%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:44:25 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 14 unt; 0 def)
% Number of atoms : 339 ( 35 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 433 ( 151 ~; 158 |; 80 &)
% ( 0 <=>; 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 : 75 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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(t57_group_2,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(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/theBenchmark.p',t57_group_2) ).
fof(t51_group_2,axiom,
! [X1] :
( ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(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/theBenchmark.p',t51_group_2) ).
fof(dt_k5_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m1_group_2(k5_autgroup(X1),k3_autgroup(X1))
& v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
& v1_group_1(k5_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_autgroup) ).
fof(dt_k3_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( l1_group_1(k3_autgroup(X1))
& v4_group_1(k3_autgroup(X1))
& v3_group_1(k3_autgroup(X1))
& v1_group_1(k3_autgroup(X1))
& ~ v3_struct_0(k3_autgroup(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_autgroup) ).
fof(t11_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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_7,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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(assume_negation,[status(cth)],[t22_autgroup]) ).
fof(c_0_8,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(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_9,plain,
! [X1] :
( ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(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_10,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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)],[c_0_7]) ).
fof(c_0_11,plain,
! [X129,X130,X131,X132] :
( k3_group_1(X131,X132) = k3_group_1(X129,X130)
| X132 != X130
| ~ m1_subset_1(X132,u1_struct_0(X131))
| ~ m1_group_2(X131,X129)
| ~ m1_subset_1(X130,u1_struct_0(X129))
| ~ l1_group_1(X129)
| ~ v4_group_1(X129)
| ~ v3_group_1(X129)
| v3_struct_0(X129) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,plain,
! [X126,X127,X128] :
( m1_subset_1(X128,u1_struct_0(X126))
| ~ m1_subset_1(X128,u1_struct_0(X127))
| ~ m1_group_2(X127,X126)
| ~ l1_group_1(X126)
| ~ v3_group_1(X126)
| v3_struct_0(X126) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_13,negated_conjecture,
( k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0)
& esk2_0 = esk3_0
& m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0)))
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
cnf(c_0_14,plain,
( X4 != X2
| ~ m1_subset_1(X4,u1_struct_0(X3))
| ~ m1_group_2(X3,X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| k3_group_1(X3,X4) = k3_group_1(X1,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| m1_subset_1(X3,u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m1_group_2(k5_autgroup(X1),k3_autgroup(X1))
& v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
& v1_group_1(k5_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k5_autgroup]) ).
cnf(c_0_19,plain,
( ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X3))
| ~ m1_group_2(X3,X1)
| v3_struct_0(X1)
| k3_group_1(X1,X2) = k3_group_1(X3,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X40] :
( ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| m1_group_2(k5_autgroup(X40),k3_autgroup(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| v1_group_3(k5_autgroup(X40),k3_autgroup(X40)) )
& ( ~ l1_group_1(X40)
| ~ v4_group_1(X40)
| ~ v3_group_1(X40)
| ~ v1_group_1(X40)
| v3_struct_0(X40)
| v1_group_1(k5_autgroup(X40)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_22,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( l1_group_1(k3_autgroup(X1))
& v4_group_1(k3_autgroup(X1))
& v3_group_1(k3_autgroup(X1))
& v1_group_1(k3_autgroup(X1))
& ~ v3_struct_0(k3_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_autgroup]) ).
cnf(c_0_23,negated_conjecture,
( ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(k5_autgroup(esk1_0),X1)
| v3_struct_0(X1)
| k3_group_1(X1,esk2_0) = k3_group_1(k5_autgroup(esk1_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| v3_struct_0(X1)
| m1_group_2(k5_autgroup(X1),k3_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_30,plain,
! [X36] :
( ( ~ l1_group_1(X36)
| ~ v4_group_1(X36)
| ~ v3_group_1(X36)
| ~ v1_group_1(X36)
| v3_struct_0(X36)
| l1_group_1(k3_autgroup(X36)) )
& ( ~ l1_group_1(X36)
| ~ v4_group_1(X36)
| ~ v3_group_1(X36)
| ~ v1_group_1(X36)
| v3_struct_0(X36)
| v4_group_1(k3_autgroup(X36)) )
& ( ~ l1_group_1(X36)
| ~ v4_group_1(X36)
| ~ v3_group_1(X36)
| ~ v1_group_1(X36)
| v3_struct_0(X36)
| v3_group_1(k3_autgroup(X36)) )
& ( ~ l1_group_1(X36)
| ~ v4_group_1(X36)
| ~ v3_group_1(X36)
| ~ v1_group_1(X36)
| v3_struct_0(X36)
| v1_group_1(k3_autgroup(X36)) )
& ( ~ l1_group_1(X36)
| ~ v4_group_1(X36)
| ~ v3_group_1(X36)
| ~ v1_group_1(X36)
| v3_struct_0(X36)
| ~ v3_struct_0(k3_autgroup(X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_31,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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]) ).
cnf(c_0_32,negated_conjecture,
( ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(k5_autgroup(esk1_0),X1)
| v3_struct_0(X1)
| m1_subset_1(esk2_0,u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
fof(c_0_33,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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]) ).
cnf(c_0_34,negated_conjecture,
( ~ v3_group_1(k3_autgroup(esk1_0))
| ~ v4_group_1(k3_autgroup(esk1_0))
| ~ l1_group_1(k3_autgroup(esk1_0))
| v3_struct_0(k3_autgroup(esk1_0))
| k3_group_1(k5_autgroup(esk1_0),esk2_0) = k3_group_1(k3_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_23,c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_35,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| v3_struct_0(X1)
| l1_group_1(k3_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X112,X113,X114] :
( k2_funct_1(X113) = k3_group_1(k3_autgroup(X112),X114)
| X113 != X114
| ~ m1_subset_1(X114,u1_struct_0(k3_autgroup(X112)))
| ~ m2_fraenkel(X113,u1_struct_0(X112),u1_struct_0(X112),k1_autgroup(X112))
| ~ l1_group_1(X112)
| ~ v4_group_1(X112)
| ~ v3_group_1(X112)
| ~ v1_group_1(X112)
| v3_struct_0(X112) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_37,negated_conjecture,
( ~ v3_group_1(k3_autgroup(esk1_0))
| ~ l1_group_1(k3_autgroup(esk1_0))
| v3_struct_0(k3_autgroup(esk1_0))
| m1_subset_1(esk2_0,u1_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
fof(c_0_38,plain,
! [X115,X116] :
( m2_fraenkel(X116,u1_struct_0(X115),u1_struct_0(X115),k1_autgroup(X115))
| ~ m2_fraenkel(X116,u1_struct_0(X115),u1_struct_0(X115),k4_autgroup(X115))
| ~ l1_group_1(X115)
| ~ v4_group_1(X115)
| ~ v3_group_1(X115)
| ~ v1_group_1(X115)
| v3_struct_0(X115) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ v3_group_1(k3_autgroup(esk1_0))
| ~ v4_group_1(k3_autgroup(esk1_0))
| v3_struct_0(k3_autgroup(esk1_0))
| k3_group_1(k5_autgroup(esk1_0),esk2_0) = k3_group_1(k3_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_34,c_0_35]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_40,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| v3_struct_0(X1)
| v4_group_1(k3_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
( X2 != X3
| ~ m1_subset_1(X3,u1_struct_0(k3_autgroup(X1)))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| k2_funct_1(X2) = k3_group_1(k3_autgroup(X1),X3)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( ~ v3_group_1(k3_autgroup(esk1_0))
| v3_struct_0(k3_autgroup(esk1_0))
| m1_subset_1(esk2_0,u1_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_43,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| v3_struct_0(X1)
| v3_group_1(k3_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
( ~ m2_fraenkel(X2,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)
| m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,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_13]) ).
cnf(c_0_46,negated_conjecture,
k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_47,negated_conjecture,
( ~ v3_group_1(k3_autgroup(esk1_0))
| v3_struct_0(k3_autgroup(esk1_0))
| k3_group_1(k5_autgroup(esk1_0),esk2_0) = k3_group_1(k3_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_39,c_0_40]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_48,plain,
( ~ 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(X2,u1_struct_0(k3_autgroup(X1)))
| v3_struct_0(X1)
| k3_group_1(k3_autgroup(X1),X2) = k2_funct_1(X2) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( v3_struct_0(k3_autgroup(esk1_0))
| m1_subset_1(esk2_0,u1_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_50,negated_conjecture,
m2_fraenkel(esk2_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_44,c_0_45]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_51,negated_conjecture,
k3_group_1(k5_autgroup(esk1_0),esk2_0) != k2_funct_1(esk2_0),
inference(rw,[status(thm)],[c_0_46,c_0_17]) ).
cnf(c_0_52,negated_conjecture,
( v3_struct_0(k3_autgroup(esk1_0))
| k3_group_1(k5_autgroup(esk1_0),esk2_0) = k3_group_1(k3_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_47,c_0_43]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_53,negated_conjecture,
( v3_struct_0(k3_autgroup(esk1_0))
| k3_group_1(k3_autgroup(esk1_0),esk2_0) = k2_funct_1(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_54,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_struct_0(k3_autgroup(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_55,negated_conjecture,
v3_struct_0(k3_autgroup(esk1_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_56,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_54,c_0_55]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 20:27:27 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 % Version: 3.5.1
% 0.19/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.49 % Starting sh5l with 300s (1) cores
% 0.19/0.49 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1338603 completed with status 0
% 0.19/0.49 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.19/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.49 % No SInE strategy applied
% 0.19/0.49 % Search class: FGHSM-FSMM31-SFFFFFNN
% 0.19/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.19/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 136s (1) cores
% 0.19/0.49 % Starting new_bool_3 with 136s (1) cores
% 0.19/0.49 % Starting new_bool_1 with 136s (1) cores
% 0.19/0.49 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1338612 completed with status 0
% 0.19/0.49 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.19/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.49 % No SInE strategy applied
% 0.19/0.49 % Search class: FGHSM-FSMM31-SFFFFFNN
% 0.19/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.19/0.49 % Preprocessing time : 0.002 s
% 0.19/0.49 % Presaturation interreduction done
% 0.19/0.49
% 0.19/0.49 % Proof found!
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start CNFRefutation
% See solution above
% 0.19/0.49 % Parsed axioms : 77
% 0.19/0.49 % Removed by relevancy pruning/SinE : 0
% 0.19/0.49 % Initial clauses : 152
% 0.19/0.49 % Removed in clause preprocessing : 15
% 0.19/0.49 % Initial clauses in saturation : 137
% 0.19/0.49 % Processed clauses : 656
% 0.19/0.49 % ...of these trivial : 1
% 0.19/0.49 % ...subsumed : 198
% 0.19/0.49 % ...remaining for further processing : 457
% 0.19/0.49 % Other redundant clauses eliminated : 16
% 0.19/0.49 % Clauses deleted for lack of memory : 0
% 0.19/0.49 % Backward-subsumed : 20
% 0.19/0.49 % Backward-rewritten : 33
% 0.19/0.49 % Generated clauses : 1195
% 0.19/0.49 % ...of the previous two non-redundant : 1053
% 0.19/0.49 % ...aggressively subsumed : 0
% 0.19/0.49 % Contextual simplify-reflections : 4
% 0.19/0.49 % Paramodulations : 1177
% 0.19/0.49 % Factorizations : 0
% 0.19/0.49 % NegExts : 0
% 0.19/0.49 % Equation resolutions : 18
% 0.19/0.49 % Disequality decompositions : 0
% 0.19/0.49 % Total rewrite steps : 173
% 0.19/0.49 % ...of those cached : 145
% 0.19/0.49 % Propositional unsat checks : 0
% 0.19/0.49 % Propositional check models : 0
% 0.19/0.49 % Propositional check unsatisfiable : 0
% 0.19/0.49 % Propositional clauses : 0
% 0.19/0.49 % Propositional clauses after purity: 0
% 0.19/0.49 % Propositional unsat core size : 0
% 0.19/0.49 % Propositional preprocessing time : 0.000
% 0.19/0.49 % Propositional encoding time : 0.000
% 0.19/0.49 % Propositional solver time : 0.000
% 0.19/0.49 % Success case prop preproc time : 0.000
% 0.19/0.49 % Success case prop encoding time : 0.000
% 0.19/0.49 % Success case prop solver time : 0.000
% 0.19/0.49 % Current number of processed clauses : 267
% 0.19/0.49 % Positive orientable unit clauses : 56
% 0.19/0.49 % Positive unorientable unit clauses: 0
% 0.19/0.49 % Negative unit clauses : 8
% 0.19/0.49 % Non-unit-clauses : 203
% 0.19/0.49 % Current number of unprocessed clauses: 640
% 0.19/0.49 % ...number of literals in the above : 3647
% 0.19/0.49 % Current number of archived formulas : 0
% 0.19/0.49 % Current number of archived clauses : 188
% 0.19/0.49 % Clause-clause subsumption calls (NU) : 15272
% 0.19/0.49 % Rec. Clause-clause subsumption calls : 4829
% 0.19/0.49 % Non-unit clause-clause subsumptions : 216
% 0.19/0.49 % Unit Clause-clause subsumption calls : 1106
% 0.19/0.49 % Rewrite failures with RHS unbound : 0
% 0.19/0.49 % BW rewrite match attempts : 11
% 0.19/0.49 % BW rewrite match successes : 5
% 0.19/0.49 % Condensation attempts : 0
% 0.19/0.49 % Condensation successes : 0
% 0.19/0.49 % Termbank termtop insertions : 27889
% 0.19/0.49 % Search garbage collected termcells : 1689
% 0.19/0.49
% 0.19/0.49 % -------------------------------------------------
% 0.19/0.49 % User time : 0.039 s
% 0.19/0.49 % System time : 0.006 s
% 0.19/0.49 % Total time : 0.046 s
% 0.19/0.49 % Maximum resident set size: 3968 pages
% 0.19/0.49
% 0.19/0.49 % -------------------------------------------------
% 0.19/0.49 % User time : 0.152 s
% 0.19/0.49 % System time : 0.032 s
% 0.19/0.49 % Total time : 0.184 s
% 0.19/0.49 % Maximum resident set size: 4608 pages
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------