TSTP Solution File: SEU037+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU037+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 0.47s 0.63s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 11 unt; 0 nHn; 32 RR)
% Number of literals : 106 ( 0 equ; 82 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 : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc11),
file('SEU037+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc11),
file('SEU037+1.p',unknown),
[] ).
cnf(31,axiom,
equal(set_intersection2(u,u),u),
file('SEU037+1.p',unknown),
[] ).
cnf(35,axiom,
in(skc12,set_intersection2(relation_dom(skc11),skc13)),
file('SEU037+1.p',unknown),
[] ).
cnf(40,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU037+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ relation(u)
| relation(relation_dom_restriction(u,v)) ),
file('SEU037+1.p',unknown),
[] ).
cnf(50,axiom,
~ equal(apply(relation_dom_restriction(skc11,skc13),skc12),apply(skc11,skc12)),
file('SEU037+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ relation(u)
| ~ function(u)
| function(relation_dom_restriction(u,v)) ),
file('SEU037+1.p',unknown),
[] ).
cnf(59,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('SEU037+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| ~ equal(u,relation_dom_restriction(v,x))
| equal(apply(u,w),apply(v,w)) ),
file('SEU037+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ equal(relation_dom(u),set_intersection2(relation_dom(v),w))
| ~ equal(apply(u,skf7(u,v)),apply(v,skf7(u,v)))
| equal(u,relation_dom_restriction(v,w)) ),
file('SEU037+1.p',unknown),
[] ).
cnf(63,plain,
in(skc12,set_intersection2(skc13,relation_dom(skc11))),
inference(rew,[status(thm),theory(equality)],[40,35]),
[iquote('0:Rew:40.0,35.0')] ).
cnf(69,plain,
( ~ relation(skc11)
| function(relation_dom_restriction(skc11,u)) ),
inference(res,[status(thm),theory(equality)],[2,55]),
[iquote('0:Res:2.0,55.0')] ).
cnf(82,plain,
relation(relation_dom_restriction(skc11,u)),
inference(res,[status(thm),theory(equality)],[1,41]),
[iquote('0:Res:1.0,41.0')] ).
cnf(95,plain,
( ~ function(skc11)
| ~ relation(skc11)
| ~ function(relation_dom_restriction(skc11,skc13))
| ~ relation(relation_dom_restriction(skc11,skc13))
| ~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13)))
| ~ equal(relation_dom_restriction(skc11,skc13),relation_dom_restriction(skc11,u)) ),
inference(res,[status(thm),theory(equality)],[60,50]),
[iquote('0:Res:60.6,50.0')] ).
cnf(98,plain,
function(relation_dom_restriction(skc11,u)),
inference(mrr,[status(thm)],[69,1]),
[iquote('0:MRR:69.0,1.0')] ).
cnf(106,plain,
( ~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13)))
| ~ equal(relation_dom_restriction(skc11,skc13),relation_dom_restriction(skc11,u)) ),
inference(mrr,[status(thm)],[95,2,1,98,82]),
[iquote('0:MRR:95.0,95.1,95.2,95.3,2.0,1.0,98.0,82.0')] ).
cnf(273,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)],[59,31]),
[iquote('0:SpR:59.5,31.0')] ).
cnf(276,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ equal(u,relation_dom_restriction(v,w))
| equal(set_intersection2(w,relation_dom(v)),relation_dom(u)) ),
inference(spr,[status(thm),theory(equality)],[59,40]),
[iquote('0:SpR:59.5,40.0')] ).
cnf(362,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)],[62]),
[iquote('0:EqR:62.5')] ).
cnf(363,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)],[362]),
[iquote('0:Obv:362.1')] ).
cnf(566,plain,
~ in(skc12,relation_dom(relation_dom_restriction(skc11,skc13))),
inference(eqr,[status(thm),theory(equality)],[106]),
[iquote('0:EqR:106.1')] ).
cnf(678,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)],[31,363]),
[iquote('0:SpL:31.0,363.2')] ).
cnf(681,plain,
( ~ relation(u)
| ~ function(u)
| equal(relation_dom_restriction(u,relation_dom(u)),u) ),
inference(obv,[status(thm),theory(equality)],[678]),
[iquote('0:Obv:678.2')] ).
cnf(683,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)],[681,273]),
[iquote('0:Rew:681.2,273.4')] ).
cnf(763,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)],[683,566]),
[iquote('0:SpL:683.5,566.0')] ).
cnf(772,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,skc13))
| ~ in(skc12,relation_dom(u)) ),
inference(ssi,[status(thm)],[763,98,82]),
[iquote('0:SSi:763.3,763.2,98.0,82.0,98.0,82.0')] ).
cnf(1229,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(skc11)
| ~ function(skc11)
| ~ equal(u,relation_dom_restriction(skc11,skc13))
| in(skc12,relation_dom(u)) ),
inference(spr,[status(thm),theory(equality)],[276,63]),
[iquote('0:SpR:276.5,63.0')] ).
cnf(1273,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,skc13))
| in(skc12,relation_dom(u)) ),
inference(ssi,[status(thm)],[1229,2,1]),
[iquote('0:SSi:1229.3,1229.2,2.0,1.0,2.0,1.0')] ).
cnf(1274,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,relation_dom_restriction(skc11,skc13)) ),
inference(mrr,[status(thm)],[1273,772]),
[iquote('0:MRR:1273.3,772.3')] ).
cnf(1309,plain,
( ~ relation(relation_dom_restriction(skc11,skc13))
| ~ function(relation_dom_restriction(skc11,skc13)) ),
inference(eqr,[status(thm),theory(equality)],[1274]),
[iquote('0:EqR:1274.2')] ).
cnf(1311,plain,
$false,
inference(ssi,[status(thm)],[1309,98,82]),
[iquote('0:SSi:1309.1,1309.0,98.0,82.0,98.0,82.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU037+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 23:32:23 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.47/0.63
% 0.47/0.63 SPASS V 3.9
% 0.47/0.63 SPASS beiseite: Proof found.
% 0.47/0.63 % SZS status Theorem
% 0.47/0.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.63 SPASS derived 959 clauses, backtracked 0 clauses, performed 1 splits and kept 488 clauses.
% 0.47/0.63 SPASS allocated 98888 KBytes.
% 0.47/0.63 SPASS spent 0:00:00.26 on the problem.
% 0.47/0.63 0:00:00.04 for the input.
% 0.47/0.63 0:00:00.04 for the FLOTTER CNF translation.
% 0.47/0.63 0:00:00.02 for inferences.
% 0.47/0.63 0:00:00.00 for the backtracking.
% 0.47/0.63 0:00:00.14 for the reduction.
% 0.47/0.63
% 0.47/0.63
% 0.47/0.63 Here is a proof with depth 3, length 32 :
% 0.47/0.63 % SZS output start Refutation
% See solution above
% 0.47/0.63 Formulae used in the proof : t71_funct_1 idempotence_k3_xboole_0 commutativity_k3_xboole_0 dt_k7_relat_1 fc4_funct_1 t68_funct_1
% 0.47/0.63
%------------------------------------------------------------------------------