%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP631+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : 300s
% DateTime : Tue May 5 04:26:36 PM UTC 2026
% Result : Theorem 19.24s 11.83s
% Output : CNFRefutation 19.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 112 ( 18 unt; 0 def)
% Number of atoms : 445 ( 53 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 539 ( 206 ~; 205 |; 96 &)
% ( 1 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-6 aty)
% Number of variables : 209 ( 9 sgn 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_funct_1(u1_group_1(X1))
& v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_group_1) ).
fof(free_g1_group_1,axiom,
! [X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ! [X3,X4] :
( g1_group_1(X1,X2) = g1_group_1(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_group_1) ).
fof(dt_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m2_relset_1(X4,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(dt_k6_autgroup,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m2_fraenkel(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_autgroup) ).
fof(dt_k4_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(dt_k6_partfun1,axiom,
! [X1] :
( v1_partfun1(k6_partfun1(X1),X1,X1)
& m2_relset_1(k6_partfun1(X1),X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(abstractness_v1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_group_1(X1)
=> X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
fof(t29_autgroup,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_autgroup) ).
fof(t24_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_autgroup) ).
fof(fc2_funct_1,axiom,
! [X1] :
( v1_relat_1(k6_relat_1(X1))
& v1_funct_1(k6_relat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : k6_partfun1(X1) = k6_relat_1(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(t23_funct_2,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> ( k7_relset_1(X1,X1,X1,X2,k6_partfun1(X1),X3) = X3
& k7_relset_1(X1,X2,X2,X2,X3,k6_partfun1(X2)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
fof(redefinition_k7_relset_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_relset_1(X5,X1,X2)
& m1_relset_1(X6,X3,X4) )
=> k7_relset_1(X1,X2,X3,X4,X5,X6) = k5_relat_1(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
fof(dt_g1_group_1,axiom,
! [X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ( v1_group_1(g1_group_1(X1,X2))
& l1_group_1(g1_group_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_group_1) ).
fof(fc1_group_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ( ~ v3_struct_0(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_1) ).
fof(redefinition_k7_funct_2,axiom,
! [X1,X2,X3,X4,X5] :
( ( ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2)
& v1_funct_1(X5)
& v1_funct_2(X5,X2,X3)
& m1_relset_1(X5,X2,X3) )
=> k7_funct_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
fof(cc1_funct_2,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> ( ( v1_funct_1(X3)
& v1_partfun1(X3,X1,X2) )
=> ( v1_funct_1(X3)
& v1_funct_2(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(c_0_20,plain,
! [X295,X296,X297] :
( ( ~ m2_relset_1(X297,X295,X296)
| m1_relset_1(X297,X295,X296) )
& ( ~ m1_relset_1(X297,X295,X296)
| m2_relset_1(X297,X295,X296) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_21,plain,
! [X227] :
( ( v1_funct_1(u1_group_1(X227))
| ~ l1_group_1(X227) )
& ( v1_funct_2(u1_group_1(X227),k2_zfmisc_1(u1_struct_0(X227),u1_struct_0(X227)),u1_struct_0(X227))
| ~ l1_group_1(X227) )
& ( m2_relset_1(u1_group_1(X227),k2_zfmisc_1(u1_struct_0(X227),u1_struct_0(X227)),u1_struct_0(X227))
| ~ l1_group_1(X227) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_group_1])])]) ).
fof(c_0_22,plain,
! [X252,X253,X254,X255] :
( ( X252 = X254
| g1_group_1(X252,X253) != g1_group_1(X254,X255)
| ~ v1_funct_1(X253)
| ~ v1_funct_2(X253,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X253,k2_zfmisc_1(X252,X252),X252) )
& ( X253 = X255
| g1_group_1(X252,X253) != g1_group_1(X254,X255)
| ~ v1_funct_1(X253)
| ~ v1_funct_2(X253,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X253,k2_zfmisc_1(X252,X252),X252) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_group_1])])])]) ).
cnf(c_0_23,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m2_relset_1(X4,X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_fraenkel]) ).
fof(c_0_26,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m2_fraenkel(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_autgroup]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_autgroup]) ).
fof(c_0_28,plain,
! [X203] :
( v1_partfun1(k6_partfun1(X203),X203,X203)
& m2_relset_1(k6_partfun1(X203),X203,X203) ),
inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).
cnf(c_0_29,plain,
( X1 = X2
| g1_group_1(X1,X3) != g1_group_1(X2,X4)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( v1_funct_1(u1_group_1(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
( m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_33,plain,
! [X166] :
( ~ l1_group_1(X166)
| ~ v1_group_1(X166)
| X166 = g1_group_1(u1_struct_0(X166),u1_group_1(X166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_group_1])]) ).
fof(c_0_34,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t29_autgroup])]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[t24_autgroup]) ).
fof(c_0_36,plain,
! [X250] :
( v1_relat_1(k6_relat_1(X250))
& v1_funct_1(k6_relat_1(X250)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_37,plain,
! [X279] : k6_partfun1(X279) = k6_relat_1(X279),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
fof(c_0_38,plain,
! [X220,X221,X222,X223] :
( ( v1_funct_1(X223)
| ~ m2_fraenkel(X223,X220,X221,X222)
| v1_xboole_0(X221)
| ~ m1_fraenkel(X222,X220,X221) )
& ( v1_funct_2(X223,X220,X221)
| ~ m2_fraenkel(X223,X220,X221,X222)
| v1_xboole_0(X221)
| ~ m1_fraenkel(X222,X220,X221) )
& ( m2_relset_1(X223,X220,X221)
| ~ m2_fraenkel(X223,X220,X221,X222)
| v1_xboole_0(X221)
| ~ m1_fraenkel(X222,X220,X221) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
fof(c_0_39,plain,
! [X201,X202] :
( v3_struct_0(X201)
| ~ v1_group_1(X201)
| ~ v3_group_1(X201)
| ~ v4_group_1(X201)
| ~ l1_group_1(X201)
| ~ m1_subset_1(X202,u1_struct_0(X201))
| m2_fraenkel(k6_autgroup(X201,X202),u1_struct_0(X201),u1_struct_0(X201),k4_autgroup(X201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_40,plain,
! [X198] :
( v3_struct_0(X198)
| ~ v1_group_1(X198)
| ~ v3_group_1(X198)
| ~ v4_group_1(X198)
| ~ l1_group_1(X198)
| m1_fraenkel(k4_autgroup(X198),u1_struct_0(X198),u1_struct_0(X198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
fof(c_0_41,plain,
! [X301,X302,X303] :
( ( k7_relset_1(X301,X301,X301,X302,k6_partfun1(X301),X303) = X303
| ~ m2_relset_1(X303,X301,X302) )
& ( k7_relset_1(X301,X302,X302,X302,X303,k6_partfun1(X302)) = X303
| ~ m2_relset_1(X303,X301,X302) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_2])])]) ).
fof(c_0_42,plain,
! [X285,X286,X287,X288,X289,X290] :
( ~ m1_relset_1(X289,X285,X286)
| ~ m1_relset_1(X290,X287,X288)
| k7_relset_1(X285,X286,X287,X288,X289,X290) = k5_relat_1(X289,X290) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_relset_1])]) ).
cnf(c_0_43,plain,
m2_relset_1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_44,plain,
( u1_struct_0(X1) = X2
| g1_group_1(u1_struct_0(X1),u1_group_1(X1)) != g1_group_1(X2,X3)
| ~ l1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_45,plain,
( X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1))
| ~ l1_group_1(X1)
| ~ v1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_46,plain,
! [X195,X196] :
( ( v1_group_1(g1_group_1(X195,X196))
| ~ v1_funct_1(X196)
| ~ v1_funct_2(X196,k2_zfmisc_1(X195,X195),X195)
| ~ m1_relset_1(X196,k2_zfmisc_1(X195,X195),X195) )
& ( l1_group_1(g1_group_1(X195,X196))
| ~ v1_funct_1(X196)
| ~ v1_funct_2(X196,k2_zfmisc_1(X195,X195),X195)
| ~ m1_relset_1(X196,k2_zfmisc_1(X195,X195),X195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g1_group_1])])]) ).
fof(c_0_47,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) )
=> ( ~ v3_struct_0(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc1_group_1]) ).
fof(c_0_48,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v1_group_1(esk1_0)
& v3_group_1(esk1_0)
& v4_group_1(esk1_0)
& l1_group_1(esk1_0)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
fof(c_0_49,plain,
! [X304] :
( v3_struct_0(X304)
| ~ v1_group_1(X304)
| ~ v3_group_1(X304)
| ~ v4_group_1(X304)
| ~ l1_group_1(X304)
| k6_autgroup(X304,k2_group_1(X304)) = k6_partfun1(u1_struct_0(X304)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
fof(c_0_50,plain,
! [X1,X2,X3,X4,X5] :
( ( ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2)
& v1_funct_1(X5)
& v1_funct_2(X5,X2,X3)
& m1_relset_1(X5,X2,X3) )
=> k7_funct_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(fof_simplification,[status(thm)],[redefinition_k7_funct_2]) ).
fof(c_0_51,plain,
! [X172,X173,X174] :
( ( v1_funct_1(X174)
| ~ v1_funct_1(X174)
| ~ v1_partfun1(X174,X172,X173)
| ~ m1_relset_1(X174,X172,X173) )
& ( v1_funct_2(X174,X172,X173)
| ~ v1_funct_1(X174)
| ~ v1_partfun1(X174,X172,X173)
| ~ m1_relset_1(X174,X172,X173) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_2])])]) ).
cnf(c_0_52,plain,
v1_funct_1(k6_relat_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_53,plain,
k6_partfun1(X1) = k6_relat_1(X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_54,plain,
( v1_funct_1(X1)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55,plain,
( v3_struct_0(X1)
| m2_fraenkel(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_56,plain,
( v3_struct_0(X1)
| m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_57,plain,
( k7_relset_1(X1,X2,X2,X2,X3,k6_partfun1(X2)) = X3
| ~ m2_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_58,plain,
( k7_relset_1(X2,X3,X5,X6,X1,X4) = k5_relat_1(X1,X4)
| ~ m1_relset_1(X1,X2,X3)
| ~ m1_relset_1(X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_59,plain,
m1_relset_1(k6_partfun1(X1),X1,X1),
inference(spm,[status(thm)],[c_0_23,c_0_43]) ).
cnf(c_0_60,plain,
( u1_struct_0(X1) = X2
| X1 != g1_group_1(X2,X3)
| ~ l1_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_61,plain,
( v1_group_1(g1_group_1(X1,X2))
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_62,plain,
( l1_group_1(g1_group_1(X1,X2))
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_63,plain,
! [X247,X248] :
( ( ~ v3_struct_0(g1_group_1(X247,X248))
| v1_xboole_0(X247)
| ~ v1_funct_1(X248)
| ~ v1_funct_2(X248,k2_zfmisc_1(X247,X247),X247)
| ~ m1_relset_1(X248,k2_zfmisc_1(X247,X247),X247) )
& ( v1_group_1(g1_group_1(X247,X248))
| v1_xboole_0(X247)
| ~ v1_funct_1(X248)
| ~ v1_funct_2(X248,k2_zfmisc_1(X247,X247),X247)
| ~ m1_relset_1(X248,k2_zfmisc_1(X247,X247),X247) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
cnf(c_0_64,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_65,plain,
( v3_struct_0(X1)
| k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_66,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_68,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_69,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_70,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_71,plain,
! [X280,X281,X282,X283,X284] :
( v1_xboole_0(X281)
| ~ v1_funct_1(X283)
| ~ v1_funct_2(X283,X280,X281)
| ~ m1_relset_1(X283,X280,X281)
| ~ v1_funct_1(X284)
| ~ v1_funct_2(X284,X281,X282)
| ~ m1_relset_1(X284,X281,X282)
| k7_funct_2(X280,X281,X282,X283,X284) = k5_relat_1(X283,X284) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])]) ).
cnf(c_0_72,plain,
( v1_funct_2(X1,X2,X3)
| ~ v1_funct_1(X1)
| ~ v1_partfun1(X1,X2,X3)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_73,plain,
v1_partfun1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_74,plain,
v1_funct_1(k6_partfun1(X1)),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_75,plain,
( v1_xboole_0(u1_struct_0(X1))
| v1_funct_1(k6_autgroup(X1,X2))
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_76,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_77,plain,
( k5_relat_1(X1,k6_partfun1(X2)) = X1
| ~ m2_relset_1(X1,X3,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]),c_0_23]) ).
cnf(c_0_78,plain,
( m2_relset_1(X1,X2,X3)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_79,plain,
( k7_relset_1(X1,X1,X1,X2,k6_partfun1(X1),X3) = X3
| ~ m2_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_80,plain,
( v1_funct_2(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_81,plain,
( u1_struct_0(g1_group_1(X1,X2)) = X1
| ~ l1_group_1(g1_group_1(X1,X2))
| ~ v1_group_1(g1_group_1(X1,X2)) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_82,plain,
( v1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ l1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_83,plain,
( l1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ l1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_84,plain,
( v1_xboole_0(X1)
| ~ v3_struct_0(g1_group_1(X1,X2))
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_85,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_partfun1(u1_struct_0(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]),c_0_68]),c_0_69])]),c_0_70]) ).
cnf(c_0_86,plain,
( v1_xboole_0(X1)
| k7_funct_2(X3,X1,X5,X2,X4) = k5_relat_1(X2,X4)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X3,X1)
| ~ m1_relset_1(X2,X3,X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X5)
| ~ m1_relset_1(X4,X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_87,plain,
v1_funct_2(k6_partfun1(X1),X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]),c_0_59])]) ).
cnf(c_0_88,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v1_funct_1(k6_autgroup(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_66]),c_0_67]),c_0_68]),c_0_69])]),c_0_70]) ).
cnf(c_0_89,plain,
( k5_relat_1(X1,k6_partfun1(X2)) = X1
| ~ m1_relset_1(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_90,plain,
( k5_relat_1(k6_partfun1(X1),X2) = X2
| ~ m2_relset_1(X2,X1,X3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_58]),c_0_59])]),c_0_23]) ).
cnf(c_0_91,plain,
( v1_funct_2(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_55]),c_0_56]) ).
cnf(c_0_92,plain,
( u1_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) = u1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_93,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_94,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_partfun1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| ~ v1_funct_2(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ m1_relset_1(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_59]),c_0_74])]),c_0_88]),c_0_89]) ).
cnf(c_0_95,plain,
( k5_relat_1(k6_partfun1(X1),X2) = X2
| ~ m1_relset_1(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_90,c_0_78]) ).
cnf(c_0_96,plain,
( v1_funct_2(k6_autgroup(g1_group_1(u1_struct_0(X1),u1_group_1(X1)),X2),u1_struct_0(X1),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ v3_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_82]),c_0_83]),c_0_93]) ).
cnf(c_0_97,plain,
( m2_relset_1(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_98,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_99,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| ~ v1_funct_2(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ m1_relset_1(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_86]),c_0_87]),c_0_59]),c_0_74])]),c_0_88]),c_0_95]) ).
cnf(c_0_100,plain,
( v1_funct_2(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_45]) ).
cnf(c_0_101,plain,
( m2_relset_1(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_55]),c_0_56]) ).
cnf(c_0_102,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_45]) ).
fof(c_0_103,plain,
! [X216] :
( ~ l1_group_1(X216)
| l1_struct_0(X216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
fof(c_0_104,plain,
! [X249] :
( v3_struct_0(X249)
| ~ l1_struct_0(X249)
| ~ v1_xboole_0(u1_struct_0(X249)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])]) ).
cnf(c_0_105,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| ~ m1_relset_1(k6_autgroup(esk1_0,esk2_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_76]),c_0_66]),c_0_67]),c_0_68]),c_0_69])]) ).
cnf(c_0_106,plain,
( m1_relset_1(k6_autgroup(X1,X2),u1_struct_0(X1),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_101]),c_0_102]) ).
cnf(c_0_107,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_109,negated_conjecture,
v1_xboole_0(u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_76]),c_0_66]),c_0_67]),c_0_68]),c_0_69])]) ).
cnf(c_0_110,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_107,c_0_66]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110])]),c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP631+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 18:50:21 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 19.24/11.83 % Version : CSE_E---1.7
% 19.24/11.83 % Problem : theBenchmark.p
% 19.24/11.83 % SZS status Theorem for theBenchmark.p
% 19.24/11.83 % SZS output start CNFRefutation
% See solution above
% 19.34/11.91 % Total time : 8.388s
%------------------------------------------------------------------------------