TSTP Solution File: GRP623+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP623+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:48:21 EDT 2022
% Result : Theorem 0.43s 0.59s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 39 ( 13 unt; 14 nHn; 39 RR)
% Number of literals : 99 ( 0 equ; 52 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v1_group_1(skc14),
file('GRP623+1.p',unknown),
[] ).
cnf(2,axiom,
v3_group_1(skc14),
file('GRP623+1.p',unknown),
[] ).
cnf(3,axiom,
v4_group_1(skc14),
file('GRP623+1.p',unknown),
[] ).
cnf(4,axiom,
l1_group_1(skc14),
file('GRP623+1.p',unknown),
[] ).
cnf(32,axiom,
~ v3_struct_0(skc14),
file('GRP623+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ l1_group_1(u)
| l1_struct_0(u) ),
file('GRP623+1.p',unknown),
[] ).
cnf(46,axiom,
~ r1_tarski(k4_autgroup(skc14),k1_autgroup(skc14)),
file('GRP623+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ r2_hidden(u,v)
| m1_subset_1(u,v) ),
file('GRP623+1.p',unknown),
[] ).
cnf(60,axiom,
( r1_tarski(u,v)
| r2_hidden(skf9(v,u),u) ),
file('GRP623+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ v1_xboole_0(u)
| ~ m1_fraenkel(u,v,w) ),
file('GRP623+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ r2_hidden(skf9(u,v),u)
| r1_tarski(w,u) ),
file('GRP623+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ l1_struct_0(u)
| ~ v1_xboole_0(u1_struct_0(u))
| v3_struct_0(u) ),
file('GRP623+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ m1_subset_1(u,v)
| v1_xboole_0(v)
| r2_hidden(u,v) ),
file('GRP623+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ m1_fraenkel(u,v,w)
| ~ m2_fraenkel(x,v,w,u)
| v1_xboole_0(w)
| m1_subset_1(x,u) ),
file('GRP623+1.p',unknown),
[] ).
cnf(86,axiom,
( ~ m1_subset_1(u,v)
| ~ m1_fraenkel(v,w,x)
| v1_xboole_0(x)
| m2_fraenkel(u,w,x,v) ),
file('GRP623+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| m1_fraenkel(k4_autgroup(u),u1_struct_0(u),u1_struct_0(u)) ),
file('GRP623+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| v3_struct_0(u)
| m1_fraenkel(k1_autgroup(u),u1_struct_0(u),u1_struct_0(u)) ),
file('GRP623+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ l1_group_1(u)
| ~ v4_group_1(u)
| ~ v3_group_1(u)
| ~ v1_group_1(u)
| ~ m2_fraenkel(v,u1_struct_0(u),u1_struct_0(u),k4_autgroup(u))
| v3_struct_0(u)
| m2_fraenkel(v,u1_struct_0(u),u1_struct_0(u),k1_autgroup(u)) ),
file('GRP623+1.p',unknown),
[] ).
cnf(105,plain,
( ~ v1_group_1(skc14)
| ~ v3_group_1(skc14)
| ~ v4_group_1(skc14)
| v3_struct_0(skc14)
| m1_fraenkel(k1_autgroup(skc14),u1_struct_0(skc14),u1_struct_0(skc14)) ),
inference(res,[status(thm),theory(equality)],[4,93]),
[iquote('0:Res:4.0,93.3')] ).
cnf(106,plain,
( ~ v1_group_1(skc14)
| ~ v3_group_1(skc14)
| ~ v4_group_1(skc14)
| v3_struct_0(skc14)
| m1_fraenkel(k4_autgroup(skc14),u1_struct_0(skc14),u1_struct_0(skc14)) ),
inference(res,[status(thm),theory(equality)],[4,92]),
[iquote('0:Res:4.0,92.3')] ).
cnf(112,plain,
l1_struct_0(skc14),
inference(res,[status(thm),theory(equality)],[4,45]),
[iquote('0:Res:4.0,45.0')] ).
cnf(120,plain,
( ~ v3_group_1(skc14)
| ~ v4_group_1(skc14)
| ~ l1_group_1(skc14)
| ~ m2_fraenkel(u,u1_struct_0(skc14),u1_struct_0(skc14),k4_autgroup(skc14))
| v3_struct_0(skc14)
| m2_fraenkel(u,u1_struct_0(skc14),u1_struct_0(skc14),k1_autgroup(skc14)) ),
inference(res,[status(thm),theory(equality)],[1,101]),
[iquote('0:Res:1.0,101.0')] ).
cnf(128,plain,
( ~ l1_struct_0(skc14)
| ~ v1_xboole_0(u1_struct_0(skc14)) ),
inference(res,[status(thm),theory(equality)],[68,32]),
[iquote('0:Res:68.2,32.0')] ).
cnf(134,plain,
~ v1_xboole_0(u1_struct_0(skc14)),
inference(mrr,[status(thm)],[128,112]),
[iquote('0:MRR:128.0,112.0')] ).
cnf(137,plain,
m1_fraenkel(k1_autgroup(skc14),u1_struct_0(skc14),u1_struct_0(skc14)),
inference(mrr,[status(thm)],[105,1,2,3,32]),
[iquote('0:MRR:105.0,105.1,105.2,105.3,1.0,2.0,3.0,32.0')] ).
cnf(138,plain,
m1_fraenkel(k4_autgroup(skc14),u1_struct_0(skc14),u1_struct_0(skc14)),
inference(mrr,[status(thm)],[106,1,2,3,32]),
[iquote('0:MRR:106.0,106.1,106.2,106.3,1.0,2.0,3.0,32.0')] ).
cnf(139,plain,
( ~ m2_fraenkel(u,u1_struct_0(skc14),u1_struct_0(skc14),k4_autgroup(skc14))
| m2_fraenkel(u,u1_struct_0(skc14),u1_struct_0(skc14),k1_autgroup(skc14)) ),
inference(mrr,[status(thm)],[120,2,3,4,32]),
[iquote('0:MRR:120.0,120.1,120.2,120.4,2.0,3.0,4.0,32.0')] ).
cnf(165,plain,
~ v1_xboole_0(k1_autgroup(skc14)),
inference(res,[status(thm),theory(equality)],[137,61]),
[iquote('0:Res:137.0,61.1')] ).
cnf(1279,plain,
( ~ m2_fraenkel(u,u1_struct_0(skc14),u1_struct_0(skc14),k4_autgroup(skc14))
| ~ m1_fraenkel(k1_autgroup(skc14),u1_struct_0(skc14),u1_struct_0(skc14))
| v1_xboole_0(u1_struct_0(skc14))
| m1_subset_1(u,k1_autgroup(skc14)) ),
inference(res,[status(thm),theory(equality)],[139,85]),
[iquote('0:Res:139.1,85.1')] ).
cnf(1282,plain,
( ~ m2_fraenkel(u,u1_struct_0(skc14),u1_struct_0(skc14),k4_autgroup(skc14))
| m1_subset_1(u,k1_autgroup(skc14)) ),
inference(mrr,[status(thm)],[1279,137,134]),
[iquote('0:MRR:1279.1,1279.2,137.0,134.0')] ).
cnf(1392,plain,
( ~ m1_subset_1(u,k4_autgroup(skc14))
| ~ m1_fraenkel(k4_autgroup(skc14),u1_struct_0(skc14),u1_struct_0(skc14))
| v1_xboole_0(u1_struct_0(skc14))
| m1_subset_1(u,k1_autgroup(skc14)) ),
inference(res,[status(thm),theory(equality)],[86,1282]),
[iquote('0:Res:86.3,1282.0')] ).
cnf(1393,plain,
( ~ m1_subset_1(u,k4_autgroup(skc14))
| m1_subset_1(u,k1_autgroup(skc14)) ),
inference(mrr,[status(thm)],[1392,138,134]),
[iquote('0:MRR:1392.1,1392.2,138.0,134.0')] ).
cnf(1397,plain,
( ~ m1_subset_1(u,k4_autgroup(skc14))
| v1_xboole_0(k1_autgroup(skc14))
| r2_hidden(u,k1_autgroup(skc14)) ),
inference(res,[status(thm),theory(equality)],[1393,72]),
[iquote('0:Res:1393.1,72.0')] ).
cnf(1401,plain,
( ~ m1_subset_1(u,k4_autgroup(skc14))
| r2_hidden(u,k1_autgroup(skc14)) ),
inference(mrr,[status(thm)],[1397,165]),
[iquote('0:MRR:1397.1,165.0')] ).
cnf(1408,plain,
( ~ r2_hidden(u,k4_autgroup(skc14))
| r2_hidden(u,k1_autgroup(skc14)) ),
inference(res,[status(thm),theory(equality)],[57,1401]),
[iquote('0:Res:57.1,1401.0')] ).
cnf(1424,plain,
( ~ r2_hidden(skf9(k1_autgroup(skc14),u),k4_autgroup(skc14))
| r1_tarski(v,k1_autgroup(skc14)) ),
inference(res,[status(thm),theory(equality)],[1408,67]),
[iquote('0:Res:1408.1,67.0')] ).
cnf(1581,plain,
( r1_tarski(k4_autgroup(skc14),k1_autgroup(skc14))
| r1_tarski(u,k1_autgroup(skc14)) ),
inference(res,[status(thm),theory(equality)],[60,1424]),
[iquote('0:Res:60.1,1424.0')] ).
cnf(1583,plain,
r1_tarski(k4_autgroup(skc14),k1_autgroup(skc14)),
inference(con,[status(thm)],[1581]),
[iquote('0:Con:1581.1')] ).
cnf(1584,plain,
$false,
inference(mrr,[status(thm)],[1583,46]),
[iquote('0:MRR:1583.0,46.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP623+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 : Tue Jun 14 00:40:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.59
% 0.43/0.59 SPASS V 3.9
% 0.43/0.59 SPASS beiseite: Proof found.
% 0.43/0.59 % SZS status Theorem
% 0.43/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.59 SPASS derived 1215 clauses, backtracked 0 clauses, performed 3 splits and kept 671 clauses.
% 0.43/0.59 SPASS allocated 98909 KBytes.
% 0.43/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.43/0.59 0:00:00.04 for the input.
% 0.43/0.59 0:00:00.04 for the FLOTTER CNF translation.
% 0.43/0.59 0:00:00.02 for inferences.
% 0.43/0.59 0:00:00.00 for the backtracking.
% 0.43/0.59 0:00:00.11 for the reduction.
% 0.43/0.59
% 0.43/0.59
% 0.43/0.59 Here is a proof with depth 7, length 39 :
% 0.43/0.59 % SZS output start Refutation
% See solution above
% 0.43/0.59 Formulae used in the proof : t14_autgroup dt_l1_group_1 t1_subset d3_tarski dt_m1_fraenkel fc1_struct_0 t2_subset redefinition_m2_fraenkel dt_k4_autgroup dt_k1_autgroup t13_autgroup
% 0.43/0.59
%------------------------------------------------------------------------------