TSTP Solution File: SET994+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET994+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:30:17 EDT 2022
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 36 ( 16 unt; 3 nHn; 36 RR)
% Number of literals : 80 ( 0 equ; 45 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
empty(empty_set),
file('SET994+1.p',unknown),
[] ).
cnf(15,axiom,
empty(n0),
file('SET994+1.p',unknown),
[] ).
cnf(20,axiom,
relation(skf8(u)),
file('SET994+1.p',unknown),
[] ).
cnf(21,axiom,
function(skf8(u)),
file('SET994+1.p',unknown),
[] ).
cnf(22,axiom,
relation(skf9(u)),
file('SET994+1.p',unknown),
[] ).
cnf(23,axiom,
function(skf9(u)),
file('SET994+1.p',unknown),
[] ).
cnf(24,axiom,
~ empty(n1),
file('SET994+1.p',unknown),
[] ).
cnf(25,axiom,
~ equal(skc7,empty_set),
file('SET994+1.p',unknown),
[] ).
cnf(26,axiom,
element(skf5(u),u),
file('SET994+1.p',unknown),
[] ).
cnf(32,axiom,
equal(relation_dom(skf8(u)),u),
file('SET994+1.p',unknown),
[] ).
cnf(33,axiom,
equal(relation_dom(skf9(u)),u),
file('SET994+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SET994+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SET994+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ in(u,v)
| equal(apply(skf8(v),u),n0) ),
file('SET994+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ in(u,v)
| equal(apply(skf9(v),u),n1) ),
file('SET994+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ function(u)
| ~ relation(u)
| ~ function(v)
| ~ relation(v)
| ~ equal(relation_dom(v),skc7)
| ~ equal(relation_dom(u),skc7)
| equal(v,u) ),
file('SET994+1.p',unknown),
[] ).
cnf(51,plain,
~ empty(skc7),
inference(res,[status(thm),theory(equality)],[37,25]),
[iquote('0:Res:37.1,25.0')] ).
cnf(78,plain,
( ~ relation(skf9(skc7))
| ~ function(skf9(skc7))
| ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(u),skc7)
| equal(skf9(skc7),u) ),
inference(res,[status(thm),theory(equality)],[33,50]),
[iquote('0:Res:33.0,50.5')] ).
cnf(79,plain,
( ~ relation(skf8(skc7))
| ~ function(skf8(skc7))
| ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(u),skc7)
| equal(skf8(skc7),u) ),
inference(res,[status(thm),theory(equality)],[32,50]),
[iquote('0:Res:32.0,50.5')] ).
cnf(84,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc7)
| equal(skf8(skc7),u) ),
inference(mrr,[status(thm)],[79,20,21]),
[iquote('0:MRR:79.0,79.1,20.0,21.0')] ).
cnf(85,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc7)
| equal(skf9(skc7),u) ),
inference(mrr,[status(thm)],[78,22,23]),
[iquote('0:MRR:78.0,78.1,22.0,23.0')] ).
cnf(97,plain,
equal(n0,empty_set),
inference(ems,[status(thm)],[37,15]),
[iquote('0:EmS:37.0,15.0')] ).
cnf(103,plain,
( ~ in(u,v)
| equal(apply(skf8(v),u),empty_set) ),
inference(rew,[status(thm),theory(equality)],[97,46]),
[iquote('0:Rew:97.0,46.1')] ).
cnf(156,plain,
( empty(u)
| in(skf5(u),u) ),
inference(res,[status(thm),theory(equality)],[26,44]),
[iquote('0:Res:26.0,44.0')] ).
cnf(387,plain,
( ~ function(skf9(u))
| ~ relation(skf9(u))
| ~ equal(u,skc7)
| equal(skf9(skc7),skf9(u)) ),
inference(spl,[status(thm),theory(equality)],[33,85]),
[iquote('0:SpL:33.0,85.2')] ).
cnf(391,plain,
( ~ equal(u,skc7)
| equal(skf9(skc7),skf9(u)) ),
inference(ssi,[status(thm)],[387,23,22]),
[iquote('0:SSi:387.1,387.0,23.0,22.0,23.0,22.0')] ).
cnf(398,plain,
( ~ equal(u,skc7)
| ~ in(v,skc7)
| equal(apply(skf9(u),v),n1) ),
inference(spr,[status(thm),theory(equality)],[391,47]),
[iquote('0:SpR:391.1,47.1')] ).
cnf(436,plain,
( ~ function(skf9(u))
| ~ relation(skf9(u))
| ~ equal(u,skc7)
| equal(skf9(u),skf8(skc7)) ),
inference(spl,[status(thm),theory(equality)],[33,84]),
[iquote('0:SpL:33.0,84.2')] ).
cnf(440,plain,
( ~ equal(u,skc7)
| equal(skf9(u),skf8(skc7)) ),
inference(ssi,[status(thm)],[436,23,22]),
[iquote('0:SSi:436.1,436.0,23.0,22.0,23.0,22.0')] ).
cnf(444,plain,
( ~ equal(u,skc7)
| ~ in(v,skc7)
| equal(apply(skf8(skc7),v),n1) ),
inference(rew,[status(thm),theory(equality)],[440,398]),
[iquote('0:Rew:440.1,398.2')] ).
cnf(455,plain,
( ~ in(u,skc7)
| equal(apply(skf8(skc7),u),n1) ),
inference(aed,[status(thm),theory(equality)],[25,444]),
[iquote('0:AED:25.0,444.0')] ).
cnf(456,plain,
( ~ in(u,skc7)
| equal(n1,empty_set) ),
inference(rew,[status(thm),theory(equality)],[103,455]),
[iquote('0:Rew:103.1,455.1')] ).
cnf(466,plain,
( empty(skc7)
| equal(n1,empty_set) ),
inference(res,[status(thm),theory(equality)],[156,456]),
[iquote('0:Res:156.1,456.0')] ).
cnf(470,plain,
equal(n1,empty_set),
inference(mrr,[status(thm)],[466,51]),
[iquote('0:MRR:466.0,51.0')] ).
cnf(471,plain,
~ empty(empty_set),
inference(rew,[status(thm),theory(equality)],[470,24]),
[iquote('0:Rew:470.0,24.0')] ).
cnf(473,plain,
$false,
inference(mrr,[status(thm)],[471,5]),
[iquote('0:MRR:471.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET994+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 23:27:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 346 clauses, backtracked 0 clauses, performed 0 splits and kept 190 clauses.
% 0.21/0.48 SPASS allocated 97907 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.48 0:00:00.03 for the input.
% 0.21/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.01 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.02 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 4, length 36 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : fc4_relat_1 spc0_boole s3_funct_1__e4_14__funct_1 s3_funct_1__e7_14__funct_1 spc1_boole t16_funct_1 existence_m1_subset_1 t6_boole t2_subset
% 0.21/0.48
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