TSTP Solution File: SET990+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET990+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 05:30:16 EDT 2022
% Result : Theorem 0.79s 0.99s
% Output : Refutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 71 ( 16 unt; 6 nHn; 71 RR)
% Number of literals : 181 ( 0 equ; 109 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SET990+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc8),
file('SET990+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc8),
file('SET990+1.p',unknown),
[] ).
cnf(4,axiom,
function(skc9),
file('SET990+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(skc9,skc8),
file('SET990+1.p',unknown),
[] ).
cnf(27,axiom,
equal(relation_dom(skc9),relation_dom(skc8)),
file('SET990+1.p',unknown),
[] ).
cnf(38,axiom,
( skP0(u)
| in(skf28(u),u) ),
file('SET990+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ equal(skf28(u),ordered_pair(v,w))
| skP0(x) ),
file('SET990+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ in(u,relation_dom(skc8))
| equal(apply(skc9,u),apply(skc8,u)) ),
file('SET990+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ relation(u)
| ~ in(v,u)
| equal(ordered_pair(skf13(v),skf12(v)),v) ),
file('SET990+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ relation(u)
| ~ equal(v,relation_dom(u))
| ~ in(ordered_pair(w,x),u)
| in(w,v) ),
file('SET990+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ in(ordered_pair(v,w),u)
| equal(w,apply(u,v)) ),
file('SET990+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,apply(u,v))
| in(ordered_pair(v,w),u) ),
file('SET990+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ skP0(u)
| ~ skP0(v)
| equal(v,u)
| in(ordered_pair(skf25(u,v),skf24(u,v)),u)
| in(ordered_pair(skf25(u,v),skf24(u,v)),v) ),
file('SET990+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ skP0(u)
| ~ skP0(v)
| ~ in(ordered_pair(skf25(u,v),skf24(u,v)),u)
| ~ in(ordered_pair(skf25(u,v),skf24(u,v)),v)
| equal(v,u) ),
file('SET990+1.p',unknown),
[] ).
cnf(67,plain,
( ~ relation(skc9)
| ~ equal(u,apply(skc9,v))
| ~ in(v,relation_dom(skc9))
| in(ordered_pair(v,u),skc9) ),
inference(res,[status(thm),theory(equality)],[4,63]),
[iquote('0:Res:4.0,63.1')] ).
cnf(68,plain,
( ~ relation(skc9)
| ~ in(ordered_pair(u,v),skc9)
| ~ in(u,relation_dom(skc9))
| equal(v,apply(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[4,62]),
[iquote('0:Res:4.0,62.1')] ).
cnf(71,plain,
( ~ relation(skc8)
| ~ equal(u,apply(skc8,v))
| ~ in(v,relation_dom(skc8))
| in(ordered_pair(v,u),skc8) ),
inference(res,[status(thm),theory(equality)],[3,63]),
[iquote('0:Res:3.0,63.1')] ).
cnf(72,plain,
( ~ relation(skc8)
| ~ in(ordered_pair(u,v),skc8)
| ~ in(u,relation_dom(skc8))
| equal(v,apply(skc8,u)) ),
inference(res,[status(thm),theory(equality)],[3,62]),
[iquote('0:Res:3.0,62.1')] ).
cnf(82,plain,
( ~ in(u,skc8)
| equal(ordered_pair(skf13(u),skf12(u)),u) ),
inference(res,[status(thm),theory(equality)],[2,55]),
[iquote('0:Res:2.0,55.0')] ).
cnf(91,plain,
( ~ in(u,skc9)
| equal(ordered_pair(skf13(u),skf12(u)),u) ),
inference(res,[status(thm),theory(equality)],[1,55]),
[iquote('0:Res:1.0,55.0')] ).
cnf(96,plain,
( ~ skP0(skc9)
| ~ skP0(skc8)
| ~ in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc9)
| ~ in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc8) ),
inference(res,[status(thm),theory(equality)],[65,23]),
[iquote('0:Res:65.4,23.0')] ).
cnf(97,plain,
( ~ skP0(skc9)
| ~ skP0(skc8)
| in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc9)
| in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc8) ),
inference(res,[status(thm),theory(equality)],[64,23]),
[iquote('0:Res:64.4,23.0')] ).
cnf(100,plain,
( ~ relation(skc8)
| ~ in(ordered_pair(u,v),skc8)
| in(u,relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[27,57]),
[iquote('0:Res:27.0,57.1')] ).
cnf(102,plain,
( ~ relation(skc9)
| ~ in(ordered_pair(u,v),skc9)
| in(u,relation_dom(skc8)) ),
inference(res,[status(thm),theory(equality)],[27,57]),
[iquote('0:Res:27.0,57.1')] ).
cnf(104,plain,
( ~ relation(skc8)
| ~ in(ordered_pair(u,v),skc8)
| in(u,relation_dom(skc8)) ),
inference(rew,[status(thm),theory(equality)],[27,100]),
[iquote('0:Rew:27.0,100.2')] ).
cnf(105,plain,
( ~ in(ordered_pair(u,v),skc8)
| in(u,relation_dom(skc8)) ),
inference(mrr,[status(thm)],[104,2]),
[iquote('0:MRR:104.0,2.0')] ).
cnf(106,plain,
( ~ in(ordered_pair(u,v),skc9)
| in(u,relation_dom(skc8)) ),
inference(mrr,[status(thm)],[102,1]),
[iquote('0:MRR:102.0,1.0')] ).
cnf(121,plain,
( ~ relation(skc9)
| ~ equal(u,apply(skc9,v))
| ~ in(v,relation_dom(skc8))
| in(ordered_pair(v,u),skc9) ),
inference(rew,[status(thm),theory(equality)],[27,67]),
[iquote('0:Rew:27.0,67.2')] ).
cnf(122,plain,
( ~ in(u,relation_dom(skc8))
| ~ equal(v,apply(skc9,u))
| in(ordered_pair(u,v),skc9) ),
inference(mrr,[status(thm)],[121,1]),
[iquote('0:MRR:121.0,1.0')] ).
cnf(123,plain,
( ~ relation(skc9)
| ~ in(ordered_pair(u,v),skc9)
| ~ in(u,relation_dom(skc8))
| equal(v,apply(skc8,u)) ),
inference(rew,[status(thm),theory(equality)],[52,68,27]),
[iquote('0:Rew:52.1,68.3,27.0,68.2')] ).
cnf(124,plain,
( ~ in(ordered_pair(u,v),skc9)
| equal(v,apply(skc8,u)) ),
inference(mrr,[status(thm)],[123,1,106]),
[iquote('0:MRR:123.0,123.2,1.0,106.1')] ).
cnf(125,plain,
( ~ in(u,relation_dom(skc8))
| ~ equal(v,apply(skc8,u))
| in(ordered_pair(u,v),skc8) ),
inference(mrr,[status(thm)],[71,2]),
[iquote('0:MRR:71.0,2.0')] ).
cnf(126,plain,
( ~ in(ordered_pair(u,v),skc8)
| equal(v,apply(skc8,u)) ),
inference(mrr,[status(thm)],[72,2,105]),
[iquote('0:MRR:72.0,72.2,2.0,105.1')] ).
cnf(532,plain,
( ~ in(u,skc9)
| ~ in(u,skc9)
| in(skf13(u),relation_dom(skc8)) ),
inference(spl,[status(thm),theory(equality)],[91,106]),
[iquote('0:SpL:91.1,106.0')] ).
cnf(535,plain,
( ~ in(u,skc9)
| ~ equal(skf28(v),u)
| skP0(w) ),
inference(spl,[status(thm),theory(equality)],[91,48]),
[iquote('0:SpL:91.1,48.0')] ).
cnf(539,plain,
( ~ in(u,skc9)
| in(skf13(u),relation_dom(skc8)) ),
inference(obv,[status(thm),theory(equality)],[532]),
[iquote('0:Obv:532.0')] ).
cnf(563,plain,
( ~ in(u,skc8)
| ~ in(u,skc8)
| in(skf13(u),relation_dom(skc8)) ),
inference(spl,[status(thm),theory(equality)],[82,105]),
[iquote('0:SpL:82.1,105.0')] ).
cnf(569,plain,
( ~ in(u,skc8)
| in(skf13(u),relation_dom(skc8)) ),
inference(obv,[status(thm),theory(equality)],[563]),
[iquote('0:Obv:563.0')] ).
cnf(576,plain,
( ~ in(u,skc9)
| ~ in(u,skc9)
| equal(apply(skc8,skf13(u)),skf12(u)) ),
inference(spl,[status(thm),theory(equality)],[91,124]),
[iquote('0:SpL:91.1,124.0')] ).
cnf(581,plain,
( ~ in(u,skc9)
| equal(apply(skc8,skf13(u)),skf12(u)) ),
inference(obv,[status(thm),theory(equality)],[576]),
[iquote('0:Obv:576.0')] ).
cnf(601,plain,
( ~ in(u,skc8)
| ~ in(u,skc8)
| equal(apply(skc8,skf13(u)),skf12(u)) ),
inference(spl,[status(thm),theory(equality)],[82,126]),
[iquote('0:SpL:82.1,126.0')] ).
cnf(607,plain,
( ~ in(u,skc8)
| equal(apply(skc8,skf13(u)),skf12(u)) ),
inference(obv,[status(thm),theory(equality)],[601]),
[iquote('0:Obv:601.0')] ).
cnf(1249,plain,
( ~ in(u,skc8)
| ~ in(skf13(u),relation_dom(skc8))
| ~ equal(apply(skc9,skf13(u)),skf12(u))
| in(u,skc9) ),
inference(spr,[status(thm),theory(equality)],[82,122]),
[iquote('0:SpR:82.1,122.2')] ).
cnf(1271,plain,
( ~ in(u,skc8)
| ~ in(skf13(u),relation_dom(skc8))
| ~ equal(apply(skc8,skf13(u)),skf12(u))
| in(u,skc9) ),
inference(rew,[status(thm),theory(equality)],[52,1249]),
[iquote('0:Rew:52.1,1249.2')] ).
cnf(1272,plain,
( ~ in(u,skc8)
| ~ in(skf13(u),relation_dom(skc8))
| ~ equal(skf12(u),skf12(u))
| in(u,skc9) ),
inference(rew,[status(thm),theory(equality)],[607,1271]),
[iquote('0:Rew:607.1,1271.2')] ).
cnf(1273,plain,
( ~ in(u,skc8)
| ~ in(skf13(u),relation_dom(skc8))
| in(u,skc9) ),
inference(obv,[status(thm),theory(equality)],[1272]),
[iquote('0:Obv:1272.2')] ).
cnf(1274,plain,
( ~ in(u,skc8)
| in(u,skc9) ),
inference(mrr,[status(thm)],[1273,569]),
[iquote('0:MRR:1273.1,569.1')] ).
cnf(1275,plain,
( ~ skP0(skc9)
| ~ skP0(skc8)
| in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc9) ),
inference(mrr,[status(thm)],[97,1274]),
[iquote('0:MRR:97.3,1274.0')] ).
cnf(1277,plain,
( ~ skP0(skc9)
| ~ skP0(skc8)
| ~ in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc8) ),
inference(mrr,[status(thm)],[96,1274]),
[iquote('0:MRR:96.2,1274.1')] ).
cnf(1404,plain,
( ~ in(u,skc9)
| ~ in(skf13(u),relation_dom(skc8))
| ~ equal(apply(skc8,skf13(u)),skf12(u))
| in(u,skc8) ),
inference(spr,[status(thm),theory(equality)],[91,125]),
[iquote('0:SpR:91.1,125.2')] ).
cnf(1424,plain,
( ~ in(u,skc9)
| ~ in(skf13(u),relation_dom(skc8))
| ~ equal(skf12(u),skf12(u))
| in(u,skc8) ),
inference(rew,[status(thm),theory(equality)],[581,1404]),
[iquote('0:Rew:581.1,1404.2')] ).
cnf(1425,plain,
( ~ in(u,skc9)
| ~ in(skf13(u),relation_dom(skc8))
| in(u,skc8) ),
inference(obv,[status(thm),theory(equality)],[1424]),
[iquote('0:Obv:1424.2')] ).
cnf(1426,plain,
( ~ in(u,skc9)
| in(u,skc8) ),
inference(mrr,[status(thm)],[1425,539]),
[iquote('0:MRR:1425.1,539.1')] ).
cnf(1428,plain,
( skP0(skc9)
| in(skf28(skc9),skc8) ),
inference(res,[status(thm),theory(equality)],[38,1426]),
[iquote('0:Res:38.1,1426.0')] ).
cnf(1498,plain,
skP0(skc9),
inference(spt,[spt(split,[position(s1)])],[1428]),
[iquote('1:Spt:1428.0')] ).
cnf(1499,plain,
( ~ skP0(skc8)
| in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc9) ),
inference(mrr,[status(thm)],[1275,1498]),
[iquote('1:MRR:1275.0,1498.0')] ).
cnf(1501,plain,
( ~ skP0(skc8)
| ~ in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc8) ),
inference(mrr,[status(thm)],[1277,1498]),
[iquote('1:MRR:1277.0,1498.0')] ).
cnf(2416,plain,
( ~ in(skf28(u),skc9)
| skP0(v) ),
inference(eqr,[status(thm),theory(equality)],[535]),
[iquote('0:EqR:535.1')] ).
cnf(2422,plain,
( skP0(skc9)
| skP0(u) ),
inference(res,[status(thm),theory(equality)],[38,2416]),
[iquote('0:Res:38.1,2416.0')] ).
cnf(2424,plain,
( ~ in(skf28(u),skc8)
| skP0(v) ),
inference(res,[status(thm),theory(equality)],[1274,2416]),
[iquote('0:Res:1274.1,2416.0')] ).
cnf(2425,plain,
skP0(skc9),
inference(con,[status(thm)],[2422]),
[iquote('0:Con:2422.1')] ).
cnf(2431,plain,
( skP0(skc8)
| skP0(u) ),
inference(res,[status(thm),theory(equality)],[38,2424]),
[iquote('0:Res:38.1,2424.0')] ).
cnf(2433,plain,
skP0(skc8),
inference(con,[status(thm)],[2431]),
[iquote('0:Con:2431.1')] ).
cnf(2434,plain,
in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc9),
inference(mrr,[status(thm)],[1499,2433]),
[iquote('1:MRR:1499.0,2433.0')] ).
cnf(2436,plain,
~ in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc8),
inference(mrr,[status(thm)],[1501,2433]),
[iquote('1:MRR:1501.0,2433.0')] ).
cnf(2474,plain,
in(ordered_pair(skf25(skc9,skc8),skf24(skc9,skc8)),skc8),
inference(res,[status(thm),theory(equality)],[2434,1426]),
[iquote('1:Res:2434.0,1426.0')] ).
cnf(2480,plain,
$false,
inference(mrr,[status(thm)],[2474,2436]),
[iquote('1:MRR:2474.0,2436.0')] ).
cnf(2484,plain,
~ skP0(skc9),
inference(spt,[spt(split,[position(sa)])],[2480,1498]),
[iquote('1:Spt:2480.0,1428.0,1498.0')] ).
cnf(2485,plain,
in(skf28(skc9),skc8),
inference(spt,[spt(split,[position(s2)])],[1428]),
[iquote('1:Spt:2480.0,1428.1')] ).
cnf(2486,plain,
$false,
inference(mrr,[status(thm)],[2484,2425]),
[iquote('1:MRR:2484.0,2425.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET990+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n020.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 : Sun Jul 10 11:37:13 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.79/0.99
% 0.79/0.99 SPASS V 3.9
% 0.79/0.99 SPASS beiseite: Proof found.
% 0.79/0.99 % SZS status Theorem
% 0.79/0.99 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.79/0.99 SPASS derived 1949 clauses, backtracked 53 clauses, performed 4 splits and kept 1080 clauses.
% 0.79/0.99 SPASS allocated 100324 KBytes.
% 0.79/0.99 SPASS spent 0:00:00.63 on the problem.
% 0.79/0.99 0:00:00.04 for the input.
% 0.79/0.99 0:00:00.06 for the FLOTTER CNF translation.
% 0.79/0.99 0:00:00.03 for inferences.
% 0.79/0.99 0:00:00.00 for the backtracking.
% 0.79/0.99 0:00:00.46 for the reduction.
% 0.79/0.99
% 0.79/0.99
% 0.79/0.99 Here is a proof with depth 5, length 71 :
% 0.79/0.99 % SZS output start Refutation
% See solution above
% 0.79/0.99 Formulae used in the proof : t9_funct_1 t112_zfmisc_1 d1_relat_1 d4_relat_1 antisymmetry_r2_hidden d4_funct_1
% 0.79/0.99
%------------------------------------------------------------------------------