TSTP Solution File: SEU075+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 14:33:50 EDT 2022
% Result : Theorem 0.39s 0.58s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 57 ( 22 unt; 7 nHn; 57 RR)
% Number of literals : 183 ( 0 equ; 120 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
function(skc14),
file('SEU075+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc14),
file('SEU075+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc13),
file('SEU075+1.p',unknown),
[] ).
cnf(4,axiom,
relation(skc13),
file('SEU075+1.p',unknown),
[] ).
cnf(5,axiom,
function(skc12),
file('SEU075+1.p',unknown),
[] ).
cnf(6,axiom,
relation(skc12),
file('SEU075+1.p',unknown),
[] ).
cnf(31,axiom,
equal(relation_rng(skc12),skc15),
file('SEU075+1.p',unknown),
[] ).
cnf(32,axiom,
equal(relation_dom(skc13),skc15),
file('SEU075+1.p',unknown),
[] ).
cnf(33,axiom,
equal(relation_dom(skc14),skc15),
file('SEU075+1.p',unknown),
[] ).
cnf(34,axiom,
~ equal(skc14,skc13),
file('SEU075+1.p',unknown),
[] ).
cnf(47,axiom,
equal(relation_composition(skc12,skc14),relation_composition(skc12,skc13)),
file('SEU075+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(skf7(u,x),relation_dom(u)) ),
file('SEU075+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| equal(apply(u,skf7(u,v)),v) ),
file('SEU075+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ function(u)
| ~ relation(u)
| ~ function(v)
| ~ relation(v)
| ~ equal(relation_dom(v),relation_dom(u))
| equal(v,u)
| in(skf14(v,w),relation_dom(v)) ),
file('SEU075+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| equal(apply(relation_composition(u,v),w),apply(v,apply(u,w))) ),
file('SEU075+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ function(u)
| ~ relation(u)
| ~ function(v)
| ~ relation(v)
| ~ equal(relation_dom(v),relation_dom(u))
| ~ equal(apply(v,skf14(v,u)),apply(u,skf14(v,u)))
| equal(v,u) ),
file('SEU075+1.p',unknown),
[] ).
cnf(82,plain,
( ~ function(skc12)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc12))
| equal(apply(skc12,skf7(skc12,u)),u) ),
inference(res,[status(thm),theory(equality)],[6,70]),
[iquote('0:Res:6.0,70.0')] ).
cnf(83,plain,
( ~ function(skc12)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc12))
| in(skf7(skc12,w),relation_dom(skc12)) ),
inference(res,[status(thm),theory(equality)],[6,69]),
[iquote('0:Res:6.0,69.0')] ).
cnf(133,plain,
( ~ relation(skc13)
| ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| equal(apply(relation_composition(u,skc13),v),apply(skc13,apply(u,v))) ),
inference(res,[status(thm),theory(equality)],[3,74]),
[iquote('0:Res:3.0,74.0')] ).
cnf(134,plain,
( ~ relation(skc13)
| ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(skc13),relation_dom(u))
| in(skf14(skc13,v),relation_dom(skc13))
| equal(skc13,u) ),
inference(res,[status(thm),theory(equality)],[3,73]),
[iquote('0:Res:3.0,73.1')] ).
cnf(147,plain,
( ~ function(skc14)
| ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(skc14),relation_dom(u))
| in(skf14(skc14,v),relation_dom(skc14))
| equal(skc14,u) ),
inference(res,[status(thm),theory(equality)],[2,73]),
[iquote('0:Res:2.0,73.0')] ).
cnf(175,plain,
( ~ function(skc12)
| ~ in(u,v)
| ~ equal(v,skc15)
| in(skf7(skc12,w),relation_dom(skc12)) ),
inference(rew,[status(thm),theory(equality)],[31,83]),
[iquote('0:Rew:31.0,83.2')] ).
cnf(176,plain,
( ~ in(u,v)
| ~ equal(v,skc15)
| in(skf7(skc12,w),relation_dom(skc12)) ),
inference(mrr,[status(thm)],[175,5]),
[iquote('0:MRR:175.0,5.0')] ).
cnf(191,plain,
( ~ function(skc12)
| ~ in(u,v)
| ~ equal(v,skc15)
| equal(apply(skc12,skf7(skc12,u)),u) ),
inference(rew,[status(thm),theory(equality)],[31,82]),
[iquote('0:Rew:31.0,82.2')] ).
cnf(192,plain,
( ~ in(u,v)
| ~ equal(v,skc15)
| equal(apply(skc12,skf7(skc12,u)),u) ),
inference(mrr,[status(thm)],[191,5]),
[iquote('0:MRR:191.0,5.0')] ).
cnf(211,plain,
( ~ function(skc14)
| ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(u),skc15)
| in(skf14(skc14,v),skc15)
| equal(skc14,u) ),
inference(rew,[status(thm),theory(equality)],[33,147]),
[iquote('0:Rew:33.0,147.4,33.0,147.3')] ).
cnf(212,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc15)
| equal(skc14,u)
| in(skf14(skc14,v),skc15) ),
inference(mrr,[status(thm)],[211,1]),
[iquote('0:MRR:211.0,1.0')] ).
cnf(215,plain,
( ~ relation(skc13)
| ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(u),skc15)
| in(skf14(skc13,v),skc15)
| equal(skc13,u) ),
inference(rew,[status(thm),theory(equality)],[32,134]),
[iquote('0:Rew:32.0,134.4,32.0,134.3')] ).
cnf(216,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc15)
| equal(skc13,u)
| in(skf14(skc13,v),skc15) ),
inference(mrr,[status(thm)],[215,4]),
[iquote('0:MRR:215.0,4.0')] ).
cnf(226,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(u))
| equal(apply(relation_composition(u,skc13),v),apply(skc13,apply(u,v))) ),
inference(mrr,[status(thm)],[133,4]),
[iquote('0:MRR:133.0,4.0')] ).
cnf(242,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc15)
| equal(skc14,u) ),
inference(spt,[spt(split,[position(s1)])],[212]),
[iquote('1:Spt:212.0,212.1,212.2,212.3')] ).
cnf(264,plain,
( ~ function(skc13)
| ~ relation(skc13)
| ~ equal(skc15,skc15)
| equal(skc14,skc13) ),
inference(spl,[status(thm),theory(equality)],[32,242]),
[iquote('1:SpL:32.0,242.2')] ).
cnf(266,plain,
( ~ function(skc13)
| ~ relation(skc13)
| equal(skc14,skc13) ),
inference(obv,[status(thm),theory(equality)],[264]),
[iquote('1:Obv:264.2')] ).
cnf(267,plain,
equal(skc14,skc13),
inference(ssi,[status(thm)],[266,3,4]),
[iquote('1:SSi:266.1,266.0,3.0,4.0,3.0,4.0')] ).
cnf(268,plain,
$false,
inference(mrr,[status(thm)],[267,34]),
[iquote('1:MRR:267.0,34.0')] ).
cnf(270,plain,
in(skf14(skc14,u),skc15),
inference(spt,[spt(split,[position(s2)])],[212]),
[iquote('1:Spt:268.0,212.4')] ).
cnf(271,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(u),skc15)
| equal(skc13,u) ),
inference(spt,[spt(split,[position(s2s1)])],[216]),
[iquote('2:Spt:216.0,216.1,216.2,216.3')] ).
cnf(272,plain,
( ~ function(skc14)
| ~ relation(skc14)
| ~ equal(skc15,skc15)
| equal(skc14,skc13) ),
inference(spl,[status(thm),theory(equality)],[33,271]),
[iquote('2:SpL:33.0,271.2')] ).
cnf(274,plain,
( ~ function(skc14)
| ~ relation(skc14)
| equal(skc14,skc13) ),
inference(obv,[status(thm),theory(equality)],[272]),
[iquote('2:Obv:272.2')] ).
cnf(275,plain,
equal(skc14,skc13),
inference(ssi,[status(thm)],[274,1,2]),
[iquote('2:SSi:274.1,274.0,1.0,2.0,1.0,2.0')] ).
cnf(276,plain,
$false,
inference(mrr,[status(thm)],[275,34]),
[iquote('2:MRR:275.0,34.0')] ).
cnf(277,plain,
in(skf14(skc13,u),skc15),
inference(spt,[spt(split,[position(s2s2)])],[216]),
[iquote('2:Spt:276.0,216.4')] ).
cnf(841,plain,
( ~ relation(skc12)
| ~ function(skc12)
| ~ relation(skc14)
| ~ function(skc14)
| ~ in(u,relation_dom(skc12))
| equal(apply(relation_composition(skc12,skc13),u),apply(skc14,apply(skc12,u))) ),
inference(spr,[status(thm),theory(equality)],[47,74]),
[iquote('0:SpR:47.0,74.5')] ).
cnf(850,plain,
( ~ relation(skc12)
| ~ function(skc12)
| ~ relation(skc14)
| ~ function(skc14)
| ~ in(u,relation_dom(skc12))
| equal(apply(skc14,apply(skc12,u)),apply(skc13,apply(skc12,u))) ),
inference(rew,[status(thm),theory(equality)],[226,841]),
[iquote('0:Rew:226.3,841.5')] ).
cnf(851,plain,
( ~ in(u,relation_dom(skc12))
| equal(apply(skc14,apply(skc12,u)),apply(skc13,apply(skc12,u))) ),
inference(ssi,[status(thm)],[850,1,2,5,6]),
[iquote('0:SSi:850.3,850.2,850.1,850.0,1.0,2.0,1.0,2.0,5.0,6.0,5.0,6.0')] ).
cnf(1151,plain,
( ~ equal(skc15,skc15)
| in(skf7(skc12,u),relation_dom(skc12)) ),
inference(res,[status(thm),theory(equality)],[277,176]),
[iquote('2:Res:277.0,176.0')] ).
cnf(1161,plain,
in(skf7(skc12,u),relation_dom(skc12)),
inference(obv,[status(thm),theory(equality)],[1151]),
[iquote('2:Obv:1151.0')] ).
cnf(1184,plain,
( ~ equal(skc15,skc15)
| equal(apply(skc12,skf7(skc12,skf14(skc13,u))),skf14(skc13,u)) ),
inference(res,[status(thm),theory(equality)],[277,192]),
[iquote('2:Res:277.0,192.0')] ).
cnf(1194,plain,
equal(apply(skc12,skf7(skc12,skf14(skc13,u))),skf14(skc13,u)),
inference(obv,[status(thm),theory(equality)],[1184]),
[iquote('2:Obv:1184.0')] ).
cnf(1224,plain,
( ~ in(skf7(skc12,skf14(skc13,u)),relation_dom(skc12))
| equal(apply(skc14,skf14(skc13,u)),apply(skc13,skf14(skc13,u))) ),
inference(spr,[status(thm),theory(equality)],[1194,851]),
[iquote('2:SpR:1194.0,851.1')] ).
cnf(1227,plain,
equal(apply(skc14,skf14(skc13,u)),apply(skc13,skf14(skc13,u))),
inference(mrr,[status(thm)],[1224,1161]),
[iquote('2:MRR:1224.0,1161.0')] ).
cnf(1288,plain,
( ~ function(skc14)
| ~ relation(skc14)
| ~ function(skc13)
| ~ relation(skc13)
| ~ equal(relation_dom(skc14),relation_dom(skc13))
| ~ equal(apply(skc13,skf14(skc13,skc14)),apply(skc13,skf14(skc13,skc14)))
| equal(skc14,skc13) ),
inference(spl,[status(thm),theory(equality)],[1227,75]),
[iquote('2:SpL:1227.0,75.5')] ).
cnf(1294,plain,
( ~ function(skc14)
| ~ relation(skc14)
| ~ function(skc13)
| ~ relation(skc13)
| ~ equal(relation_dom(skc14),relation_dom(skc13))
| equal(skc14,skc13) ),
inference(obv,[status(thm),theory(equality)],[1288]),
[iquote('2:Obv:1288.5')] ).
cnf(1295,plain,
( ~ function(skc14)
| ~ relation(skc14)
| ~ function(skc13)
| ~ relation(skc13)
| ~ equal(skc15,skc15)
| equal(skc14,skc13) ),
inference(rew,[status(thm),theory(equality)],[33,1294,32]),
[iquote('2:Rew:33.0,1294.4,32.0,1294.4')] ).
cnf(1296,plain,
( ~ function(skc14)
| ~ relation(skc14)
| ~ function(skc13)
| ~ relation(skc13)
| equal(skc14,skc13) ),
inference(obv,[status(thm),theory(equality)],[1295]),
[iquote('2:Obv:1295.4')] ).
cnf(1297,plain,
equal(skc14,skc13),
inference(ssi,[status(thm)],[1296,3,4,1,2]),
[iquote('2:SSi:1296.3,1296.2,1296.1,1296.0,3.0,4.0,3.0,4.0,1.0,2.0,1.0,2.0')] ).
cnf(1298,plain,
$false,
inference(mrr,[status(thm)],[1297,34]),
[iquote('2:MRR:1297.0,34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.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 08:30:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.39/0.58
% 0.39/0.58 SPASS V 3.9
% 0.39/0.58 SPASS beiseite: Proof found.
% 0.39/0.58 % SZS status Theorem
% 0.39/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.58 SPASS derived 949 clauses, backtracked 64 clauses, performed 16 splits and kept 595 clauses.
% 0.39/0.58 SPASS allocated 98752 KBytes.
% 0.39/0.58 SPASS spent 0:00:00.23 on the problem.
% 0.39/0.58 0:00:00.03 for the input.
% 0.39/0.58 0:00:00.05 for the FLOTTER CNF translation.
% 0.39/0.58 0:00:00.01 for inferences.
% 0.39/0.58 0:00:00.00 for the backtracking.
% 0.39/0.58 0:00:00.09 for the reduction.
% 0.39/0.58
% 0.39/0.58
% 0.39/0.58 Here is a proof with depth 5, length 57 :
% 0.39/0.58 % SZS output start Refutation
% See solution above
% 0.39/0.58 Formulae used in the proof : t156_funct_1 d5_funct_1 antisymmetry_r2_hidden t9_funct_1 t23_funct_1
% 0.39/0.58
%------------------------------------------------------------------------------