TSTP Solution File: SET995+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 05:30:18 EDT 2022
% Result : Theorem 0.36s 0.57s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 30 ( 14 unt; 2 nHn; 30 RR)
% Number of literals : 80 ( 0 equ; 51 neg)
% Maximal clause size : 7 ( 2 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,
function(skc10),
file('SET995+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc10),
file('SET995+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc9),
file('SET995+1.p',unknown),
[] ).
cnf(4,axiom,
relation(skc9),
file('SET995+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(skc10,skc9),
file('SET995+1.p',unknown),
[] ).
cnf(27,axiom,
equal(relation_rng(skc9),singleton(skc11)),
file('SET995+1.p',unknown),
[] ).
cnf(28,axiom,
equal(relation_rng(skc10),singleton(skc11)),
file('SET995+1.p',unknown),
[] ).
cnf(29,axiom,
equal(relation_dom(skc10),relation_dom(skc9)),
file('SET995+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET995+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,relation_rng(u))
| ~ equal(x,apply(u,v))
| in(x,w) ),
file('SET995+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ function(u)
| ~ relation(u)
| ~ function(v)
| ~ relation(v)
| ~ equal(relation_dom(v),relation_dom(u))
| equal(v,u)
| in(skf16(v,w),relation_dom(v)) ),
file('SET995+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ function(u)
| ~ relation(u)
| ~ function(v)
| ~ relation(v)
| ~ equal(relation_dom(v),relation_dom(u))
| ~ equal(apply(v,skf16(v,u)),apply(u,skf16(v,u)))
| equal(v,u) ),
file('SET995+1.p',unknown),
[] ).
cnf(114,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ relation(skc10)
| ~ function(skc10)
| ~ equal(apply(skc10,skf16(skc9,skc10)),apply(skc9,skf16(skc9,skc10)))
| equal(skc10,skc9) ),
inference(res,[status(thm),theory(equality)],[29,62]),
[iquote('0:Res:29.0,62.5')] ).
cnf(115,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ relation(skc10)
| ~ function(skc10)
| in(skf16(skc9,u),relation_dom(skc9))
| equal(skc10,skc9) ),
inference(res,[status(thm),theory(equality)],[29,61]),
[iquote('0:Res:29.0,61.4')] ).
cnf(123,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ in(u,relation_dom(skc10))
| ~ equal(v,apply(skc10,u))
| in(v,singleton(skc11)) ),
inference(res,[status(thm),theory(equality)],[28,60]),
[iquote('0:Res:28.0,60.2')] ).
cnf(130,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ in(u,relation_dom(skc9))
| ~ equal(v,apply(skc9,u))
| in(v,singleton(skc11)) ),
inference(res,[status(thm),theory(equality)],[27,60]),
[iquote('0:Res:27.0,60.2')] ).
cnf(161,plain,
( ~ in(u,relation_dom(skc9))
| ~ equal(v,apply(skc9,u))
| in(v,singleton(skc11)) ),
inference(mrr,[status(thm)],[130,4,3]),
[iquote('0:MRR:130.0,130.1,4.0,3.0')] ).
cnf(162,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ in(u,relation_dom(skc9))
| ~ equal(v,apply(skc10,u))
| in(v,singleton(skc11)) ),
inference(rew,[status(thm),theory(equality)],[29,123]),
[iquote('0:Rew:29.0,123.2')] ).
cnf(163,plain,
( ~ in(u,relation_dom(skc9))
| ~ equal(v,apply(skc10,u))
| in(v,singleton(skc11)) ),
inference(mrr,[status(thm)],[162,2,1]),
[iquote('0:MRR:162.0,162.1,2.0,1.0')] ).
cnf(164,plain,
in(skf16(skc9,u),relation_dom(skc9)),
inference(mrr,[status(thm)],[115,4,3,2,1,23]),
[iquote('0:MRR:115.0,115.1,115.2,115.3,115.5,4.0,3.0,2.0,1.0,23.0')] ).
cnf(187,plain,
~ equal(apply(skc10,skf16(skc9,skc10)),apply(skc9,skf16(skc9,skc10))),
inference(mrr,[status(thm)],[114,4,3,2,1,23]),
[iquote('0:MRR:114.0,114.1,114.2,114.3,114.5,4.0,3.0,2.0,1.0,23.0')] ).
cnf(360,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[50]),
[iquote('0:EqR:50.1')] ).
cnf(862,plain,
( ~ in(u,relation_dom(skc9))
| in(apply(skc10,u),singleton(skc11)) ),
inference(eqr,[status(thm),theory(equality)],[163]),
[iquote('0:EqR:163.1')] ).
cnf(873,plain,
( ~ in(u,relation_dom(skc9))
| equal(apply(skc10,u),skc11) ),
inference(res,[status(thm),theory(equality)],[862,360]),
[iquote('0:Res:862.1,360.0')] ).
cnf(888,plain,
equal(apply(skc10,skf16(skc9,u)),skc11),
inference(res,[status(thm),theory(equality)],[164,873]),
[iquote('0:Res:164.0,873.0')] ).
cnf(898,plain,
~ equal(apply(skc9,skf16(skc9,skc10)),skc11),
inference(rew,[status(thm),theory(equality)],[888,187]),
[iquote('0:Rew:888.0,187.0')] ).
cnf(1124,plain,
( ~ in(u,relation_dom(skc9))
| in(apply(skc9,u),singleton(skc11)) ),
inference(eqr,[status(thm),theory(equality)],[161]),
[iquote('0:EqR:161.1')] ).
cnf(1172,plain,
( ~ in(u,relation_dom(skc9))
| equal(apply(skc9,u),skc11) ),
inference(res,[status(thm),theory(equality)],[1124,360]),
[iquote('0:Res:1124.1,360.0')] ).
cnf(1189,plain,
equal(apply(skc9,skf16(skc9,u)),skc11),
inference(res,[status(thm),theory(equality)],[164,1172]),
[iquote('0:Res:164.0,1172.0')] ).
cnf(1198,plain,
$false,
inference(unc,[status(thm)],[1189,898]),
[iquote('0:UnC:1189.0,898.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 17:26:29 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.36/0.57
% 0.36/0.57 SPASS V 3.9
% 0.36/0.57 SPASS beiseite: Proof found.
% 0.36/0.57 % SZS status Theorem
% 0.36/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.57 SPASS derived 917 clauses, backtracked 50 clauses, performed 4 splits and kept 550 clauses.
% 0.36/0.57 SPASS allocated 98585 KBytes.
% 0.36/0.57 SPASS spent 0:00:00.22 on the problem.
% 0.36/0.57 0:00:00.03 for the input.
% 0.36/0.57 0:00:00.05 for the FLOTTER CNF translation.
% 0.36/0.57 0:00:00.01 for inferences.
% 0.36/0.57 0:00:00.00 for the backtracking.
% 0.36/0.57 0:00:00.09 for the reduction.
% 0.36/0.57
% 0.36/0.57
% 0.36/0.57 Here is a proof with depth 4, length 30 :
% 0.36/0.57 % SZS output start Refutation
% See solution above
% 0.36/0.57 Formulae used in the proof : t17_funct_1 d1_tarski antisymmetry_r2_hidden d5_funct_1 t9_funct_1
% 0.36/0.57
%------------------------------------------------------------------------------