TSTP Solution File: SEU283+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU283+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 14:35:49 EDT 2022
% Result : Theorem 0.53s 0.74s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 44 ( 9 unt; 4 nHn; 44 RR)
% Number of literals : 119 ( 0 equ; 80 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
relation(skf9(u)),
file('SEU283+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ skP0(u)
| function(skf9(u)) ),
file('SEU283+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ equal(singleton(skf10(u)),singleton(skf10(u)))
| skP0(v) ),
file('SEU283+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ skP0(u)
| ~ in(ordered_pair(v,w),skf9(u))
| in(v,u) ),
file('SEU283+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ skP0(u)
| ~ in(ordered_pair(v,w),skf9(u))
| equal(w,singleton(v)) ),
file('SEU283+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ in(skf13(u,v),v)
| ~ in(ordered_pair(skf13(u,v),w),u) ),
file('SEU283+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc7)
| in(skf8(v),skc7) ),
file('SEU283+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ relation(u)
| ~ equal(v,relation_dom(u))
| ~ in(ordered_pair(w,x),u)
| in(w,v) ),
file('SEU283+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ skP0(u)
| ~ in(v,u)
| ~ equal(w,singleton(v))
| in(ordered_pair(v,w),skf9(u)) ),
file('SEU283+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc7)
| ~ equal(apply(u,skf8(u)),singleton(skf8(u))) ),
file('SEU283+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ relation(u)
| equal(v,relation_dom(u))
| in(skf13(u,v),v)
| in(ordered_pair(skf13(u,v),skf14(v,u)),u) ),
file('SEU283+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,apply(u,v))
| in(ordered_pair(v,w),u) ),
file('SEU283+1.p',unknown),
[] ).
cnf(55,plain,
skP0(u),
inference(obv,[status(thm),theory(equality)],[37]),
[iquote('0:Obv:37.0')] ).
cnf(56,plain,
function(skf9(u)),
inference(mrr,[status(thm)],[24,55]),
[iquote('0:MRR:24.0,55.0')] ).
cnf(57,plain,
( ~ in(ordered_pair(u,v),skf9(w))
| in(u,w) ),
inference(mrr,[status(thm)],[40,55]),
[iquote('0:MRR:40.0,55.0')] ).
cnf(58,plain,
( ~ in(ordered_pair(u,v),skf9(w))
| equal(v,singleton(u)) ),
inference(mrr,[status(thm)],[42,55]),
[iquote('0:MRR:42.0,55.0')] ).
cnf(59,plain,
( ~ in(u,v)
| ~ equal(w,singleton(u))
| in(ordered_pair(u,w),skf9(v)) ),
inference(mrr,[status(thm)],[46,55]),
[iquote('0:MRR:46.0,55.0')] ).
cnf(78,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc7) ),
inference(spt,[spt(split,[position(s1)])],[44]),
[iquote('1:Spt:44.0,44.1,44.2')] ).
cnf(163,plain,
( ~ in(skf13(skf9(u),v),u)
| ~ equal(w,singleton(skf13(skf9(u),v)))
| ~ in(skf13(skf9(u),v),v) ),
inference(res,[status(thm),theory(equality)],[59,43]),
[iquote('0:Res:59.2,43.1')] ).
cnf(168,plain,
( ~ in(skf13(skf9(u),v),u)
| ~ in(skf13(skf9(u),v),v) ),
inference(aed,[status(thm),theory(equality)],[163]),
[iquote('0:AED:163.1')] ).
cnf(180,plain,
( ~ relation(skf9(u))
| ~ in(v,u)
| ~ equal(w,singleton(v))
| ~ equal(x,relation_dom(skf9(u)))
| in(v,x) ),
inference(res,[status(thm),theory(equality)],[59,45]),
[iquote('0:Res:59.2,45.2')] ).
cnf(181,plain,
( ~ relation(skf9(u))
| ~ in(v,u)
| ~ equal(w,relation_dom(skf9(u)))
| in(v,w) ),
inference(aed,[status(thm),theory(equality)],[180]),
[iquote('0:AED:180.2')] ).
cnf(182,plain,
( ~ in(u,v)
| ~ equal(w,relation_dom(skf9(v)))
| in(u,w) ),
inference(ssi,[status(thm)],[181,56,15]),
[iquote('0:SSi:181.0,56.0,15.0')] ).
cnf(237,plain,
( ~ relation(skf9(u))
| equal(v,relation_dom(skf9(u)))
| in(skf13(skf9(u),v),v)
| in(skf13(skf9(u),v),u) ),
inference(res,[status(thm),theory(equality)],[51,57]),
[iquote('0:Res:51.3,57.0')] ).
cnf(240,plain,
( equal(u,relation_dom(skf9(v)))
| in(skf13(skf9(v),u),u)
| in(skf13(skf9(v),u),v) ),
inference(ssi,[status(thm)],[237,56,15]),
[iquote('0:SSi:237.0,56.0,15.0')] ).
cnf(260,plain,
( ~ function(skf9(u))
| ~ relation(skf9(u))
| ~ in(v,relation_dom(skf9(u)))
| ~ equal(w,apply(skf9(u),v))
| equal(w,singleton(v)) ),
inference(res,[status(thm),theory(equality)],[53,58]),
[iquote('0:Res:53.4,58.0')] ).
cnf(270,plain,
( ~ in(u,relation_dom(skf9(v)))
| ~ equal(w,apply(skf9(v),u))
| equal(w,singleton(u)) ),
inference(ssi,[status(thm)],[260,56,15]),
[iquote('0:SSi:260.1,260.0,56.0,15.0,56.0,15.0')] ).
cnf(829,plain,
( ~ in(u,relation_dom(skf9(v)))
| equal(apply(skf9(v),u),singleton(u)) ),
inference(eqr,[status(thm),theory(equality)],[270]),
[iquote('0:EqR:270.1')] ).
cnf(911,plain,
( equal(relation_dom(skf9(u)),u)
| in(skf13(skf9(u),u),u) ),
inference(fac,[status(thm)],[240]),
[iquote('0:Fac:240.1,240.2')] ).
cnf(969,plain,
( ~ in(skf13(skf9(u),u),u)
| equal(relation_dom(skf9(u)),u) ),
inference(res,[status(thm),theory(equality)],[911,168]),
[iquote('0:Res:911.1,168.0')] ).
cnf(980,plain,
equal(relation_dom(skf9(u)),u),
inference(mrr,[status(thm)],[969,911]),
[iquote('0:MRR:969.0,911.1')] ).
cnf(990,plain,
( ~ in(u,v)
| ~ equal(w,v)
| in(u,w) ),
inference(rew,[status(thm),theory(equality)],[980,182]),
[iquote('0:Rew:980.0,182.1')] ).
cnf(1053,plain,
( ~ in(u,v)
| equal(apply(skf9(v),u),singleton(u)) ),
inference(rew,[status(thm),theory(equality)],[980,829]),
[iquote('0:Rew:980.0,829.0')] ).
cnf(1233,plain,
( ~ function(skf9(u))
| ~ relation(skf9(u))
| ~ equal(u,skc7) ),
inference(spl,[status(thm),theory(equality)],[980,78]),
[iquote('1:SpL:980.0,78.2')] ).
cnf(1241,plain,
~ equal(u,skc7),
inference(ssi,[status(thm)],[1233,56,15]),
[iquote('1:SSi:1233.1,1233.0,56.0,15.0,56.0,15.0')] ).
cnf(1242,plain,
$false,
inference(unc,[status(thm)],[1241,980]),
[iquote('1:UnC:1241.0,980.0')] ).
cnf(1244,plain,
in(skf8(u),skc7),
inference(spt,[spt(split,[position(s2)])],[44]),
[iquote('1:Spt:1242.0,44.3')] ).
cnf(1289,plain,
( ~ equal(u,skc7)
| in(skf8(v),u) ),
inference(res,[status(thm),theory(equality)],[1244,990]),
[iquote('1:Res:1244.0,990.0')] ).
cnf(1633,plain,
( ~ function(skf9(u))
| ~ relation(skf9(u))
| ~ in(skf8(skf9(u)),u)
| ~ equal(relation_dom(skf9(u)),skc7)
| ~ equal(singleton(skf8(skf9(u))),singleton(skf8(skf9(u)))) ),
inference(spl,[status(thm),theory(equality)],[1053,50]),
[iquote('0:SpL:1053.1,50.3')] ).
cnf(1634,plain,
( ~ function(skf9(u))
| ~ relation(skf9(u))
| ~ in(skf8(skf9(u)),u)
| ~ equal(relation_dom(skf9(u)),skc7) ),
inference(obv,[status(thm),theory(equality)],[1633]),
[iquote('0:Obv:1633.4')] ).
cnf(1635,plain,
( ~ function(skf9(u))
| ~ relation(skf9(u))
| ~ in(skf8(skf9(u)),u)
| ~ equal(u,skc7) ),
inference(rew,[status(thm),theory(equality)],[980,1634]),
[iquote('0:Rew:980.0,1634.3')] ).
cnf(1636,plain,
( ~ in(skf8(skf9(u)),u)
| ~ equal(u,skc7) ),
inference(ssi,[status(thm)],[1635,56,15]),
[iquote('0:SSi:1635.1,1635.0,56.0,15.0,56.0,15.0')] ).
cnf(1637,plain,
~ equal(u,skc7),
inference(mrr,[status(thm)],[1636,1289]),
[iquote('1:MRR:1636.0,1289.1')] ).
cnf(1638,plain,
$false,
inference(unc,[status(thm)],[1637,980]),
[iquote('1:UnC:1637.0,980.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU283+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 20:28:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.53/0.74
% 0.53/0.74 SPASS V 3.9
% 0.53/0.74 SPASS beiseite: Proof found.
% 0.53/0.74 % SZS status Theorem
% 0.53/0.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.74 SPASS derived 1218 clauses, backtracked 13 clauses, performed 1 splits and kept 623 clauses.
% 0.53/0.74 SPASS allocated 98985 KBytes.
% 0.53/0.74 SPASS spent 0:00:00.37 on the problem.
% 0.53/0.74 0:00:00.04 for the input.
% 0.53/0.74 0:00:00.05 for the FLOTTER CNF translation.
% 0.53/0.74 0:00:00.02 for inferences.
% 0.53/0.74 0:00:00.00 for the backtracking.
% 0.53/0.74 0:00:00.24 for the reduction.
% 0.53/0.74
% 0.53/0.74
% 0.53/0.74 Here is a proof with depth 4, length 44 :
% 0.53/0.74 % SZS output start Refutation
% See solution above
% 0.53/0.74 Formulae used in the proof : s1_funct_1__e16_22__wellord2__1 rc3_relat_1 d4_relat_1 antisymmetry_r2_hidden s2_funct_1__e16_22__wellord2__1 d4_funct_1
% 0.53/0.74
%------------------------------------------------------------------------------