TSTP Solution File: SEU039+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU039+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:33:40 EDT 2022
% Result : Theorem 55.37s 55.56s
% Output : Refutation 55.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 11 unt; 0 nHn; 44 RR)
% Number of literals : 140 ( 0 equ; 106 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc11),
file('SEU039+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc11),
file('SEU039+1.p',unknown),
[] ).
cnf(23,axiom,
in(skc12,skc13),
file('SEU039+1.p',unknown),
[] ).
cnf(28,axiom,
in(skc12,relation_dom(skc11)),
file('SEU039+1.p',unknown),
[] ).
cnf(33,axiom,
equal(set_intersection2(u,u),u),
file('SEU039+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ relation(u)
| relation(relation_dom_restriction(u,v)) ),
file('SEU039+1.p',unknown),
[] ).
cnf(50,axiom,
~ in(apply(skc11,skc12),relation_rng(relation_dom_restriction(skc11,skc13))),
file('SEU039+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ relation(u)
| ~ function(u)
| function(relation_dom_restriction(u,v)) ),
file('SEU039+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SEU039+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| equal(apply(relation_dom_restriction(u,w),v),apply(u,v)) ),
file('SEU039+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ equal(u,relation_dom_restriction(v,w))
| equal(relation_dom(u),set_intersection2(relation_dom(v),w)) ),
file('SEU039+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,relation_rng(u))
| ~ equal(x,apply(u,v))
| in(x,w) ),
file('SEU039+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ equal(relation_dom(u),set_intersection2(relation_dom(v),w))
| ~ equal(apply(u,skf16(u,v)),apply(v,skf16(u,v)))
| equal(u,relation_dom_restriction(v,w)) ),
file('SEU039+1.p',unknown),
[] ).
cnf(91,plain,
( ~ relation(skc11)
| function(relation_dom_restriction(skc11,u)) ),
inference(res,[status(thm),theory(equality)],[2,59]),
[iquote('0:Res:2.0,59.0')] ).
cnf(100,plain,
( ~ function(skc11)
| ~ function(u)
| ~ relation(u)
| ~ equal(u,relation_dom_restriction(skc11,v))
| equal(relation_dom(u),set_intersection2(relation_dom(skc11),v)) ),
inference(res,[status(thm),theory(equality)],[1,75]),
[iquote('0:Res:1.0,75.1')] ).
cnf(111,plain,
relation(relation_dom_restriction(skc11,u)),
inference(res,[status(thm),theory(equality)],[1,44]),
[iquote('0:Res:1.0,44.0')] ).
cnf(126,plain,
( ~ equal(u,set_intersection2(v,skc13))
| ~ in(skc12,v)
| in(skc12,u) ),
inference(res,[status(thm),theory(equality)],[23,65]),
[iquote('0:Res:23.0,65.1')] ).
cnf(129,plain,
( ~ function(u)
| ~ relation(u)
| equal(apply(relation_dom_restriction(u,skc13),skc12),apply(u,skc12)) ),
inference(res,[status(thm),theory(equality)],[23,69]),
[iquote('0:Res:23.0,69.2')] ).
cnf(148,plain,
( ~ equal(relation_rng(relation_dom_restriction(skc11,skc13)),set_intersection2(u,v))
| ~ in(apply(skc11,skc12),v)
| ~ in(apply(skc11,skc12),u) ),
inference(res,[status(thm),theory(equality)],[65,50]),
[iquote('0:Res:65.3,50.0')] ).
cnf(151,plain,
function(relation_dom_restriction(skc11,u)),
inference(mrr,[status(thm)],[91,1]),
[iquote('0:MRR:91.0,1.0')] ).
cnf(159,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,v))
| equal(relation_dom(u),set_intersection2(relation_dom(skc11),v)) ),
inference(mrr,[status(thm)],[100,2]),
[iquote('0:MRR:100.0,2.0')] ).
cnf(182,plain,
( ~ function(skc11)
| equal(apply(relation_dom_restriction(skc11,skc13),skc12),apply(skc11,skc12)) ),
inference(res,[status(thm),theory(equality)],[1,129]),
[iquote('0:Res:1.0,129.0')] ).
cnf(187,plain,
equal(apply(relation_dom_restriction(skc11,skc13),skc12),apply(skc11,skc12)),
inference(mrr,[status(thm)],[182,2]),
[iquote('0:MRR:182.0,2.0')] ).
cnf(763,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ equal(u,relation_dom_restriction(v,relation_dom(v)))
| equal(relation_dom(u),relation_dom(v)) ),
inference(spr,[status(thm),theory(equality)],[75,33]),
[iquote('0:SpR:75.5,33.0')] ).
cnf(811,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,relation_rng(u))
| in(apply(u,v),w) ),
inference(eqr,[status(thm),theory(equality)],[76]),
[iquote('0:EqR:76.4')] ).
cnf(888,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ equal(set_intersection2(relation_dom(u),v),relation_dom(u))
| equal(relation_dom_restriction(u,v),u) ),
inference(eqr,[status(thm),theory(equality)],[79]),
[iquote('0:EqR:79.5')] ).
cnf(891,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(set_intersection2(relation_dom(u),v),relation_dom(u))
| equal(relation_dom_restriction(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[888]),
[iquote('0:Obv:888.1')] ).
cnf(3860,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(u),relation_dom(u))
| equal(relation_dom_restriction(u,relation_dom(u)),u) ),
inference(spl,[status(thm),theory(equality)],[33,891]),
[iquote('0:SpL:33.0,891.2')] ).
cnf(3868,plain,
( ~ relation(u)
| ~ function(u)
| equal(relation_dom_restriction(u,relation_dom(u)),u) ),
inference(obv,[status(thm),theory(equality)],[3860]),
[iquote('0:Obv:3860.2')] ).
cnf(3870,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ equal(u,v)
| equal(relation_dom(u),relation_dom(v)) ),
inference(rew,[status(thm),theory(equality)],[3868,763]),
[iquote('0:Rew:3868.2,763.4')] ).
cnf(32659,plain,
( ~ in(skc12,u)
| in(skc12,set_intersection2(u,skc13)) ),
inference(eqr,[status(thm),theory(equality)],[126]),
[iquote('0:EqR:126.0')] ).
cnf(32716,plain,
( ~ function(relation_dom_restriction(skc11,skc13))
| ~ relation(relation_dom_restriction(skc11,skc13))
| ~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13)))
| ~ equal(u,relation_rng(relation_dom_restriction(skc11,skc13)))
| in(apply(skc11,skc12),u) ),
inference(spr,[status(thm),theory(equality)],[187,811]),
[iquote('0:SpR:187.0,811.4')] ).
cnf(32726,plain,
( ~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13)))
| ~ equal(u,relation_rng(relation_dom_restriction(skc11,skc13)))
| in(apply(skc11,skc12),u) ),
inference(ssi,[status(thm)],[32716,151,111]),
[iquote('0:SSi:32716.1,32716.0,151.0,111.0,151.0,111.0')] ).
cnf(33001,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,skc13))
| ~ in(skc12,relation_dom(skc11))
| in(skc12,relation_dom(u)) ),
inference(spr,[status(thm),theory(equality)],[159,32659]),
[iquote('0:SpR:159.3,32659.1')] ).
cnf(33021,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,skc13))
| in(skc12,relation_dom(u)) ),
inference(mrr,[status(thm)],[33001,28]),
[iquote('0:MRR:33001.3,28.0')] ).
cnf(33245,plain,
( ~ equal(relation_rng(relation_dom_restriction(skc11,skc13)),u)
| ~ in(apply(skc11,skc12),u)
| ~ in(apply(skc11,skc12),u) ),
inference(spl,[status(thm),theory(equality)],[33,148]),
[iquote('0:SpL:33.0,148.0')] ).
cnf(33265,plain,
( ~ equal(relation_rng(relation_dom_restriction(skc11,skc13)),u)
| ~ in(apply(skc11,skc12),u) ),
inference(obv,[status(thm),theory(equality)],[33245]),
[iquote('0:Obv:33245.1')] ).
cnf(33266,plain,
( ~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13)))
| ~ equal(u,relation_rng(relation_dom_restriction(skc11,skc13))) ),
inference(mrr,[status(thm)],[32726,33265]),
[iquote('0:MRR:32726.2,33265.1')] ).
cnf(33267,plain,
~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13))),
inference(aed,[status(thm),theory(equality)],[33266]),
[iquote('0:AED:33266.1')] ).
cnf(33282,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(relation_dom_restriction(skc11,skc13))
| ~ function(relation_dom_restriction(skc11,skc13))
| ~ equal(u,relation_dom_restriction(skc11,skc13))
| ~ in(skc12,relation_dom(u)) ),
inference(spl,[status(thm),theory(equality)],[3870,33267]),
[iquote('0:SpL:3870.5,33267.0')] ).
cnf(33287,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,skc13))
| ~ in(skc12,relation_dom(u)) ),
inference(ssi,[status(thm)],[33282,151,111]),
[iquote('0:SSi:33282.3,33282.2,151.0,111.0,151.0,111.0')] ).
cnf(33288,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,skc13)) ),
inference(mrr,[status(thm)],[33287,33021]),
[iquote('0:MRR:33287.3,33021.3')] ).
cnf(41011,plain,
( ~ relation(relation_dom_restriction(skc11,skc13))
| ~ function(relation_dom_restriction(skc11,skc13)) ),
inference(eqr,[status(thm),theory(equality)],[33288]),
[iquote('0:EqR:33288.2')] ).
cnf(41017,plain,
$false,
inference(ssi,[status(thm)],[41011,151,111]),
[iquote('0:SSi:41011.1,41011.0,151.0,111.0,151.0,111.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU039+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 13:31:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 55.37/55.56
% 55.37/55.56 SPASS V 3.9
% 55.37/55.56 SPASS beiseite: Proof found.
% 55.37/55.56 % SZS status Theorem
% 55.37/55.56 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.37/55.56 SPASS derived 32819 clauses, backtracked 265 clauses, performed 4 splits and kept 15948 clauses.
% 55.37/55.56 SPASS allocated 131660 KBytes.
% 55.37/55.56 SPASS spent 0:0:53.10 on the problem.
% 55.37/55.56 0:00:00.03 for the input.
% 55.37/55.56 0:00:00.06 for the FLOTTER CNF translation.
% 55.37/55.56 0:00:00.42 for inferences.
% 55.37/55.56 0:00:00.83 for the backtracking.
% 55.37/55.56 0:0:51.41 for the reduction.
% 55.37/55.56
% 55.37/55.56
% 55.37/55.56 Here is a proof with depth 5, length 44 :
% 55.37/55.56 % SZS output start Refutation
% See solution above
% 55.37/55.56 Formulae used in the proof : t73_funct_1 idempotence_k3_xboole_0 dt_k7_relat_1 fc4_funct_1 d3_xboole_0 antisymmetry_r2_hidden t72_funct_1 t68_funct_1 d5_funct_1
% 55.37/55.56
%------------------------------------------------------------------------------