TSTP Solution File: GRP639+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP639+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : Sat Jul 16 11:48:32 EDT 2022
% Result : Theorem 0.46s 0.66s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of clauses : 53 ( 17 unt; 11 nHn; 53 RR)
% Number of literals : 144 ( 0 equ; 93 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v1_funct_1(skc11),
file('GRP639+1.p',unknown),
[] ).
cnf(2,axiom,
v3_group_1(skc9),
file('GRP639+1.p',unknown),
[] ).
cnf(3,axiom,
v4_group_1(skc9),
file('GRP639+1.p',unknown),
[] ).
cnf(4,axiom,
l1_group_1(skc9),
file('GRP639+1.p',unknown),
[] ).
cnf(14,axiom,
~ v3_struct_0(skc9),
file('GRP639+1.p',unknown),
[] ).
cnf(25,axiom,
m1_subset_1(skc12,k1_zfmisc_1(u1_struct_0(skc9))),
file('GRP639+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ l1_group_1(u)
| l1_struct_0(u) ),
file('GRP639+1.p',unknown),
[] ).
cnf(30,axiom,
v1_funct_2(skc11,u1_struct_0(skc9),u1_struct_0(skc10)),
file('GRP639+1.p',unknown),
[] ).
cnf(31,axiom,
m2_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10)),
file('GRP639+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| v1_relat_1(u) ),
file('GRP639+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ m2_relset_1(u,v,w)
| m1_relset_1(u,v,w) ),
file('GRP639+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ m2_relset_1(u,v,w)
| m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w))) ),
file('GRP639+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ l1_group_1(u)
| ~ v3_group_1(u)
| ~ m1_group_2(v,u)
| v3_struct_0(u)
| v3_group_1(v) ),
file('GRP639+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ l1_group_1(u)
| ~ v3_group_1(u)
| ~ m1_group_2(v,u)
| v3_struct_0(u)
| l1_group_1(v) ),
file('GRP639+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ v1_relat_1(u)
| ~ r1_tarski(v,w)
| r1_tarski(k9_relat_1(u,v),k9_relat_1(u,w)) ),
file('GRP639+1.p',unknown),
[] ).
cnf(66,axiom,
~ r1_tarski(k2_funct_2(u1_struct_0(skc9),u1_struct_0(skc10),skc11,skc12),k2_funct_2(u1_struct_0(skc9),u1_struct_0(skc10),skc11,u1_struct_0(k5_group_4(skc9,skc12)))),
file('GRP639+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ v3_group_1(u)
| ~ v4_group_1(u)
| ~ l1_group_1(u)
| ~ m1_subset_1(v,k1_zfmisc_1(u1_struct_0(u)))
| v3_struct_0(u)
| v1_group_1(k5_group_4(u,v)) ),
file('GRP639+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ v1_funct_1(u)
| ~ m1_relset_1(u,v,w)
| ~ v1_funct_2(u,v,w)
| equal(k2_funct_2(v,w,u,x),k9_relat_1(u,x)) ),
file('GRP639+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ v3_group_1(u)
| ~ v4_group_1(u)
| ~ l1_group_1(u)
| ~ m1_subset_1(v,k1_zfmisc_1(u1_struct_0(u)))
| v3_struct_0(u)
| m1_group_2(k5_group_4(u,v),u) ),
file('GRP639+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ v1_group_1(u)
| ~ l1_group_1(v)
| ~ v4_group_1(v)
| ~ v3_group_1(v)
| ~ m1_group_2(u,v)
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(v)))
| ~ equal(u,k5_group_4(v,w))
| v3_struct_0(v)
| r1_tarski(w,u1_struct_0(u)) ),
file('GRP639+1.p',unknown),
[] ).
cnf(122,plain,
( ~ v4_group_1(skc9)
| ~ v3_group_1(skc9)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc9)))
| m1_group_2(k5_group_4(skc9,u),skc9)
| v3_struct_0(skc9) ),
inference(res,[status(thm),theory(equality)],[4,75]),
[iquote('0:Res:4.0,75.0')] ).
cnf(123,plain,
( ~ v4_group_1(skc9)
| ~ v3_group_1(skc9)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc9)))
| v1_group_1(k5_group_4(skc9,u))
| v3_struct_0(skc9) ),
inference(res,[status(thm),theory(equality)],[4,69]),
[iquote('0:Res:4.0,69.0')] ).
cnf(124,plain,
( ~ v3_group_1(skc9)
| ~ m1_group_2(u,skc9)
| v3_group_1(u)
| v3_struct_0(skc9) ),
inference(res,[status(thm),theory(equality)],[4,61]),
[iquote('0:Res:4.0,61.1')] ).
cnf(125,plain,
( ~ v3_group_1(skc9)
| ~ m1_group_2(u,skc9)
| l1_group_1(u)
| v3_struct_0(skc9) ),
inference(res,[status(thm),theory(equality)],[4,62]),
[iquote('0:Res:4.0,62.1')] ).
cnf(131,plain,
l1_struct_0(skc9),
inference(res,[status(thm),theory(equality)],[4,27]),
[iquote('0:Res:4.0,27.0')] ).
cnf(180,plain,
( ~ m1_group_2(u,skc9)
| v3_group_1(u) ),
inference(mrr,[status(thm)],[124,2,14]),
[iquote('0:MRR:124.0,124.3,2.0,14.0')] ).
cnf(181,plain,
( ~ m1_group_2(u,skc9)
| l1_group_1(u) ),
inference(mrr,[status(thm)],[125,2,14]),
[iquote('0:MRR:125.0,125.3,2.0,14.0')] ).
cnf(185,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc9)))
| v1_group_1(k5_group_4(skc9,u)) ),
inference(mrr,[status(thm)],[123,3,2,14]),
[iquote('0:MRR:123.0,123.1,123.4,3.0,2.0,14.0')] ).
cnf(187,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc9)))
| m1_group_2(k5_group_4(skc9,u),skc9) ),
inference(mrr,[status(thm)],[122,3,2,14]),
[iquote('0:MRR:122.0,122.1,122.4,3.0,2.0,14.0')] ).
cnf(235,plain,
( ~ m2_relset_1(u,v,w)
| v1_relat_1(u) ),
inference(res,[status(thm),theory(equality)],[54,46]),
[iquote('0:Res:54.1,46.0')] ).
cnf(236,plain,
v1_relat_1(skc11),
inference(res,[status(thm),theory(equality)],[31,235]),
[iquote('0:Res:31.0,235.0')] ).
cnf(272,plain,
v1_group_1(k5_group_4(skc9,skc12)),
inference(res,[status(thm),theory(equality)],[25,185]),
[iquote('0:Res:25.0,185.0')] ).
cnf(294,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc9)))
| l1_group_1(k5_group_4(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[187,181]),
[iquote('0:Res:187.1,181.0')] ).
cnf(295,plain,
( ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc9)))
| v3_group_1(k5_group_4(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[187,180]),
[iquote('0:Res:187.1,180.0')] ).
cnf(299,plain,
l1_group_1(k5_group_4(skc9,skc12)),
inference(res,[status(thm),theory(equality)],[25,294]),
[iquote('0:Res:25.0,294.0')] ).
cnf(316,plain,
v3_group_1(k5_group_4(skc9,skc12)),
inference(res,[status(thm),theory(equality)],[25,295]),
[iquote('0:Res:25.0,295.0')] ).
cnf(412,plain,
( ~ v1_funct_1(skc11)
| ~ m1_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ v1_funct_2(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ r1_tarski(k9_relat_1(skc11,skc12),k2_funct_2(u1_struct_0(skc9),u1_struct_0(skc10),skc11,u1_struct_0(k5_group_4(skc9,skc12)))) ),
inference(spl,[status(thm),theory(equality)],[74,66]),
[iquote('0:SpL:74.3,66.0')] ).
cnf(413,plain,
( ~ v1_funct_1(skc11)
| ~ m1_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ v1_funct_2(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ r1_tarski(k9_relat_1(skc11,skc12),k9_relat_1(skc11,u1_struct_0(k5_group_4(skc9,skc12)))) ),
inference(rew,[status(thm),theory(equality)],[74,412]),
[iquote('0:Rew:74.3,412.3')] ).
cnf(414,plain,
( ~ m1_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ v1_funct_2(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ r1_tarski(k9_relat_1(skc11,skc12),k9_relat_1(skc11,u1_struct_0(k5_group_4(skc9,skc12)))) ),
inference(ssi,[status(thm)],[413,1,236]),
[iquote('0:SSi:413.0,1.0,236.0')] ).
cnf(415,plain,
( ~ m1_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ r1_tarski(k9_relat_1(skc11,skc12),k9_relat_1(skc11,u1_struct_0(k5_group_4(skc9,skc12)))) ),
inference(mrr,[status(thm)],[414,30]),
[iquote('0:MRR:414.1,30.0')] ).
cnf(486,plain,
( ~ v1_group_1(u)
| ~ l1_group_1(skc9)
| ~ v4_group_1(skc9)
| ~ v3_group_1(skc9)
| ~ m1_group_2(u,skc9)
| ~ equal(u,k5_group_4(skc9,skc12))
| v3_struct_0(skc9)
| r1_tarski(skc12,u1_struct_0(u)) ),
inference(res,[status(thm),theory(equality)],[25,78]),
[iquote('0:Res:25.0,78.5')] ).
cnf(492,plain,
( ~ v1_group_1(u)
| ~ m1_group_2(u,skc9)
| ~ equal(u,k5_group_4(skc9,skc12))
| v3_struct_0(skc9)
| r1_tarski(skc12,u1_struct_0(u)) ),
inference(ssi,[status(thm)],[486,3,2,4,131]),
[iquote('0:SSi:486.3,486.2,486.1,3.0,2.0,4.0,131.0,3.0,2.0,4.0,131.0,3.0,2.0,4.0,131.0')] ).
cnf(493,plain,
( ~ v1_group_1(u)
| ~ m1_group_2(u,skc9)
| ~ equal(u,k5_group_4(skc9,skc12))
| r1_tarski(skc12,u1_struct_0(u)) ),
inference(mrr,[status(thm)],[492,14]),
[iquote('0:MRR:492.3,14.0')] ).
cnf(863,plain,
( ~ v1_relat_1(skc11)
| ~ r1_tarski(skc12,u1_struct_0(k5_group_4(skc9,skc12)))
| ~ m1_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10)) ),
inference(res,[status(thm),theory(equality)],[63,415]),
[iquote('0:Res:63.2,415.1')] ).
cnf(864,plain,
( ~ r1_tarski(skc12,u1_struct_0(k5_group_4(skc9,skc12)))
| ~ m1_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10)) ),
inference(ssi,[status(thm)],[863,1,236]),
[iquote('0:SSi:863.0,1.0,236.0')] ).
cnf(1397,plain,
( ~ m2_relset_1(skc11,u1_struct_0(skc9),u1_struct_0(skc10))
| ~ r1_tarski(skc12,u1_struct_0(k5_group_4(skc9,skc12))) ),
inference(res,[status(thm),theory(equality)],[50,864]),
[iquote('0:Res:50.1,864.1')] ).
cnf(1398,plain,
~ r1_tarski(skc12,u1_struct_0(k5_group_4(skc9,skc12))),
inference(mrr,[status(thm)],[1397,31]),
[iquote('0:MRR:1397.0,31.0')] ).
cnf(1399,plain,
( ~ v1_group_1(k5_group_4(skc9,skc12))
| ~ m1_group_2(k5_group_4(skc9,skc12),skc9)
| ~ equal(k5_group_4(skc9,skc12),k5_group_4(skc9,skc12)) ),
inference(res,[status(thm),theory(equality)],[493,1398]),
[iquote('0:Res:493.3,1398.0')] ).
cnf(1400,plain,
( ~ v1_group_1(k5_group_4(skc9,skc12))
| ~ m1_group_2(k5_group_4(skc9,skc12),skc9) ),
inference(obv,[status(thm),theory(equality)],[1399]),
[iquote('0:Obv:1399.2')] ).
cnf(1401,plain,
~ m1_group_2(k5_group_4(skc9,skc12),skc9),
inference(ssi,[status(thm)],[1400,272,299,316]),
[iquote('0:SSi:1400.0,272.0,299.0,316.0')] ).
cnf(1403,plain,
( ~ v3_group_1(skc9)
| ~ v4_group_1(skc9)
| ~ l1_group_1(skc9)
| ~ m1_subset_1(skc12,k1_zfmisc_1(u1_struct_0(skc9)))
| v3_struct_0(skc9) ),
inference(res,[status(thm),theory(equality)],[75,1401]),
[iquote('0:Res:75.5,1401.0')] ).
cnf(1405,plain,
( ~ m1_subset_1(skc12,k1_zfmisc_1(u1_struct_0(skc9)))
| v3_struct_0(skc9) ),
inference(ssi,[status(thm)],[1403,3,2,4,131]),
[iquote('0:SSi:1403.2,1403.1,1403.0,3.0,2.0,4.0,131.0,3.0,2.0,4.0,131.0,3.0,2.0,4.0,131.0')] ).
cnf(1406,plain,
$false,
inference(mrr,[status(thm)],[1405,25,14]),
[iquote('0:MRR:1405.0,1405.1,25.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP639+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:52:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.66
% 0.46/0.66 SPASS V 3.9
% 0.46/0.66 SPASS beiseite: Proof found.
% 0.46/0.66 % SZS status Theorem
% 0.46/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.66 SPASS derived 1068 clauses, backtracked 32 clauses, performed 2 splits and kept 799 clauses.
% 0.46/0.66 SPASS allocated 99265 KBytes.
% 0.46/0.66 SPASS spent 0:00:00.30 on the problem.
% 0.46/0.66 0:00:00.04 for the input.
% 0.46/0.66 0:00:00.04 for the FLOTTER CNF translation.
% 0.46/0.66 0:00:00.03 for inferences.
% 0.46/0.66 0:00:00.00 for the backtracking.
% 0.46/0.66 0:00:00.16 for the reduction.
% 0.46/0.66
% 0.46/0.66
% 0.46/0.66 Here is a proof with depth 5, length 53 :
% 0.46/0.66 % SZS output start Refutation
% See solution above
% 0.46/0.66 Formulae used in the proof : t12_latsubgr dt_l1_group_1 cc1_relset_1 redefinition_m2_relset_1 dt_m2_relset_1 dt_m1_group_2 t156_relat_1 dt_k5_group_4 redefinition_k2_funct_2 d5_group_4
% 0.46/0.66
%------------------------------------------------------------------------------