%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP638+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:48:31 EDT 2022
% Result : Theorem 0.45s 0.61s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of clauses : 68 ( 29 unt; 12 nHn; 68 RR)
% Number of literals : 173 ( 0 equ; 99 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v1_funct_1(skc14),
file('GRP638+1.p',unknown),
[] ).
cnf(2,axiom,
v3_group_1(skc12),
file('GRP638+1.p',unknown),
[] ).
cnf(3,axiom,
v4_group_1(skc12),
file('GRP638+1.p',unknown),
[] ).
cnf(4,axiom,
l1_group_1(skc12),
file('GRP638+1.p',unknown),
[] ).
cnf(5,axiom,
v3_group_1(skc13),
file('GRP638+1.p',unknown),
[] ).
cnf(6,axiom,
v4_group_1(skc13),
file('GRP638+1.p',unknown),
[] ).
cnf(7,axiom,
l1_group_1(skc13),
file('GRP638+1.p',unknown),
[] ).
cnf(13,axiom,
m1_group_2(skc18,skc12),
file('GRP638+1.p',unknown),
[] ).
cnf(14,axiom,
m1_group_2(skc17,skc12),
file('GRP638+1.p',unknown),
[] ).
cnf(15,axiom,
m1_group_2(skc16,skc13),
file('GRP638+1.p',unknown),
[] ).
cnf(17,axiom,
~ v3_struct_0(skc13),
file('GRP638+1.p',unknown),
[] ).
cnf(18,axiom,
~ v3_struct_0(skc12),
file('GRP638+1.p',unknown),
[] ).
cnf(24,axiom,
m1_group_6(skc15,skc13,skc16),
file('GRP638+1.p',unknown),
[] ).
cnf(31,axiom,
~ m1_group_6(skc17,skc12,skc18),
file('GRP638+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ l1_group_1(u)
| l1_struct_0(u) ),
file('GRP638+1.p',unknown),
[] ).
cnf(36,axiom,
m2_relset_1(skc14,u1_struct_0(skc12),u1_struct_0(skc13)),
file('GRP638+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| v1_relat_1(u) ),
file('GRP638+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ m2_relset_1(u,v,w)
| m1_relset_1(u,v,w) ),
file('GRP638+1.p',unknown),
[] ).
cnf(59,axiom,
equal(k3_funct_2(u1_struct_0(skc12),u1_struct_0(skc13),skc14,u1_struct_0(skc16)),u1_struct_0(skc18)),
file('GRP638+1.p',unknown),
[] ).
cnf(60,axiom,
equal(k3_funct_2(u1_struct_0(skc12),u1_struct_0(skc13),skc14,u1_struct_0(skc15)),u1_struct_0(skc17)),
file('GRP638+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ m2_relset_1(u,v,w)
| m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w))) ),
file('GRP638+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ l1_group_1(u)
| ~ v3_group_1(u)
| ~ m1_group_2(v,u)
| v3_struct_0(u)
| v3_group_1(v) ),
file('GRP638+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ l1_group_1(u)
| ~ v3_group_1(u)
| ~ m1_group_2(v,u)
| v3_struct_0(u)
| l1_group_1(v) ),
file('GRP638+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ v1_relat_1(u)
| ~ r1_tarski(v,w)
| r1_tarski(k10_relat_1(u,v),k10_relat_1(u,w)) ),
file('GRP638+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ l1_group_1(u)
| ~ v3_group_1(u)
| ~ v3_struct_0(v)
| ~ m1_group_2(v,u)
| v3_struct_0(u) ),
file('GRP638+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ v1_funct_1(u)
| ~ m1_relset_1(u,v,w)
| equal(k3_funct_2(v,w,u,x),k10_relat_1(u,x)) ),
file('GRP638+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ v3_group_1(u)
| ~ v4_group_1(u)
| ~ l1_group_1(u)
| ~ m1_group_2(v,w)
| ~ m1_group_2(w,u)
| v3_struct_0(u)
| m1_group_6(v,u,w) ),
file('GRP638+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ v3_group_1(u)
| ~ v4_group_1(u)
| ~ l1_group_1(u)
| ~ m1_group_2(v,u)
| ~ m1_group_6(w,u,v)
| v3_struct_0(u)
| m1_group_2(w,v) ),
file('GRP638+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ v3_group_1(u)
| ~ l1_group_1(u)
| ~ v3_group_1(v)
| ~ l1_group_1(v)
| ~ m1_group_2(v,u)
| r1_tarski(u1_struct_0(v),u1_struct_0(u))
| v3_struct_0(u)
| v3_struct_0(v) ),
file('GRP638+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ m1_group_2(v,u)
| ~ m1_group_2(w,u)
| ~ r1_tarski(u1_struct_0(w),u1_struct_0(v))
| v3_struct_0(u)
| m1_group_2(w,v) ),
file('GRP638+1.p',unknown),
[] ).
cnf(86,plain,
( ~ l1_group_1(u)
| ~ v3_group_1(u)
| ~ m1_group_2(v,u)
| v3_struct_0(u)
| r1_tarski(u1_struct_0(v),u1_struct_0(u)) ),
inference(mrr,[status(thm)],[81,67,68,70]),
[iquote('0:MRR:81.2,81.3,81.7,67.3,68.3,70.0')] ).
cnf(96,plain,
( ~ v3_group_1(skc13)
| ~ m1_group_2(u,skc13)
| v3_group_1(u)
| v3_struct_0(skc13) ),
inference(res,[status(thm),theory(equality)],[7,67]),
[iquote('0:Res:7.0,67.1')] ).
cnf(97,plain,
( ~ v3_group_1(skc13)
| ~ m1_group_2(u,skc13)
| l1_group_1(u)
| v3_struct_0(skc13) ),
inference(res,[status(thm),theory(equality)],[7,68]),
[iquote('0:Res:7.0,68.1')] ).
cnf(102,plain,
l1_struct_0(skc13),
inference(res,[status(thm),theory(equality)],[7,32]),
[iquote('0:Res:7.0,32.0')] ).
cnf(104,plain,
( ~ v3_struct_0(u)
| ~ v3_group_1(skc13)
| ~ m1_group_2(u,skc13)
| v3_struct_0(skc13) ),
inference(res,[status(thm),theory(equality)],[7,70]),
[iquote('0:Res:7.0,70.2')] ).
cnf(137,plain,
l1_struct_0(skc12),
inference(res,[status(thm),theory(equality)],[4,32]),
[iquote('0:Res:4.0,32.0')] ).
cnf(147,plain,
( ~ v4_group_1(skc12)
| ~ l1_group_1(skc12)
| ~ m1_group_2(u,skc12)
| ~ m1_group_2(v,skc12)
| ~ r1_tarski(u1_struct_0(u),u1_struct_0(v))
| v3_struct_0(skc12)
| m1_group_2(u,v) ),
inference(res,[status(thm),theory(equality)],[2,82]),
[iquote('0:Res:2.0,82.0')] ).
cnf(182,plain,
( ~ m1_group_2(u,skc13)
| v3_group_1(u) ),
inference(mrr,[status(thm)],[96,5,17]),
[iquote('0:MRR:96.0,96.3,5.0,17.0')] ).
cnf(183,plain,
( ~ m1_group_2(u,skc13)
| l1_group_1(u) ),
inference(mrr,[status(thm)],[97,5,17]),
[iquote('0:MRR:97.0,97.3,5.0,17.0')] ).
cnf(186,plain,
( ~ v3_struct_0(u)
| ~ m1_group_2(u,skc13) ),
inference(mrr,[status(thm)],[104,5,17]),
[iquote('0:MRR:104.1,104.3,5.0,17.0')] ).
cnf(200,plain,
( ~ m1_group_2(u,skc12)
| ~ m1_group_2(v,skc12)
| ~ r1_tarski(u1_struct_0(v),u1_struct_0(u))
| m1_group_2(v,u) ),
inference(mrr,[status(thm)],[147,3,4,18]),
[iquote('0:MRR:147.0,147.1,147.5,3.0,4.0,18.0')] ).
cnf(218,plain,
v3_group_1(skc16),
inference(res,[status(thm),theory(equality)],[15,182]),
[iquote('0:Res:15.0,182.0')] ).
cnf(224,plain,
l1_group_1(skc16),
inference(res,[status(thm),theory(equality)],[15,183]),
[iquote('0:Res:15.0,183.0')] ).
cnf(230,plain,
~ v3_struct_0(skc16),
inference(res,[status(thm),theory(equality)],[15,186]),
[iquote('0:Res:15.0,186.1')] ).
cnf(285,plain,
( ~ m2_relset_1(u,v,w)
| v1_relat_1(u) ),
inference(res,[status(thm),theory(equality)],[61,51]),
[iquote('0:Res:61.1,51.0')] ).
cnf(288,plain,
v1_relat_1(skc14),
inference(res,[status(thm),theory(equality)],[36,285]),
[iquote('0:Res:36.0,285.0')] ).
cnf(492,plain,
( ~ v1_funct_1(skc14)
| ~ m1_relset_1(skc14,u1_struct_0(skc12),u1_struct_0(skc13))
| equal(k10_relat_1(skc14,u1_struct_0(skc15)),u1_struct_0(skc17)) ),
inference(spr,[status(thm),theory(equality)],[73,60]),
[iquote('0:SpR:73.2,60.0')] ).
cnf(493,plain,
( ~ v1_funct_1(skc14)
| ~ m1_relset_1(skc14,u1_struct_0(skc12),u1_struct_0(skc13))
| equal(k10_relat_1(skc14,u1_struct_0(skc16)),u1_struct_0(skc18)) ),
inference(spr,[status(thm),theory(equality)],[73,59]),
[iquote('0:SpR:73.2,59.0')] ).
cnf(495,plain,
( ~ m1_relset_1(skc14,u1_struct_0(skc12),u1_struct_0(skc13))
| equal(k10_relat_1(skc14,u1_struct_0(skc15)),u1_struct_0(skc17)) ),
inference(ssi,[status(thm)],[492,1,288]),
[iquote('0:SSi:492.0,1.0,288.0')] ).
cnf(496,plain,
( ~ m1_relset_1(skc14,u1_struct_0(skc12),u1_struct_0(skc13))
| equal(k10_relat_1(skc14,u1_struct_0(skc16)),u1_struct_0(skc18)) ),
inference(ssi,[status(thm)],[493,1,288]),
[iquote('0:SSi:493.0,1.0,288.0')] ).
cnf(555,plain,
( ~ v3_group_1(skc12)
| ~ v4_group_1(skc12)
| ~ l1_group_1(skc12)
| ~ m1_group_2(skc17,skc18)
| ~ m1_group_2(skc18,skc12)
| v3_struct_0(skc12) ),
inference(res,[status(thm),theory(equality)],[78,31]),
[iquote('0:Res:78.6,31.0')] ).
cnf(556,plain,
( ~ m1_group_2(skc17,skc18)
| ~ m1_group_2(skc18,skc12)
| v3_struct_0(skc12) ),
inference(ssi,[status(thm)],[555,3,2,4,137]),
[iquote('0:SSi:555.2,555.1,555.0,3.0,2.0,4.0,137.0,3.0,2.0,4.0,137.0,3.0,2.0,4.0,137.0')] ).
cnf(557,plain,
~ m1_group_2(skc17,skc18),
inference(mrr,[status(thm)],[556,13,18]),
[iquote('0:MRR:556.1,556.2,13.0,18.0')] ).
cnf(606,plain,
( ~ v3_group_1(skc13)
| ~ v4_group_1(skc13)
| ~ l1_group_1(skc13)
| ~ m1_group_2(skc16,skc13)
| v3_struct_0(skc13)
| m1_group_2(skc15,skc16) ),
inference(res,[status(thm),theory(equality)],[24,79]),
[iquote('0:Res:24.0,79.4')] ).
cnf(611,plain,
( ~ m1_group_2(skc16,skc13)
| v3_struct_0(skc13)
| m1_group_2(skc15,skc16) ),
inference(ssi,[status(thm)],[606,6,5,7,102]),
[iquote('0:SSi:606.2,606.1,606.0,6.0,5.0,7.0,102.0,6.0,5.0,7.0,102.0,6.0,5.0,7.0,102.0')] ).
cnf(612,plain,
m1_group_2(skc15,skc16),
inference(mrr,[status(thm)],[611,15,17]),
[iquote('0:MRR:611.0,611.1,15.0,17.0')] ).
cnf(1035,plain,
( ~ m2_relset_1(skc14,u1_struct_0(skc12),u1_struct_0(skc13))
| equal(k10_relat_1(skc14,u1_struct_0(skc15)),u1_struct_0(skc17)) ),
inference(res,[status(thm),theory(equality)],[55,495]),
[iquote('0:Res:55.1,495.0')] ).
cnf(1036,plain,
equal(k10_relat_1(skc14,u1_struct_0(skc15)),u1_struct_0(skc17)),
inference(mrr,[status(thm)],[1035,36]),
[iquote('0:MRR:1035.0,36.0')] ).
cnf(1038,plain,
( ~ v1_relat_1(skc14)
| ~ r1_tarski(u1_struct_0(skc15),u)
| r1_tarski(u1_struct_0(skc17),k10_relat_1(skc14,u)) ),
inference(spr,[status(thm),theory(equality)],[1036,69]),
[iquote('0:SpR:1036.0,69.2')] ).
cnf(1054,plain,
( ~ r1_tarski(u1_struct_0(skc15),u)
| r1_tarski(u1_struct_0(skc17),k10_relat_1(skc14,u)) ),
inference(ssi,[status(thm)],[1038,1,288]),
[iquote('0:SSi:1038.0,1.0,288.0')] ).
cnf(1067,plain,
( ~ m2_relset_1(skc14,u1_struct_0(skc12),u1_struct_0(skc13))
| equal(k10_relat_1(skc14,u1_struct_0(skc16)),u1_struct_0(skc18)) ),
inference(res,[status(thm),theory(equality)],[55,496]),
[iquote('0:Res:55.1,496.0')] ).
cnf(1068,plain,
equal(k10_relat_1(skc14,u1_struct_0(skc16)),u1_struct_0(skc18)),
inference(mrr,[status(thm)],[1067,36]),
[iquote('0:MRR:1067.0,36.0')] ).
cnf(1693,plain,
( ~ r1_tarski(u1_struct_0(skc15),u1_struct_0(skc16))
| r1_tarski(u1_struct_0(skc17),u1_struct_0(skc18)) ),
inference(spr,[status(thm),theory(equality)],[1068,1054]),
[iquote('0:SpR:1068.0,1054.1')] ).
cnf(1698,plain,
( ~ r1_tarski(u1_struct_0(skc15),u1_struct_0(skc16))
| ~ m1_group_2(skc18,skc12)
| ~ m1_group_2(skc17,skc12)
| m1_group_2(skc17,skc18) ),
inference(res,[status(thm),theory(equality)],[1693,200]),
[iquote('0:Res:1693.1,200.2')] ).
cnf(1701,plain,
~ r1_tarski(u1_struct_0(skc15),u1_struct_0(skc16)),
inference(mrr,[status(thm)],[1698,13,14,557]),
[iquote('0:MRR:1698.1,1698.2,1698.3,13.0,14.0,557.0')] ).
cnf(1702,plain,
( ~ l1_group_1(skc16)
| ~ v3_group_1(skc16)
| ~ m1_group_2(skc15,skc16)
| v3_struct_0(skc16) ),
inference(res,[status(thm),theory(equality)],[86,1701]),
[iquote('0:Res:86.4,1701.0')] ).
cnf(1703,plain,
( ~ m1_group_2(skc15,skc16)
| v3_struct_0(skc16) ),
inference(ssi,[status(thm)],[1702,218,224]),
[iquote('0:SSi:1702.1,1702.0,218.0,224.0,218.0,224.0')] ).
cnf(1704,plain,
$false,
inference(mrr,[status(thm)],[1703,612,230]),
[iquote('0:MRR:1703.0,1703.1,612.0,230.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP638+1 : TPTP v8.1.0. Released v3.4.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 11:12:27 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.45/0.61
% 0.45/0.61 SPASS V 3.9
% 0.45/0.61 SPASS beiseite: Proof found.
% 0.45/0.61 % SZS status Theorem
% 0.45/0.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.61 SPASS derived 1396 clauses, backtracked 37 clauses, performed 4 splits and kept 772 clauses.
% 0.45/0.61 SPASS allocated 98994 KBytes.
% 0.45/0.61 SPASS spent 0:00:00.23 on the problem.
% 0.45/0.61 0:00:00.03 for the input.
% 0.45/0.61 0:00:00.04 for the FLOTTER CNF translation.
% 0.45/0.61 0:00:00.03 for inferences.
% 0.45/0.61 0:00:00.00 for the backtracking.
% 0.45/0.61 0:00:00.09 for the reduction.
% 0.45/0.61
% 0.45/0.61
% 0.45/0.61 Here is a proof with depth 6, length 68 :
% 0.45/0.61 % SZS output start Refutation
% See solution above
% 0.45/0.61 Formulae used in the proof : t11_latsubgr dt_l1_group_1 cc1_relset_1 redefinition_m2_relset_1 dt_m2_relset_1 dt_m1_group_2 t178_relat_1 redefinition_k3_funct_2 redefinition_m1_group_6 d5_group_2 t66_group_2
% 0.45/0.61
%------------------------------------------------------------------------------