%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP622+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 : n021.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 04:26:33 PM UTC 2026
% Result : Theorem 7.09s 4.61s
% Output : CNFRefutation 7.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 9 unt; 0 def)
% Number of atoms : 293 ( 7 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 353 ( 137 ~; 137 |; 52 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 140 ( 1 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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_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(redefinition_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
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_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(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(t12_autgroup,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_autgroup) ).
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(d3_tarski,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t12_funct_2,axiom,
! [X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X1,X1)
& m2_relset_1(X2,X1,X1) )
=> r2_hidden(X2,k1_funct_2(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
fof(redefinition_k1_fraenkel,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_fraenkel) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(c_0_14,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_15,plain,
! [X189,X190] :
( ( ~ v3_struct_0(g1_group_1(X189,X190))
| v1_xboole_0(X189)
| ~ v1_funct_1(X190)
| ~ v1_funct_2(X190,k2_zfmisc_1(X189,X189),X189)
| ~ m1_relset_1(X190,k2_zfmisc_1(X189,X189),X189) )
& ( v1_group_1(g1_group_1(X189,X190))
| v1_xboole_0(X189)
| ~ v1_funct_1(X190)
| ~ v1_funct_2(X190,k2_zfmisc_1(X189,X189),X189)
| ~ m1_relset_1(X190,k2_zfmisc_1(X189,X189),X189) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_16,plain,
! [X167] :
( ( v1_funct_1(u1_group_1(X167))
| ~ l1_group_1(X167) )
& ( v1_funct_2(u1_group_1(X167),k2_zfmisc_1(u1_struct_0(X167),u1_struct_0(X167)),u1_struct_0(X167))
| ~ l1_group_1(X167) )
& ( m2_relset_1(u1_group_1(X167),k2_zfmisc_1(u1_struct_0(X167),u1_struct_0(X167)),u1_struct_0(X167))
| ~ l1_group_1(X167) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_group_1])])]) ).
fof(c_0_17,plain,
! [X222,X223,X224] :
( ( ~ m2_relset_1(X224,X222,X223)
| m1_relset_1(X224,X222,X223) )
& ( ~ m1_relset_1(X224,X222,X223)
| m2_relset_1(X224,X222,X223) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_18,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_19,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).
cnf(c_0_20,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_15]) ).
cnf(c_0_21,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_16]) ).
cnf(c_0_22,plain,
( v1_funct_1(u1_group_1(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
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_16]) ).
fof(c_0_25,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]) ).
fof(c_0_26,plain,
! [X160,X161,X162,X163] :
( ( v1_funct_1(X163)
| ~ m2_fraenkel(X163,X160,X161,X162)
| v1_xboole_0(X161)
| ~ m1_fraenkel(X162,X160,X161) )
& ( v1_funct_2(X163,X160,X161)
| ~ m2_fraenkel(X163,X160,X161,X162)
| v1_xboole_0(X161)
| ~ m1_fraenkel(X162,X160,X161) )
& ( m2_relset_1(X163,X160,X161)
| ~ m2_fraenkel(X163,X160,X161,X162)
| v1_xboole_0(X161)
| ~ m1_fraenkel(X162,X160,X161) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_27,plain,
! [X218,X219,X220,X221] :
( ( ~ m2_fraenkel(X221,X218,X219,X220)
| m1_subset_1(X221,X220)
| v1_xboole_0(X219)
| ~ m1_fraenkel(X220,X218,X219) )
& ( ~ m1_subset_1(X221,X220)
| m2_fraenkel(X221,X218,X219,X220)
| v1_xboole_0(X219)
| ~ m1_fraenkel(X220,X218,X219) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
fof(c_0_28,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]) ).
cnf(c_0_29,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ 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)
| ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_30,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_31,plain,
! [X125] :
( ~ l1_group_1(X125)
| ~ v1_group_1(X125)
| X125 = g1_group_1(u1_struct_0(X125),u1_group_1(X125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_group_1])]) ).
fof(c_0_32,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t12_autgroup])]) ).
fof(c_0_33,plain,
! [X191] :
( v3_struct_0(X191)
| ~ l1_struct_0(X191)
| ~ v1_xboole_0(u1_struct_0(X191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
fof(c_0_34,plain,
! [X156] :
( ~ l1_group_1(X156)
| l1_struct_0(X156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
fof(c_0_35,plain,
! [X145,X146,X147,X148,X149] :
( ( ~ r1_tarski(X145,X146)
| ~ r2_hidden(X147,X145)
| r2_hidden(X147,X146) )
& ( r2_hidden(esk2_2(X148,X149),X148)
| r1_tarski(X148,X149) )
& ( ~ r2_hidden(esk2_2(X148,X149),X149)
| r1_tarski(X148,X149) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(c_0_36,plain,
! [X226,X227] :
( ~ v1_funct_1(X227)
| ~ v1_funct_2(X227,X226,X226)
| ~ m2_relset_1(X227,X226,X226)
| r2_hidden(X227,k1_funct_2(X226,X226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_funct_2])]) ).
cnf(c_0_37,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_26]) ).
cnf(c_0_38,plain,
( m2_fraenkel(X1,X3,X4,X2)
| v1_xboole_0(X4)
| ~ m1_subset_1(X1,X2)
| ~ m1_fraenkel(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_39,plain,
! [X155] :
( v3_struct_0(X155)
| ~ v1_group_1(X155)
| ~ v3_group_1(X155)
| ~ v4_group_1(X155)
| ~ l1_group_1(X155)
| m1_fraenkel(k4_autgroup(X155),u1_struct_0(X155),u1_struct_0(X155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
cnf(c_0_40,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(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_41,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_31]) ).
cnf(c_0_42,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_26]) ).
cnf(c_0_43,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_26]) ).
fof(c_0_44,plain,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_fraenkel]) ).
fof(c_0_45,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)
& ~ r1_tarski(k4_autgroup(esk1_0),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
cnf(c_0_46,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_47,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,plain,
( r1_tarski(X1,X2)
| ~ r2_hidden(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,plain,
( r2_hidden(X1,k1_funct_2(X2,X2))
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,X2,X2)
| ~ m2_relset_1(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,plain,
( m2_relset_1(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m1_fraenkel(X4,X2,X3)
| ~ m1_subset_1(X1,X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_51,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_39]) ).
cnf(c_0_52,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_40,c_0_41]) ).
cnf(c_0_53,plain,
( v1_xboole_0(X1)
| v1_funct_1(X2)
| ~ m1_fraenkel(X3,X4,X1)
| ~ m1_subset_1(X2,X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_54,plain,
( v1_funct_2(X1,X2,X3)
| v1_xboole_0(X3)
| ~ m1_fraenkel(X4,X2,X3)
| ~ m1_subset_1(X1,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
fof(c_0_55,plain,
! [X228,X229] :
( ~ r2_hidden(X228,X229)
| m1_subset_1(X228,X229) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_56,plain,
! [X216,X217] :
( v1_xboole_0(X217)
| k1_fraenkel(X216,X217) = k1_funct_2(X216,X217) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])]) ).
cnf(c_0_57,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_59,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_60,plain,
( r1_tarski(X1,k1_funct_2(X2,X2))
| ~ m2_relset_1(esk2_2(X1,k1_funct_2(X2,X2)),X2,X2)
| ~ v1_funct_2(esk2_2(X1,k1_funct_2(X2,X2)),X2,X2)
| ~ v1_funct_1(esk2_2(X1,k1_funct_2(X2,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_61,plain,
( m2_relset_1(X1,u1_struct_0(X2),u1_struct_0(X2))
| v1_xboole_0(u1_struct_0(X2))
| ~ m1_subset_1(X1,k4_autgroup(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_62,plain,
( v1_xboole_0(u1_struct_0(X1))
| v1_funct_1(X2)
| ~ m1_subset_1(X2,k4_autgroup(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_53,c_0_51]),c_0_52]) ).
cnf(c_0_63,plain,
( v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))
| v1_xboole_0(u1_struct_0(X2))
| ~ m1_subset_1(X1,k4_autgroup(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_52]) ).
cnf(c_0_64,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
( r2_hidden(esk2_2(X1,X2),X1)
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_66,negated_conjecture,
~ r1_tarski(k4_autgroup(esk1_0),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_67,plain,
( v1_xboole_0(X1)
| k1_fraenkel(X2,X1) = k1_funct_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_69,plain,
( v1_xboole_0(u1_struct_0(X1))
| r1_tarski(X2,k1_funct_2(u1_struct_0(X1),u1_struct_0(X1)))
| ~ m1_subset_1(esk2_2(X2,k1_funct_2(u1_struct_0(X1),u1_struct_0(X1))),k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63]) ).
cnf(c_0_70,plain,
( m1_subset_1(esk2_2(X1,X2),X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
~ r1_tarski(k4_autgroup(esk1_0),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_72,plain,
( v1_xboole_0(u1_struct_0(X1))
| r1_tarski(k4_autgroup(X1),k1_funct_2(u1_struct_0(X1),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_69,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_74,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_75,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_76,negated_conjecture,
$false,
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_71,c_0_72]),c_0_59]),c_0_73]),c_0_74]),c_0_75])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP622+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % 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
% 0.16/0.32 % Computer : n021.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 18:47:25 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 7.09/4.61 % Version : CSE_E---1.7
% 7.09/4.61 % Problem : theBenchmark.p
% 7.09/4.61 % SZS status Theorem for theBenchmark.p
% 7.09/4.61 % SZS output start CNFRefutation
% See solution above
% 7.09/4.63 % Total time : 3.372s
%------------------------------------------------------------------------------