TSTP Solution File: SEU191+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU191+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 14:34:51 EDT 2022
% Result : Theorem 22.30s 22.47s
% Output : Refutation 22.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 15 unt; 2 nHn; 51 RR)
% Number of literals : 154 ( 0 equ; 110 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc8),
file('SEU191+1.p',unknown),
[] ).
cnf(9,axiom,
relation(identity_relation(u)),
file('SEU191+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ relation(u)
| ~ relation(v)
| relation(relation_composition(v,u)) ),
file('SEU191+1.p',unknown),
[] ).
cnf(30,axiom,
( in(skc11,skc9)
| in(ordered_pair(skc11,skc10),relation_composition(identity_relation(skc9),skc8)) ),
file('SEU191+1.p',unknown),
[] ).
cnf(31,axiom,
( in(ordered_pair(skc11,skc10),skc8)
| in(ordered_pair(skc11,skc10),relation_composition(identity_relation(skc9),skc8)) ),
file('SEU191+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ relation(u)
| ~ equal(u,identity_relation(v))
| ~ in(ordered_pair(w,x),u)
| in(w,v) ),
file('SEU191+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ relation(u)
| ~ equal(u,identity_relation(v))
| ~ in(ordered_pair(w,x),u)
| equal(w,x) ),
file('SEU191+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ in(skc11,skc9)
| ~ in(ordered_pair(skc11,skc10),skc8)
| ~ in(ordered_pair(skc11,skc10),relation_composition(identity_relation(skc9),skc8)) ),
file('SEU191+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ relation(u)
| ~ equal(v,w)
| ~ in(v,x)
| ~ equal(u,identity_relation(x))
| in(ordered_pair(v,w),u) ),
file('SEU191+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ equal(u,relation_composition(w,v))
| ~ in(ordered_pair(x,y),u)
| in(ordered_pair(skf9(v,y,z,x1),y),v) ),
file('SEU191+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ equal(u,relation_composition(w,v))
| ~ in(ordered_pair(x,y),u)
| in(ordered_pair(x,skf9(v,y,w,x)),w) ),
file('SEU191+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ equal(u,relation_composition(w,v))
| ~ in(ordered_pair(x,y),v)
| ~ in(ordered_pair(z,x),w)
| in(ordered_pair(z,y),u) ),
file('SEU191+1.p',unknown),
[] ).
cnf(64,plain,
( ~ relation(u)
| ~ relation(v)
| ~ equal(u,relation_composition(v,skc8))
| ~ in(ordered_pair(w,x),u)
| in(ordered_pair(w,skf9(skc8,x,v,w)),v) ),
inference(res,[status(thm),theory(equality)],[1,39]),
[iquote('0:Res:1.0,39.1')] ).
cnf(66,plain,
( ~ relation(u)
| relation(relation_composition(u,skc8)) ),
inference(res,[status(thm),theory(equality)],[1,25]),
[iquote('0:Res:1.0,25.1')] ).
cnf(115,plain,
in(ordered_pair(skc11,skc10),relation_composition(identity_relation(skc9),skc8)),
inference(spt,[spt(split,[position(s1)])],[30]),
[iquote('1:Spt:30.1')] ).
cnf(116,plain,
( ~ in(skc11,skc9)
| ~ in(ordered_pair(skc11,skc10),skc8) ),
inference(mrr,[status(thm)],[34,115]),
[iquote('1:MRR:34.2,115.0')] ).
cnf(283,plain,
( ~ relation(identity_relation(u))
| ~ equal(v,w)
| ~ in(v,u)
| in(ordered_pair(v,w),identity_relation(u)) ),
inference(eqr,[status(thm),theory(equality)],[36]),
[iquote('0:EqR:36.3')] ).
cnf(284,plain,
( ~ equal(u,v)
| ~ in(u,w)
| in(ordered_pair(u,v),identity_relation(w)) ),
inference(ssi,[status(thm)],[283,9]),
[iquote('0:SSi:283.0,9.0')] ).
cnf(444,plain,
( ~ relation(relation_composition(u,v))
| ~ relation(v)
| ~ relation(u)
| ~ in(ordered_pair(w,x),relation_composition(u,v))
| in(ordered_pair(w,skf9(v,x,u,w)),u) ),
inference(eqr,[status(thm),theory(equality)],[39]),
[iquote('0:EqR:39.3')] ).
cnf(450,plain,
( ~ relation(u)
| ~ relation(v)
| ~ in(ordered_pair(w,x),relation_composition(v,u))
| in(ordered_pair(w,skf9(u,x,v,w)),v) ),
inference(ssi,[status(thm)],[444,25]),
[iquote('0:SSi:444.0,25.2')] ).
cnf(465,plain,
( ~ relation(relation_composition(u,v))
| ~ relation(v)
| ~ relation(u)
| ~ in(ordered_pair(w,x),relation_composition(u,v))
| in(ordered_pair(skf9(v,x,y,z),x),v) ),
inference(eqr,[status(thm),theory(equality)],[38]),
[iquote('0:EqR:38.3')] ).
cnf(471,plain,
( ~ relation(u)
| ~ relation(v)
| ~ in(ordered_pair(w,x),relation_composition(v,u))
| in(ordered_pair(skf9(u,x,y,z),x),u) ),
inference(ssi,[status(thm)],[465,25]),
[iquote('0:SSi:465.0,25.2')] ).
cnf(502,plain,
( ~ relation(relation_composition(u,v))
| ~ relation(v)
| ~ relation(u)
| ~ in(ordered_pair(w,x),v)
| ~ in(ordered_pair(y,w),u)
| in(ordered_pair(y,x),relation_composition(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[41]),
[iquote('0:EqR:41.3')] ).
cnf(508,plain,
( ~ relation(u)
| ~ relation(v)
| ~ in(ordered_pair(w,x),u)
| ~ in(ordered_pair(y,w),v)
| in(ordered_pair(y,x),relation_composition(v,u)) ),
inference(ssi,[status(thm)],[502,25]),
[iquote('0:SSi:502.0,25.2')] ).
cnf(1319,plain,
( ~ relation(u)
| ~ relation(v)
| ~ relation(v)
| ~ in(ordered_pair(w,x),relation_composition(v,u))
| ~ equal(v,identity_relation(y))
| equal(skf9(u,x,v,w),w) ),
inference(res,[status(thm),theory(equality)],[450,33]),
[iquote('0:Res:450.3,33.2')] ).
cnf(1330,plain,
( ~ relation(u)
| ~ relation(v)
| ~ in(ordered_pair(w,x),relation_composition(v,u))
| ~ equal(v,identity_relation(y))
| equal(skf9(u,x,v,w),w) ),
inference(obv,[status(thm),theory(equality)],[1319]),
[iquote('0:Obv:1319.1')] ).
cnf(1357,plain,
( ~ relation(skc8)
| ~ relation(identity_relation(skc9))
| in(ordered_pair(skf9(skc8,skc10,u,v),skc10),skc8) ),
inference(res,[status(thm),theory(equality)],[115,471]),
[iquote('1:Res:115.0,471.2')] ).
cnf(1367,plain,
in(ordered_pair(skf9(skc8,skc10,u,v),skc10),skc8),
inference(ssi,[status(thm)],[1357,9,1]),
[iquote('1:SSi:1357.1,1357.0,9.0,1.0')] ).
cnf(1805,plain,
( ~ relation(relation_composition(u,skc8))
| ~ relation(u)
| ~ in(ordered_pair(v,w),relation_composition(u,skc8))
| in(ordered_pair(v,skf9(skc8,w,u,v)),u) ),
inference(eqr,[status(thm),theory(equality)],[64]),
[iquote('0:EqR:64.2')] ).
cnf(1812,plain,
( ~ relation(u)
| ~ in(ordered_pair(v,w),relation_composition(u,skc8))
| in(ordered_pair(v,skf9(skc8,w,u,v)),u) ),
inference(ssi,[status(thm)],[1805,66]),
[iquote('0:SSi:1805.0,66.1')] ).
cnf(6131,plain,
( ~ relation(u)
| ~ relation(u)
| ~ in(ordered_pair(v,w),relation_composition(u,skc8))
| ~ equal(u,identity_relation(x))
| in(v,x) ),
inference(res,[status(thm),theory(equality)],[1812,32]),
[iquote('0:Res:1812.2,32.2')] ).
cnf(6149,plain,
( ~ relation(u)
| ~ in(ordered_pair(v,w),relation_composition(u,skc8))
| ~ equal(u,identity_relation(x))
| in(v,x) ),
inference(obv,[status(thm),theory(equality)],[6131]),
[iquote('0:Obv:6131.0')] ).
cnf(6715,plain,
( ~ relation(identity_relation(skc9))
| ~ equal(identity_relation(skc9),identity_relation(u))
| in(skc11,u) ),
inference(res,[status(thm),theory(equality)],[115,6149]),
[iquote('1:Res:115.0,6149.1')] ).
cnf(6741,plain,
( ~ equal(identity_relation(skc9),identity_relation(u))
| in(skc11,u) ),
inference(ssi,[status(thm)],[6715,9]),
[iquote('1:SSi:6715.0,9.0')] ).
cnf(13373,plain,
( ~ relation(skc8)
| ~ relation(identity_relation(skc9))
| ~ equal(identity_relation(skc9),identity_relation(u))
| equal(skf9(skc8,skc10,identity_relation(skc9),skc11),skc11) ),
inference(res,[status(thm),theory(equality)],[115,1330]),
[iquote('1:Res:115.0,1330.2')] ).
cnf(13410,plain,
( ~ equal(identity_relation(skc9),identity_relation(u))
| equal(skf9(skc8,skc10,identity_relation(skc9),skc11),skc11) ),
inference(ssi,[status(thm)],[13373,9,1]),
[iquote('1:SSi:13373.1,13373.0,9.0,1.0')] ).
cnf(13462,plain,
equal(skf9(skc8,skc10,identity_relation(skc9),skc11),skc11),
inference(eqr,[status(thm),theory(equality)],[13410]),
[iquote('1:EqR:13410.0')] ).
cnf(13478,plain,
in(ordered_pair(skc11,skc10),skc8),
inference(spr,[status(thm),theory(equality)],[13462,1367]),
[iquote('1:SpR:13462.0,1367.0')] ).
cnf(13495,plain,
~ in(skc11,skc9),
inference(mrr,[status(thm)],[116,13478]),
[iquote('1:MRR:116.1,13478.0')] ).
cnf(13500,plain,
~ equal(identity_relation(skc9),identity_relation(skc9)),
inference(res,[status(thm),theory(equality)],[6741,13495]),
[iquote('1:Res:6741.1,13495.0')] ).
cnf(13501,plain,
$false,
inference(obv,[status(thm),theory(equality)],[13500]),
[iquote('1:Obv:13500.0')] ).
cnf(13502,plain,
~ in(ordered_pair(skc11,skc10),relation_composition(identity_relation(skc9),skc8)),
inference(spt,[spt(split,[position(sa)])],[13501,115]),
[iquote('1:Spt:13501.0,30.1,115.0')] ).
cnf(13503,plain,
in(skc11,skc9),
inference(spt,[spt(split,[position(s2)])],[30]),
[iquote('1:Spt:13501.0,30.0')] ).
cnf(13507,plain,
in(ordered_pair(skc11,skc10),skc8),
inference(mrr,[status(thm)],[31,13502]),
[iquote('1:MRR:31.1,13502.0')] ).
cnf(13628,plain,
( ~ relation(skc8)
| ~ relation(u)
| ~ in(ordered_pair(v,skc11),u)
| in(ordered_pair(v,skc10),relation_composition(u,skc8)) ),
inference(res,[status(thm),theory(equality)],[13507,508]),
[iquote('1:Res:13507.0,508.2')] ).
cnf(13680,plain,
( ~ relation(u)
| ~ in(ordered_pair(v,skc11),u)
| in(ordered_pair(v,skc10),relation_composition(u,skc8)) ),
inference(ssi,[status(thm)],[13628,1]),
[iquote('1:SSi:13628.0,1.0')] ).
cnf(13846,plain,
( ~ relation(identity_relation(skc9))
| ~ in(ordered_pair(skc11,skc11),identity_relation(skc9)) ),
inference(res,[status(thm),theory(equality)],[13680,13502]),
[iquote('1:Res:13680.2,13502.0')] ).
cnf(13861,plain,
~ in(ordered_pair(skc11,skc11),identity_relation(skc9)),
inference(ssi,[status(thm)],[13846,9]),
[iquote('1:SSi:13846.0,9.0')] ).
cnf(13898,plain,
( ~ equal(skc11,skc11)
| ~ in(skc11,skc9) ),
inference(res,[status(thm),theory(equality)],[284,13861]),
[iquote('1:Res:284.2,13861.0')] ).
cnf(13899,plain,
~ in(skc11,skc9),
inference(obv,[status(thm),theory(equality)],[13898]),
[iquote('1:Obv:13898.0')] ).
cnf(13900,plain,
$false,
inference(mrr,[status(thm)],[13899,13503]),
[iquote('1:MRR:13899.0,13503.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU191+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.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 : Mon Jun 20 00:35:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 22.30/22.47
% 22.30/22.47 SPASS V 3.9
% 22.30/22.47 SPASS beiseite: Proof found.
% 22.30/22.47 % SZS status Theorem
% 22.30/22.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.30/22.47 SPASS derived 10308 clauses, backtracked 333 clauses, performed 3 splits and kept 4513 clauses.
% 22.30/22.47 SPASS allocated 114808 KBytes.
% 22.30/22.47 SPASS spent 0:0:21.21 on the problem.
% 22.30/22.47 0:00:00.03 for the input.
% 22.30/22.47 0:00:00.08 for the FLOTTER CNF translation.
% 22.30/22.47 0:00:00.19 for inferences.
% 22.30/22.47 0:00:00.42 for the backtracking.
% 22.30/22.47 0:0:20.41 for the reduction.
% 22.30/22.47
% 22.30/22.47
% 22.30/22.47 Here is a proof with depth 5, length 51 :
% 22.30/22.47 % SZS output start Refutation
% See solution above
% 22.30/22.47 Formulae used in the proof : t74_relat_1 dt_k6_relat_1 dt_k5_relat_1 d10_relat_1 d8_relat_1
% 22.30/22.47
%------------------------------------------------------------------------------