnf(416,plain,
( empty(singleton(u))
| equal(skf18(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[273,411]),
[iquote('0:Res:273.1,411.0')] ).
cnf(467,plain,
equal(skf18(singleton(u)),u),
inference(mrr,[status(thm)],[416,30]),
[iquote('0:MRR:416.0,30.0')] ).
cnf(476,plain,
~ equal(relation_inverse_image(skc10,singleton(skc11)),empty_set),
inference(res,[status(thm),theory(equality)],[46,126]),
[iquote('1:Res:46.1,126.0')] ).
cnf(487,plain,
( empty(singleton(u))
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[467,273]),
[iquote('0:SpR:467.0,273.1')] ).
cnf(490,plain,
in(u,singleton(u)),
inference(mrr,[status(thm)],[487,415]),
[iquote('0:MRR:487.0,415.0')] ).
cnf(611,plain,
( ~ function(skc10)
| ~ relation(skc10)
| ~ one_to_one(skc10)
| ~ in(skc11,relation_rng(skc10))
| ~ subset(singleton(skf23(skc11,skc10)),singleton(u)) ),
inference(spl,[status(thm),theory(equality)],[74,126]),
[iquote('1:SpL:74.4,126.0')] ).
cnf(617,plain,
( ~ in(skc11,relation_rng(skc10))
| ~ subset(singleton(skf23(skc11,skc10)),singleton(u)) ),
inference(ssi,[status(thm)],[611,1,2,125]),
[iquote('1:SSi:611.2,611.1,611.0,1.0,2.0,125.0,1.0,2.0,125.0,1.0,2.0,125.0')] ).
cnf(636,plain,
( in(u,relation_rng(skc10))
| equal(relation_inverse_image(skc10,singleton(u)),empty_set) ),
inference(res,[status(thm),theory(equality)],[224,109]),
[iquote('0:Res:224.1,109.0')] ).
cnf(655,plain,
( ~ equal(empty_set,empty_set)
| in(skc11,relation_rng(skc10)) ),
inference(spl,[status(thm),theory(equality)],[636,476]),
[iquote('1:SpL:636.1,476.0')] ).
cnf(658,plain,
in(skc11,relation_rng(skc10)),
inference(obv,[status(thm),theory(equality)],[655]),
[iquote('1:Obv:655.0')] ).
cnf(661,plain,
~ subset(singleton(skf23(skc11,skc10)),singleton(u)),
inference(mrr,[status(thm)],[617,658]),
[iquote('1:MRR:617.0,658.0')] ).
cnf(663,plain,
$false,
inference(unc,[status(thm)],[661,26]),
[iquote('1:UnC:661.0,26.0')] ).
cnf(666,plain,
~ one_to_one(skc10),
inference(spt,[spt(split,[position(sa)])],[663,125]),
[iquote('1:Spt:663.0,112.0,125.0')] ).
cnf(667,plain,
in(skf22(skc10),relation_rng(skc10)),
inference(spt,[spt(split,[position(s2)])],[112]),
[iquote('1:Spt:663.0,112.1')] ).
cnf(668,plain,
subset(relation_inverse_image(skc10,singleton(u)),singleton(skf11(u))),
inference(mrr,[status(thm)],[54,666]),
[iquote('1:MRR:54.0,666.0')] ).
cnf(669,plain,
~ equal(relation_inverse_image(skc10,singleton(skf22(skc10))),singleton(u)),
inference(mrr,[status(thm)],[113,666]),
[iquote('1:MRR:113.1,666.0')] ).
cnf(721,plain,
( equal(relation_inverse_image(skc10,singleton(u)),empty_set)
| equal(relation_inverse_image(skc10,singleton(u)),singleton(skf11(u))) ),
inference(res,[status(thm),theory(equality)],[668,60]),
[iquote('1:Res:668.0,60.0')] ).
cnf(830,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)],[80]),
[iquote('0:EqR:80.3')] ).
cnf(966,plain,
( ~ equal(singleton(u),empty_set)
| equal(skf19(singleton(u)),empty_set) ),
inference(eqf,[status(thm),theory(equality)],[294]),
[iquote('0:EqF:294.1,294.0')] ).
cnf(1011,plain,
( ~ equal(singleton(u),empty_set)
| ~ empty(empty_set)
| empty(singleton(u)) ),
inference(spl,[status(thm),theory(equality)],[966,39]),
[iquote('0:SpL:966.1,39.0')] ).
cnf(1018,plain,
~ equal(singleton(u),empty_set),
inference(mrr,[status(thm)],[1011,7,415]),
[iquote('0:MRR:1011.1,1011.2,7.0,415.0')] ).
cnf(1089,plain,
( ~ equal(singleton(skf11(skf22(skc10))),singleton(u))
| equal(relation_inverse_image(skc10,singleton(skf22(skc10))),empty_set) ),
inference(spl,[status(thm),theory(equality)],[721,669]),
[iquote('1:SpL:721.1,669.0')] ).
cnf(1152,plain,
( ~ in(u,relation_rng(skc10))
| in(skf14(skc10,v),relation_dom(skc10)) ),
inference(eqr,[status(thm),theory(equality)],[116]),
[iquote('0:EqR:116.1')] ).
cnf(1179,plain,
in(skf14(skc10,u),relation_dom(skc10)),
inference(res,[status(thm),theory(equality)],[667,1152]),
[iquote('1:Res:667.0,1152.0')] ).
cnf(1183,plain,
( ~ in(u,relation_inverse_image(skc10,v))
| in(apply(skc10,u),v) ),
inference(eqr,[status(thm),theory(equality)],[115]),
[iquote('0:EqR:115.1')] ).
cnf(1268,plain,
( ~ in(u,relation_rng(skc10))
| equal(apply(skc10,skf14(skc10,u)),u) ),
inference(eqr,[status(thm),theory(equality)],[118]),
[iquote('0:EqR:118.1')] ).
cnf(1515,plain,
( ~ empty(u)
| ~ in(v,relation_inverse_image(skc10,u)) ),
inference(res,[status(thm),theory(equality)],[1183,44]),
[iquote('0:Res:1183.1,44.1')] ).
cnf(1639,plain,
( ~ empty(u)
| empty(relation_inverse_image(skc10,u)) ),
inference(res,[status(thm),theory(equality)],[273,1515]),
[iquote('0:Res:273.1,1515.1')] ).
cnf(1656,plain,
( ~ empty(u)
| equal(relation_inverse_image(skc10,u),empty_set) ),
inference(ems,[status(thm)],[40,1639]),
[iquote('0:EmS:40.0,1639.1')] ).
cnf(1803,plain,
( ~ empty(u)
| equal(v,relation_inverse_image(skc10,u))
| in(skf12(u,skc10,v),v) ),
inference(res,[status(thm),theory(equality)],[123,44]),
[iquote('0:Res:123.1,44.1')] ).
cnf(1834,plain,
( ~ empty(u)
| equal(v,empty_set)
| in(skf12(u,skc10,v),v) ),
inference(rew,[status(thm),theory(equality)],[1656,1803]),
[iquote('0:Rew:1656.1,1803.1')] ).
cnf(2887,plain,
( ~ function(skc10)
| ~ relation(skc10)
| ~ in(skf12(u,skc10,v),relation_dom(skc10))
| equal(v,relation_inverse_image(skc10,u))
| in(skf12(u,skc10,v),v)
| in(skf12(u,skc10,v),relation_inverse_image(skc10,u)) ),
inference(res,[status(thm),theory(equality)],[123,830]),
[iquote('0:Res:123.1,830.3')] ).
cnf(2891,plain,
( ~ in(skf12(u,skc10,v),relation_dom(skc10))
| equal(v,relation_inverse_image(skc10,u))
| in(skf12(u,skc10,v),v)
| in(skf12(u,skc10,v),relation_inverse_image(skc10,u)) ),
inference(ssi,[status(thm)],[2887,1,2]),
[iquote('0:SSi:2887.1,2887.0,1.0,2.0,1.0,2.0')] ).
cnf(2892,plain,
( equal(u,relation_inverse_image(skc10,v))
| in(skf12(v,skc10,u),u)
| in(skf12(v,skc10,u),relation_inverse_image(skc10,v)) ),
inference(mrr,[status(thm)],[2891,121]),
[iquote('0:MRR:2891.0,121.2')] ).
cnf(4339,plain,
( ~ empty(u)
| equal(singleton(v),empty_set)
| equal(skf12(u,skc10,singleton(v)),v) ),
inference(res,[status(thm),theory(equality)],[1834,411]),
[iquote('0:Res:1834.2,411.0')] ).
cnf(4349,plain,
( ~ empty(u)
| equal(skf12(u,skc10,singleton(v)),v) ),
inference(mrr,[status(thm)],[4339,1018]),
[iquote('0:MRR:4339.1,1018.0')] ).
cnf(4612,plain,
equal(relation_inverse_image(skc10,singleton(skf22(skc10))),empty_set),
inference(eqr,[status(thm),theory(equality)],[1089]),
[iquote('1:EqR:1089.0')] ).
cnf(6597,plain,
( equal(u,relation_inverse_image(skc10,singleton(skf22(skc10))))
| in(skf12(singleton(skf22(skc10)),skc10,u),u)
| in(skf12(singleton(skf22(skc10)),skc10,u),empty_set) ),
inference(spr,[status(thm),theory(equality)],[4612,2892]),
[iquote('1:SpR:4612.0,2892.2')] ).
cnf(6653,plain,
( equal(u,empty_set)
| in(skf12(singleton(skf22(skc10)),skc10,u),u)
| in(skf12(singleton(skf22(skc10)),skc10,u),empty_set) ),
inference(rew,[status(thm),theory(equality)],[4612,6597]),
[iquote('1:Rew:4612.0,6597.0')] ).
cnf(6654,plain,
( equal(u,empty_set)
| in(skf12(singleton(skf22(skc10)),skc10,u),u) ),
inference(mrr,[status(thm)],[6653,315]),
[iquote('1:MRR:6653.2,315.0')] ).
cnf(6681,plain,
( equal(singleton(u),empty_set)
| equal(skf12(singleton(skf22(skc10)),skc10,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[6654,411]),
[iquote('1:Res:6654.1,411.0')] ).
cnf(6699,plain,
equal(skf12(singleton(skf22(skc10)),skc10,singleton(u)),u),
inference(mrr,[status(thm)],[6681,1018]),
[iquote('1:MRR:6681.0,1018.0')] ).
cnf(6731,plain,
( ~ in(apply(skc10,u),singleton(skf22(skc10)))
| ~ in(skf12(singleton(skf22(skc10)),skc10,singleton(u)),singleton(u))
| ~ in(skf12(singleton(skf22(skc10)),skc10,singleton(u)),relation_dom(skc10)) ),
inference(spl,[status(thm),theory(equality)],[6699,77]),
[iquote('1:SpL:6699.0,77.0')] ).
cnf(6741,plain,
( ~ in(apply(skc10,u),singleton(skf22(skc10)))
| ~ in(u,singleton(u))
| ~ in(u,relation_dom(skc10)) ),
inference(rew,[status(thm),theory(equality)],[6699,6731]),
[iquote('1:Rew:6699.0,6731.2,6699.0,6731.1')] ).
cnf(6742,plain,
( ~ in(apply(skc10,u),singleton(skf22(skc10)))
| ~ in(u,relation_dom(skc10)) ),
inference(mrr,[status(thm)],[6741,490]),
[iquote('1:MRR:6741.1,490.0')] ).
cnf(6761,plain,
( ~ in(u,relation_rng(skc10))
| ~ in(u,singleton(skf22(skc10)))
| ~ in(skf14(skc10,u),relation_dom(skc10)) ),
inference(spl,[status(thm),theory(equality)],[1268,6742]),
[iquote('1:SpL:1268.1,6742.0')] ).
cnf(6777,plain,
( ~ in(u,relation_rng(skc10))
| ~ in(u,singleton(skf22(skc10))) ),
inference(mrr,[status(thm)],[6761,1179]),
[iquote('1:MRR:6761.2,1179.0')] ).
cnf(6818,plain,
( ~ empty(u)
| ~ in(skf12(u,skc10,singleton(skf22(skc10))),relation_rng(skc10))
| equal(singleton(skf22(skc10)),empty_set) ),
inference(res,[status(thm),theory(equality)],[1834,6777]),
[iquote('1:Res:1834.2,6777.1')] ).
cnf(6856,plain,
( ~ empty(u)
| ~ in(skf22(skc10),relation_rng(skc10))
| equal(singleton(skf22(skc10)),empty_set) ),
inference(rew,[status(thm),theory(equality)],[4349,6818]),
[iquote('1:Rew:4349.1,6818.1')] ).
cnf(6857,plain,
~ empty(u),
inference(mrr,[status(thm)],[6856,667,1018]),
[iquote('1:MRR:6856.1,6856.2,667.0,1018.0')] ).
cnf(6858,plain,
$false,
inference(unc,[status(thm)],[6857,7]),
[iquote('1:UnC:6857.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU078+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 : Sun Jun 19 15:07:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.17
% 1.93/2.17 SPASS V 3.9
% 1.93/2.17 SPASS beiseite: Proof found.
% 1.93/2.17 % SZS status Theorem
% 1.93/2.17 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.93/2.17 SPASS derived 5464 clauses, backtracked 55 clauses, performed 4 splits and kept 2792 clauses.
% 1.93/2.17 SPASS allocated 104070 KBytes.
% 1.93/2.17 SPASS spent 0:00:01.83 on the problem.
% 1.93/2.17 0:00:00.04 for the input.
% 1.93/2.17 0:00:00.06 for the FLOTTER CNF translation.
% 1.93/2.17 0:00:00.08 for inferences.
% 1.93/2.17 0:00:00.05 for the backtracking.
% 1.93/2.17 0:00:01.55 for the reduction.
% 1.93/2.17
% 1.93/2.17
% 1.93/2.17 Here is a proof with depth 8, length 114 :
% 1.93/2.17 % SZS output start Refutation
% See solution above
% 2.03/2.23 Formulae used in the proof : t159_funct_1 fc4_relat_1 rc2_subset_1 reflexivity_r1_tarski existence_m1_subset_1 fc2_subset_1 rc1_subset_1 t6_boole symmetry_r1_xboole_0 t56_zfmisc_1 t7_boole t39_zfmisc_1 t3_subset t2_subset d1_tarski antisymmetry_r2_hidden t5_subset t144_funct_1 t173_relat_1 d5_funct_1 d13_funct_1
% 2.03/2.23
%------------------------------------------------------------------------------