%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP628+2 : 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 : n031.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 04:26:35 PM UTC 2026
% Result : Theorem 7.81s 5.62s
% Output : CNFRefutation 7.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 22 unt; 0 def)
% Number of atoms : 374 ( 41 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 485 ( 174 ~; 176 |; 89 &)
% ( 2 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k5_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_group_1(k5_autgroup(X1))
& v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
& m1_group_2(k5_autgroup(X1),k3_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_autgroup) ).
fof(t22_autgroup,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k5_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k5_autgroup(X1),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_autgroup) ).
fof(dt_k3_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( ~ v3_struct_0(k3_autgroup(X1))
& v1_group_1(k3_autgroup(X1))
& v3_group_1(k3_autgroup(X1))
& v4_group_1(k3_autgroup(X1))
& l1_group_1(k3_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_autgroup) ).
fof(d5_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& v1_group_3(X2,k3_autgroup(X1))
& m1_group_2(X2,k3_autgroup(X1)) )
=> ( X2 = k5_autgroup(X1)
<=> u1_struct_0(X2) = k4_autgroup(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_autgroup) ).
fof(t51_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+246.ax',t51_group_2) ).
fof(t57_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_group_2(X3,X1)
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X3))
=> ( X4 = X2
=> k3_group_1(X3,X4) = k3_group_1(X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+246.ax',t57_group_2) ).
fof(t11_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k3_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k3_autgroup(X1),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_autgroup) ).
fof(t13_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_autgroup) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_group_1(k5_autgroup(X1))
& v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
& m1_group_2(k5_autgroup(X1),k3_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k5_autgroup]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k5_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k5_autgroup(X1),X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t22_autgroup])]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( ~ v3_struct_0(k3_autgroup(X1))
& v1_group_1(k3_autgroup(X1))
& v3_group_1(k3_autgroup(X1))
& v4_group_1(k3_autgroup(X1))
& l1_group_1(k3_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_autgroup]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& v1_group_3(X2,k3_autgroup(X1))
& m1_group_2(X2,k3_autgroup(X1)) )
=> ( X2 = k5_autgroup(X1)
<=> u1_struct_0(X2) = k4_autgroup(X1) ) ) ),
inference(fof_simplification,[status(thm)],[d5_autgroup]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[t51_group_2]) ).
fof(c_0_13,plain,
! [X1559] :
( ( v1_group_1(k5_autgroup(X1559))
| v3_struct_0(X1559)
| ~ v1_group_1(X1559)
| ~ v3_group_1(X1559)
| ~ v4_group_1(X1559)
| ~ l1_group_1(X1559) )
& ( v1_group_3(k5_autgroup(X1559),k3_autgroup(X1559))
| v3_struct_0(X1559)
| ~ v1_group_1(X1559)
| ~ v3_group_1(X1559)
| ~ v4_group_1(X1559)
| ~ l1_group_1(X1559) )
& ( m1_group_2(k5_autgroup(X1559),k3_autgroup(X1559))
| v3_struct_0(X1559)
| ~ v1_group_1(X1559)
| ~ v3_group_1(X1559)
| ~ v4_group_1(X1559)
| ~ l1_group_1(X1559) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_14,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)
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0)))
& esk2_0 = esk3_0
& k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_15,plain,
! [X2036] :
( ( ~ v3_struct_0(k3_autgroup(X2036))
| v3_struct_0(X2036)
| ~ v1_group_1(X2036)
| ~ v3_group_1(X2036)
| ~ v4_group_1(X2036)
| ~ l1_group_1(X2036) )
& ( v1_group_1(k3_autgroup(X2036))
| v3_struct_0(X2036)
| ~ v1_group_1(X2036)
| ~ v3_group_1(X2036)
| ~ v4_group_1(X2036)
| ~ l1_group_1(X2036) )
& ( v3_group_1(k3_autgroup(X2036))
| v3_struct_0(X2036)
| ~ v1_group_1(X2036)
| ~ v3_group_1(X2036)
| ~ v4_group_1(X2036)
| ~ l1_group_1(X2036) )
& ( v4_group_1(k3_autgroup(X2036))
| v3_struct_0(X2036)
| ~ v1_group_1(X2036)
| ~ v3_group_1(X2036)
| ~ v4_group_1(X2036)
| ~ l1_group_1(X2036) )
& ( l1_group_1(k3_autgroup(X2036))
| v3_struct_0(X2036)
| ~ v1_group_1(X2036)
| ~ v3_group_1(X2036)
| ~ v4_group_1(X2036)
| ~ l1_group_1(X2036) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_16,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_group_2(X3,X1)
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X3))
=> ( X4 = X2
=> k3_group_1(X3,X4) = k3_group_1(X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t57_group_2]) ).
fof(c_0_17,plain,
! [X1560,X1561] :
( ( X1561 != k5_autgroup(X1560)
| u1_struct_0(X1561) = k4_autgroup(X1560)
| ~ v1_group_1(X1561)
| ~ v1_group_3(X1561,k3_autgroup(X1560))
| ~ m1_group_2(X1561,k3_autgroup(X1560))
| v3_struct_0(X1560)
| ~ v1_group_1(X1560)
| ~ v3_group_1(X1560)
| ~ v4_group_1(X1560)
| ~ l1_group_1(X1560) )
& ( u1_struct_0(X1561) != k4_autgroup(X1560)
| X1561 = k5_autgroup(X1560)
| ~ v1_group_1(X1561)
| ~ v1_group_3(X1561,k3_autgroup(X1560))
| ~ m1_group_2(X1561,k3_autgroup(X1560))
| v3_struct_0(X1560)
| ~ v1_group_1(X1560)
| ~ v3_group_1(X1560)
| ~ v4_group_1(X1560)
| ~ l1_group_1(X1560) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_18,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k3_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k3_autgroup(X1),X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t11_autgroup]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[t13_autgroup]) ).
fof(c_0_20,plain,
! [X1902,X1903,X1904] :
( v3_struct_0(X1902)
| ~ v3_group_1(X1902)
| ~ l1_group_1(X1902)
| ~ m1_group_2(X1903,X1902)
| ~ m1_subset_1(X1904,u1_struct_0(X1903))
| m1_subset_1(X1904,u1_struct_0(X1902)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_21,plain,
( m1_group_2(k5_autgroup(X1),k3_autgroup(X1))
| v3_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_13]) ).
cnf(c_0_22,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,plain,
( v3_group_1(k3_autgroup(X1))
| v3_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_15]) ).
cnf(c_0_28,plain,
( l1_group_1(k3_autgroup(X1))
| v3_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_15]) ).
cnf(c_0_29,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k3_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_30,plain,
! [X1529,X1530,X1531,X1532] :
( v3_struct_0(X1529)
| ~ v3_group_1(X1529)
| ~ v4_group_1(X1529)
| ~ l1_group_1(X1529)
| ~ m1_subset_1(X1530,u1_struct_0(X1529))
| ~ m1_group_2(X1531,X1529)
| ~ m1_subset_1(X1532,u1_struct_0(X1531))
| X1532 != X1530
| k3_group_1(X1531,X1532) = k3_group_1(X1529,X1530) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_31,plain,
( u1_struct_0(X1) = k4_autgroup(X2)
| v3_struct_0(X2)
| X1 != k5_autgroup(X2)
| ~ v1_group_1(X1)
| ~ v1_group_3(X1,k3_autgroup(X2))
| ~ m1_group_2(X1,k3_autgroup(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,plain,
( v1_group_1(k5_autgroup(X1))
| v3_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_13]) ).
cnf(c_0_33,plain,
( v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
| v3_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_13]) ).
fof(c_0_34,plain,
! [X2043,X2044,X2045] :
( v3_struct_0(X2043)
| ~ v1_group_1(X2043)
| ~ v3_group_1(X2043)
| ~ v4_group_1(X2043)
| ~ l1_group_1(X2043)
| ~ m2_fraenkel(X2044,u1_struct_0(X2043),u1_struct_0(X2043),k1_autgroup(X2043))
| ~ m1_subset_1(X2045,u1_struct_0(k3_autgroup(X2043)))
| X2044 != X2045
| k2_funct_1(X2044) = k3_group_1(k3_autgroup(X2043),X2045) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_35,plain,
! [X1650,X1651] :
( v3_struct_0(X1650)
| ~ v1_group_1(X1650)
| ~ v3_group_1(X1650)
| ~ v4_group_1(X1650)
| ~ l1_group_1(X1650)
| ~ m2_fraenkel(X1651,u1_struct_0(X1650),u1_struct_0(X1650),k4_autgroup(X1650))
| m2_fraenkel(X1651,u1_struct_0(X1650),u1_struct_0(X1650),k1_autgroup(X1650)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_36,negated_conjecture,
m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_37,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38,plain,
( v3_struct_0(X1)
| m1_subset_1(X3,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_subset_1(X3,u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_39,negated_conjecture,
m1_group_2(k5_autgroup(esk1_0),k3_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_40,negated_conjecture,
v3_group_1(k3_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_41,negated_conjecture,
l1_group_1(k3_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_42,negated_conjecture,
~ v3_struct_0(k3_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_43,plain,
( v3_struct_0(X1)
| k3_group_1(X3,X4) = k3_group_1(X1,X2)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_group_2(X3,X1)
| ~ m1_subset_1(X4,u1_struct_0(X3))
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
( v4_group_1(k3_autgroup(X1))
| v3_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_15]) ).
cnf(c_0_45,plain,
( u1_struct_0(k5_autgroup(X1)) = k4_autgroup(X1)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ l1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_32]),c_0_21]),c_0_33]) ).
cnf(c_0_46,plain,
( v3_struct_0(X1)
| k2_funct_1(X2) = k3_group_1(k3_autgroup(X1),X3)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m1_subset_1(X3,u1_struct_0(k3_autgroup(X1)))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( v3_struct_0(X1)
| m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(k3_autgroup(esk1_0)))
| ~ m1_subset_1(X1,u1_struct_0(k5_autgroup(esk1_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_50,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_51,plain,
( k3_group_1(X1,X2) = k3_group_1(X3,X2)
| v3_struct_0(X1)
| ~ m1_group_2(X3,X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_38]) ).
cnf(c_0_52,negated_conjecture,
v4_group_1(k3_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_53,negated_conjecture,
u1_struct_0(k5_autgroup(esk1_0)) = k4_autgroup(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_54,plain,
( k3_group_1(k3_autgroup(X1),X2) = k2_funct_1(X2)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X1))) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_55,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_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_47,c_0_48]),c_0_23]),c_0_24]),c_0_25]),c_0_22])]),c_0_26]) ).
cnf(c_0_56,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k3_autgroup(esk1_0))),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_58,negated_conjecture,
( k3_group_1(k5_autgroup(esk1_0),X1) = k3_group_1(k3_autgroup(esk1_0),X1)
| ~ m1_subset_1(X1,k4_autgroup(esk1_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_51,c_0_39]),c_0_52]),c_0_40]),c_0_41]),c_0_53])]),c_0_42]) ).
cnf(c_0_59,negated_conjecture,
m1_subset_1(esk3_0,k4_autgroup(esk1_0)),
inference(rw,[status(thm)],[c_0_50,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
k3_group_1(k3_autgroup(esk1_0),esk3_0) = k2_funct_1(esk3_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_23]),c_0_24]),c_0_25]),c_0_22]),c_0_56])]),c_0_26]) ).
cnf(c_0_61,negated_conjecture,
k3_group_1(k5_autgroup(esk1_0),esk3_0) != k2_funct_1(esk3_0),
inference(rw,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP628+2 : 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
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:51:09 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 7.81/5.62 % Version : CSE_E---1.7
% 7.81/5.62 % Problem : theBenchmark.p
% 7.81/5.62 % SZS status Theorem for theBenchmark.p
% 7.81/5.62 % SZS output start CNFRefutation
% See solution above
% 7.81/5.64 % Total time : 4.401s
%------------------------------------------------------------------------------