%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP628+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 1.95s 1.95s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 18 unt; 0 def)
% Number of atoms : 317 ( 31 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 403 ( 142 ~; 145 |; 76 &)
% ( 0 <=>; 40 =>; 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 : 72 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',t57_group_2) ).
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/sandbox/benchmark/theBenchmark.p',t51_group_2) ).
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/sandbox/benchmark/theBenchmark.p',t22_autgroup) ).
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/sandbox/benchmark/theBenchmark.p',dt_k5_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/sandbox/benchmark/theBenchmark.p',dt_k3_autgroup) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(c_0_7,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_8,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_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,
! [X266,X267,X268,X269] :
( v3_struct_0(X266)
| ~ v3_group_1(X266)
| ~ v4_group_1(X266)
| ~ l1_group_1(X266)
| ~ m1_subset_1(X267,u1_struct_0(X266))
| ~ m1_group_2(X268,X266)
| ~ m1_subset_1(X269,u1_struct_0(X268))
| X269 != X267
| k3_group_1(X268,X269) = k3_group_1(X266,X267) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X263,X264,X265] :
( v3_struct_0(X263)
| ~ v3_group_1(X263)
| ~ l1_group_1(X263)
| ~ m1_group_2(X264,X263)
| ~ m1_subset_1(X265,u1_struct_0(X264))
| m1_subset_1(X265,u1_struct_0(X263)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,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_13,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_14,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]) ).
cnf(c_0_15,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_10]) ).
cnf(c_0_16,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_11]) ).
cnf(c_0_17,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X177] :
( ( v1_group_1(k5_autgroup(X177))
| v3_struct_0(X177)
| ~ v1_group_1(X177)
| ~ v3_group_1(X177)
| ~ v4_group_1(X177)
| ~ l1_group_1(X177) )
& ( v1_group_3(k5_autgroup(X177),k3_autgroup(X177))
| v3_struct_0(X177)
| ~ v1_group_1(X177)
| ~ v3_group_1(X177)
| ~ v4_group_1(X177)
| ~ l1_group_1(X177) )
& ( m1_group_2(k5_autgroup(X177),k3_autgroup(X177))
| v3_struct_0(X177)
| ~ v1_group_1(X177)
| ~ v3_group_1(X177)
| ~ v4_group_1(X177)
| ~ l1_group_1(X177) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_20,plain,
! [X173] :
( ( ~ v3_struct_0(k3_autgroup(X173))
| v3_struct_0(X173)
| ~ v1_group_1(X173)
| ~ v3_group_1(X173)
| ~ v4_group_1(X173)
| ~ l1_group_1(X173) )
& ( v1_group_1(k3_autgroup(X173))
| v3_struct_0(X173)
| ~ v1_group_1(X173)
| ~ v3_group_1(X173)
| ~ v4_group_1(X173)
| ~ l1_group_1(X173) )
& ( v3_group_1(k3_autgroup(X173))
| v3_struct_0(X173)
| ~ v1_group_1(X173)
| ~ v3_group_1(X173)
| ~ v4_group_1(X173)
| ~ l1_group_1(X173) )
& ( v4_group_1(k3_autgroup(X173))
| v3_struct_0(X173)
| ~ v1_group_1(X173)
| ~ v3_group_1(X173)
| ~ v4_group_1(X173)
| ~ l1_group_1(X173) )
& ( l1_group_1(k3_autgroup(X173))
| v3_struct_0(X173)
| ~ v1_group_1(X173)
| ~ v3_group_1(X173)
| ~ v4_group_1(X173)
| ~ l1_group_1(X173) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_21,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_22,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]) ).
cnf(c_0_23,plain,
( k3_group_1(X1,X2) = k3_group_1(X3,X2)
| v3_struct_0(X1)
| ~ m1_group_2(X3,X1)
| ~ m1_subset_1(X2,u1_struct_0(X3))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]) ).
cnf(c_0_24,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,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_19]) ).
cnf(c_0_26,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,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_20]) ).
cnf(c_0_32,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_20]) ).
cnf(c_0_33,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_20]) ).
fof(c_0_34,plain,
! [X249,X250,X251] :
( v3_struct_0(X249)
| ~ v1_group_1(X249)
| ~ v3_group_1(X249)
| ~ v4_group_1(X249)
| ~ l1_group_1(X249)
| ~ m2_fraenkel(X250,u1_struct_0(X249),u1_struct_0(X249),k1_autgroup(X249))
| ~ m1_subset_1(X251,u1_struct_0(k3_autgroup(X249)))
| X250 != X251
| k2_funct_1(X250) = k3_group_1(k3_autgroup(X249),X251) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_35,plain,
! [X252,X253] :
( v3_struct_0(X252)
| ~ v1_group_1(X252)
| ~ v3_group_1(X252)
| ~ v4_group_1(X252)
| ~ l1_group_1(X252)
| ~ m2_fraenkel(X253,u1_struct_0(X252),u1_struct_0(X252),k4_autgroup(X252))
| m2_fraenkel(X253,u1_struct_0(X252),u1_struct_0(X252),k1_autgroup(X252)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_36,negated_conjecture,
k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
( k3_group_1(X1,esk2_0) = k3_group_1(k5_autgroup(esk1_0),esk2_0)
| v3_struct_0(X1)
| ~ m1_group_2(k5_autgroup(esk1_0),X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_38,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_25,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_39,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_31,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_40,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_32,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_41,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_33,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_42,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_43,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_44,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_12]) ).
cnf(c_0_45,negated_conjecture,
k3_group_1(k5_autgroup(esk1_0),esk2_0) != k2_funct_1(esk2_0),
inference(rw,[status(thm)],[c_0_36,c_0_18]) ).
cnf(c_0_46,negated_conjecture,
( k3_group_1(k5_autgroup(esk1_0),esk2_0) = k3_group_1(k3_autgroup(esk1_0),esk2_0)
| v3_struct_0(k3_autgroup(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_47,plain,
( k3_group_1(k3_autgroup(X1),X2) = k2_funct_1(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,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) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_48,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_43,c_0_44]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_49,negated_conjecture,
( m1_subset_1(esk2_0,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ m1_group_2(k5_autgroup(esk1_0),X1)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_50,negated_conjecture,
( v3_struct_0(k3_autgroup(esk1_0))
| k3_group_1(k3_autgroup(esk1_0),esk2_0) != k2_funct_1(esk2_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( k3_group_1(k3_autgroup(esk1_0),esk2_0) = k2_funct_1(esk2_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_47,c_0_48]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_52,negated_conjecture,
( m1_subset_1(esk2_0,u1_struct_0(k3_autgroup(esk1_0)))
| v3_struct_0(k3_autgroup(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_38]),c_0_39]),c_0_41])]) ).
cnf(c_0_53,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_20]) ).
cnf(c_0_54,negated_conjecture,
v3_struct_0(k3_autgroup(esk1_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_55,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_53,c_0_54]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP628+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:49:02 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.95/1.95 % Version : CSE_E---1.7
% 1.95/1.95 % Problem : theBenchmark.p
% 1.95/1.95 % SZS status Theorem for theBenchmark.p
% 1.95/1.95 % SZS output start CNFRefutation
% See solution above
% 1.95/1.95 % Total time : 1.371s
%------------------------------------------------------------------------------