TSTP Solution File: SEU061+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 14:33:47 EDT 2022
% Result : Theorem 138.76s 139.05s
% Output : Refutation 138.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 61 ( 19 unt; 13 nHn; 61 RR)
% Number of literals : 149 ( 0 equ; 76 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc10),
file('SEU061+1.p',unknown),
[] ).
cnf(6,axiom,
empty(empty_set),
file('SEU061+1.p',unknown),
[] ).
cnf(23,axiom,
empty(skf23(u)),
file('SEU061+1.p',unknown),
[] ).
cnf(26,axiom,
element(skf21(u),u),
file('SEU061+1.p',unknown),
[] ).
cnf(34,axiom,
element(skf23(u),powerset(u)),
file('SEU061+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU061+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU061+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU061+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ equal(relation_inverse_image(skc10,singleton(skc11)),empty_set)
| in(skc11,relation_rng(skc10)) ),
file('SEU061+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ in(skc11,relation_rng(skc10))
| equal(relation_inverse_image(skc10,singleton(skc11)),empty_set) ),
file('SEU061+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU061+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SEU061+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU061+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ relation(u)
| ~ equal(v,relation_rng(u))
| ~ in(ordered_pair(w,x),u)
| in(x,v) ),
file('SEU061+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(ordered_pair(skf17(u,v),v),u) ),
file('SEU061+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ relation(u)
| equal(v,relation_inverse_image(u,w))
| in(skf13(w,u,v),v)
| in(skf14(w,x,y),w) ),
file('SEU061+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(x,relation_inverse_image(u,w))
| ~ in(ordered_pair(y,v),u)
| in(y,x) ),
file('SEU061+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ relation(u)
| equal(v,relation_inverse_image(u,w))
| in(ordered_pair(skf13(w,u,v),skf14(w,v,u)),u)
| in(skf13(w,u,v),v) ),
file('SEU061+1.p',unknown),
[] ).
cnf(73,plain,
( ~ in(u,v)
| ~ equal(w,relation_inverse_image(skc10,v))
| ~ in(ordered_pair(x,u),skc10)
| in(x,w) ),
inference(res,[status(thm),theory(equality)],[1,68]),
[iquote('0:Res:1.0,68.0')] ).
cnf(78,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc10))
| in(ordered_pair(skf17(skc10,u),u),skc10) ),
inference(res,[status(thm),theory(equality)],[1,63]),
[iquote('0:Res:1.0,63.0')] ).
cnf(79,plain,
( ~ equal(u,relation_rng(skc10))
| ~ in(ordered_pair(v,w),skc10)
| in(w,u) ),
inference(res,[status(thm),theory(equality)],[1,61]),
[iquote('0:Res:1.0,61.0')] ).
cnf(81,plain,
equal(skf23(u),empty_set),
inference(ems,[status(thm)],[38,23]),
[iquote('0:EmS:38.0,23.0')] ).
cnf(93,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[81,34]),
[iquote('0:Rew:81.0,34.0')] ).
cnf(121,plain,
( empty(u)
| in(skf21(u),u) ),
inference(res,[status(thm),theory(equality)],[26,48]),
[iquote('0:Res:26.0,48.0')] ).
cnf(143,plain,
~ in(skc11,relation_rng(skc10)),
inference(spt,[spt(split,[position(s1)])],[52]),
[iquote('1:Spt:52.0')] ).
cnf(144,plain,
~ equal(relation_inverse_image(skc10,singleton(skc11)),empty_set),
inference(mrr,[status(thm)],[51,143]),
[iquote('1:MRR:51.1,143.0')] ).
cnf(169,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[93,58]),
[iquote('0:Res:93.0,58.2')] ).
cnf(174,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[169,6]),
[iquote('0:EmS:169.0,6.0')] ).
cnf(218,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[56]),
[iquote('0:EqR:56.1')] ).
cnf(220,plain,
( ~ empty(singleton(u))
| ~ equal(v,u) ),
inference(res,[status(thm),theory(equality)],[218,42]),
[iquote('0:Res:218.1,42.1')] ).
cnf(224,plain,
~ empty(singleton(u)),
inference(aed,[status(thm),theory(equality)],[220]),
[iquote('0:AED:220.1')] ).
cnf(232,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.1')] ).
cnf(239,plain,
( empty(singleton(u))
| equal(skf21(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[121,232]),
[iquote('0:Res:121.1,232.0')] ).
cnf(242,plain,
equal(skf21(singleton(u)),u),
inference(mrr,[status(thm)],[239,224]),
[iquote('0:MRR:239.0,224.0')] ).
cnf(246,plain,
( empty(singleton(u))
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[242,121]),
[iquote('0:SpR:242.0,121.1')] ).
cnf(249,plain,
in(u,singleton(u)),
inference(mrr,[status(thm)],[246,224]),
[iquote('0:MRR:246.0,224.0')] ).
cnf(313,plain,
( ~ relation(u)
| ~ in(v,relation_rng(u))
| in(ordered_pair(skf17(u,v),v),u) ),
inference(eqr,[status(thm),theory(equality)],[63]),
[iquote('0:EqR:63.2')] ).
cnf(394,plain,
( ~ relation(u)
| equal(v,relation_inverse_image(u,singleton(w)))
| in(skf13(singleton(w),u,v),v)
| equal(skf14(singleton(w),x,y),w) ),
inference(res,[status(thm),theory(equality)],[64,232]),
[iquote('0:Res:64.3,232.0')] ).
cnf(518,plain,
( ~ relation(u)
| ~ relation(u)
| ~ equal(v,relation_rng(u))
| equal(w,relation_inverse_image(u,x))
| in(skf13(x,u,w),w)
| in(skf14(x,w,u),v) ),
inference(res,[status(thm),theory(equality)],[69,61]),
[iquote('0:Res:69.2,61.2')] ).
cnf(529,plain,
( ~ relation(u)
| ~ equal(v,relation_rng(u))
| equal(w,relation_inverse_image(u,x))
| in(skf13(x,u,w),w)
| in(skf14(x,w,u),v) ),
inference(obv,[status(thm),theory(equality)],[518]),
[iquote('0:Obv:518.0')] ).
cnf(1064,plain,
( ~ relation(skc10)
| ~ in(u,relation_rng(skc10))
| ~ equal(v,relation_rng(skc10))
| in(u,v) ),
inference(res,[status(thm),theory(equality)],[313,79]),
[iquote('0:Res:313.2,79.1')] ).
cnf(1067,plain,
( ~ in(u,relation_rng(skc10))
| ~ equal(v,relation_rng(skc10))
| in(u,v) ),
inference(ssi,[status(thm)],[1064,1]),
[iquote('0:SSi:1064.0,1.0')] ).
cnf(1222,plain,
( ~ in(u,relation_rng(skc10))
| in(ordered_pair(skf17(skc10,u),u),skc10) ),
inference(eqr,[status(thm),theory(equality)],[78]),
[iquote('0:EqR:78.1')] ).
cnf(1991,plain,
( ~ in(u,v)
| ~ in(ordered_pair(w,u),skc10)
| in(w,relation_inverse_image(skc10,v)) ),
inference(eqr,[status(thm),theory(equality)],[73]),
[iquote('0:EqR:73.1')] ).
cnf(2310,plain,
( ~ relation(u)
| equal(v,relation_inverse_image(u,w))
| in(skf13(w,u,v),v)
| in(skf14(w,v,u),relation_rng(u)) ),
inference(eqr,[status(thm),theory(equality)],[529]),
[iquote('0:EqR:529.1')] ).
cnf(4791,plain,
( ~ in(u,relation_rng(skc10))
| ~ in(u,v)
| in(skf17(skc10,u),relation_inverse_image(skc10,v)) ),
inference(res,[status(thm),theory(equality)],[1222,1991]),
[iquote('0:Res:1222.1,1991.1')] ).
cnf(13903,plain,
( ~ relation(u)
| ~ relation(v)
| equal(w,relation_inverse_image(u,singleton(x)))
| in(skf13(singleton(x),u,w),w)
| equal(y,relation_inverse_image(v,singleton(x)))
| in(skf13(singleton(x),v,y),y)
| in(x,relation_rng(v)) ),
inference(spr,[status(thm),theory(equality)],[394,2310]),
[iquote('0:SpR:394.3,2310.3')] ).
cnf(14009,plain,
( ~ relation(u)
| equal(v,relation_inverse_image(u,singleton(w)))
| in(skf13(singleton(w),u,v),v)
| in(w,relation_rng(u)) ),
inference(con,[status(thm)],[13903]),
[iquote('0:Con:13903.0')] ).
cnf(43422,plain,
( ~ relation(u)
| equal(relation_inverse_image(u,singleton(v)),empty_set)
| in(v,relation_rng(u)) ),
inference(res,[status(thm),theory(equality)],[14009,174]),
[iquote('0:Res:14009.2,174.0')] ).
cnf(43629,plain,
( ~ relation(skc10)
| ~ equal(empty_set,empty_set)
| in(skc11,relation_rng(skc10)) ),
inference(spl,[status(thm),theory(equality)],[43422,144]),
[iquote('1:SpL:43422.1,144.0')] ).
cnf(43644,plain,
( ~ relation(skc10)
| in(skc11,relation_rng(skc10)) ),
inference(obv,[status(thm),theory(equality)],[43629]),
[iquote('1:Obv:43629.1')] ).
cnf(43645,plain,
in(skc11,relation_rng(skc10)),
inference(ssi,[status(thm)],[43644,1]),
[iquote('1:SSi:43644.0,1.0')] ).
cnf(43646,plain,
$false,
inference(mrr,[status(thm)],[43645,143]),
[iquote('1:MRR:43645.0,143.0')] ).
cnf(43662,plain,
in(skc11,relation_rng(skc10)),
inference(spt,[spt(split,[position(sa)])],[43646,143]),
[iquote('1:Spt:43646.0,52.0,143.0')] ).
cnf(43663,plain,
equal(relation_inverse_image(skc10,singleton(skc11)),empty_set),
inference(spt,[spt(split,[position(s2)])],[52]),
[iquote('1:Spt:43646.0,52.1')] ).
cnf(43802,plain,
( ~ in(u,relation_rng(skc10))
| ~ in(u,singleton(skc11))
| in(skf17(skc10,u),empty_set) ),
inference(spr,[status(thm),theory(equality)],[43663,4791]),
[iquote('1:SpR:43663.0,4791.2')] ).
cnf(43825,plain,
( ~ in(u,relation_rng(skc10))
| ~ in(u,singleton(skc11)) ),
inference(mrr,[status(thm)],[43802,174]),
[iquote('1:MRR:43802.2,174.0')] ).
cnf(43833,plain,
( ~ equal(u,relation_rng(skc10))
| in(skc11,u) ),
inference(res,[status(thm),theory(equality)],[43662,1067]),
[iquote('1:Res:43662.0,1067.0')] ).
cnf(46816,plain,
( ~ equal(relation_rng(skc10),relation_rng(skc10))
| ~ in(skc11,singleton(skc11)) ),
inference(res,[status(thm),theory(equality)],[43833,43825]),
[iquote('1:Res:43833.1,43825.0')] ).
cnf(46899,plain,
~ in(skc11,singleton(skc11)),
inference(obv,[status(thm),theory(equality)],[46816]),
[iquote('1:Obv:46816.0')] ).
cnf(46900,plain,
$false,
inference(mrr,[status(thm)],[46899,249]),
[iquote('1:MRR:46899.0,249.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jun 19 20:02:30 EDT 2022
% 0.11/0.32 % CPUTime :
% 138.76/139.05
% 138.76/139.05 SPASS V 3.9
% 138.76/139.05 SPASS beiseite: Proof found.
% 138.76/139.05 % SZS status Theorem
% 138.76/139.05 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 138.76/139.05 SPASS derived 38950 clauses, backtracked 2230 clauses, performed 6 splits and kept 22049 clauses.
% 138.76/139.05 SPASS allocated 139097 KBytes.
% 138.76/139.05 SPASS spent 0:2:16.05 on the problem.
% 138.76/139.05 0:00:00.03 for the input.
% 138.76/139.05 0:00:00.05 for the FLOTTER CNF translation.
% 138.76/139.05 0:00:00.89 for inferences.
% 138.76/139.05 0:00:06.01 for the backtracking.
% 138.76/139.05 0:02:08.31 for the reduction.
% 138.76/139.05
% 138.76/139.05
% 138.76/139.05 Here is a proof with depth 5, length 61 :
% 138.76/139.05 % SZS output start Refutation
% See solution above
% 138.76/139.05 Formulae used in the proof : t142_funct_1 fc4_relat_1 rc2_subset_1 existence_m1_subset_1 t6_boole t7_boole t2_subset d1_tarski antisymmetry_r2_hidden t5_subset d5_relat_1 d14_relat_1
% 138.76/139.05
%------------------------------------------------------------------------------