%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:40:26 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 15 unt; 0 def)
% Number of atoms : 335 ( 33 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 437 ( 157 ~; 156 |; 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 : 78 ( 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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t51_group_2) ).
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/sandbox/benchmark/theBenchmark.p',t11_autgroup) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',dt_k3_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/sandbox/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,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]) ).
fof(c_0_11,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_12,plain,
! [X13,X14,X15,X16] :
( k3_group_1(X15,X16) = k3_group_1(X13,X14)
| X16 != X14
| ~ m1_subset_1(X16,u1_struct_0(X15))
| ~ m1_group_2(X15,X13)
| ~ m1_subset_1(X14,u1_struct_0(X13))
| ~ l1_group_1(X13)
| ~ v4_group_1(X13)
| ~ v3_group_1(X13)
| v3_struct_0(X13) ),
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_13,plain,
! [X21,X22,X23] :
( m1_subset_1(X23,u1_struct_0(X21))
| ~ m1_subset_1(X23,u1_struct_0(X22))
| ~ m1_group_2(X22,X21)
| ~ l1_group_1(X21)
| ~ v3_group_1(X21)
| v3_struct_0(X21) ),
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_14,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]) ).
fof(c_0_15,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]) ).
fof(c_0_16,plain,
! [X10,X11,X12] :
( k2_funct_1(X11) = k3_group_1(k3_autgroup(X10),X12)
| X11 != X12
| ~ m1_subset_1(X12,u1_struct_0(k3_autgroup(X10)))
| ~ m2_fraenkel(X11,u1_struct_0(X10),u1_struct_0(X10),k1_autgroup(X10))
| ~ l1_group_1(X10)
| ~ v4_group_1(X10)
| ~ v3_group_1(X10)
| ~ v1_group_1(X10)
| v3_struct_0(X10) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_17,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]) ).
fof(c_0_18,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_11])])])]) ).
cnf(c_0_19,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_12]) ).
cnf(c_0_20,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_13]) ).
fof(c_0_21,plain,
! [X17] :
( ( ~ l1_group_1(X17)
| ~ v4_group_1(X17)
| ~ v3_group_1(X17)
| ~ v1_group_1(X17)
| v3_struct_0(X17)
| m1_group_2(k5_autgroup(X17),k3_autgroup(X17)) )
& ( ~ l1_group_1(X17)
| ~ v4_group_1(X17)
| ~ v3_group_1(X17)
| ~ v1_group_1(X17)
| v3_struct_0(X17)
| v1_group_3(k5_autgroup(X17),k3_autgroup(X17)) )
& ( ~ l1_group_1(X17)
| ~ v4_group_1(X17)
| ~ v3_group_1(X17)
| ~ v1_group_1(X17)
| v3_struct_0(X17)
| v1_group_1(k5_autgroup(X17)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_22,plain,
! [X42] :
( ( ~ l1_group_1(X42)
| ~ v4_group_1(X42)
| ~ v3_group_1(X42)
| ~ v1_group_1(X42)
| v3_struct_0(X42)
| l1_group_1(k3_autgroup(X42)) )
& ( ~ l1_group_1(X42)
| ~ v4_group_1(X42)
| ~ v3_group_1(X42)
| ~ v1_group_1(X42)
| v3_struct_0(X42)
| v4_group_1(k3_autgroup(X42)) )
& ( ~ l1_group_1(X42)
| ~ v4_group_1(X42)
| ~ v3_group_1(X42)
| ~ v1_group_1(X42)
| v3_struct_0(X42)
| v3_group_1(k3_autgroup(X42)) )
& ( ~ l1_group_1(X42)
| ~ v4_group_1(X42)
| ~ v3_group_1(X42)
| ~ v1_group_1(X42)
| v3_struct_0(X42)
| v1_group_1(k3_autgroup(X42)) )
& ( ~ l1_group_1(X42)
| ~ v4_group_1(X42)
| ~ v3_group_1(X42)
| ~ v1_group_1(X42)
| v3_struct_0(X42)
| ~ v3_struct_0(k3_autgroup(X42)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_23,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_16]) ).
fof(c_0_24,plain,
! [X37,X38] :
( m2_fraenkel(X38,u1_struct_0(X37),u1_struct_0(X37),k1_autgroup(X37))
| ~ m2_fraenkel(X38,u1_struct_0(X37),u1_struct_0(X37),k4_autgroup(X37))
| ~ l1_group_1(X37)
| ~ v4_group_1(X37)
| ~ v3_group_1(X37)
| ~ v1_group_1(X37)
| v3_struct_0(X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_25,negated_conjecture,
k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,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_19]),c_0_20]) ).
cnf(c_0_28,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_29,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_22]) ).
cnf(c_0_30,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_22]) ).
cnf(c_0_31,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_22]) ).
cnf(c_0_32,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_22]) ).
cnf(c_0_33,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,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_23]) ).
cnf(c_0_35,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_24]) ).
cnf(c_0_36,negated_conjecture,
k3_group_1(k5_autgroup(esk1_0),esk2_0) != k2_funct_1(esk2_0),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(k5_autgroup(X1)))
| v3_struct_0(X1)
| k3_group_1(k5_autgroup(X1),X2) = k3_group_1(k3_autgroup(X1),X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_38,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(rw,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_39,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_40,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_44,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),k4_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(spm,[status(thm)],[c_0_34,c_0_35]) ).
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_18]) ).
cnf(c_0_46,negated_conjecture,
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_36,c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( ~ m1_subset_1(esk2_0,u1_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(spm,[status(thm)],[c_0_44,c_0_45]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_48,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_20,c_0_38]) ).
cnf(c_0_49,negated_conjecture,
~ m1_subset_1(esk2_0,u1_struct_0(k3_autgroup(esk1_0))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,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_48,c_0_28]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( ~ v3_group_1(k3_autgroup(esk1_0))
| ~ l1_group_1(k3_autgroup(esk1_0))
| v3_struct_0(k3_autgroup(esk1_0)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,negated_conjecture,
( ~ l1_group_1(k3_autgroup(esk1_0))
| 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_29]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_53,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_31]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_54,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_32,c_0_53]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:21:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.12/0.46 % Version: 3.5.1
% 0.12/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.46 % Starting sh5l with 300s (1) cores
% 0.12/0.46 % new_bool_1 with pid 793576 completed with status 0
% 0.12/0.46 % Result found by new_bool_1
% 0.12/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.46 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.12/0.46 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.46 % SubtermCWHack with pid 793578 completed with status 0
% 0.12/0.46 % Result found by SubtermCWHack
% 0.12/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.46 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.12/0.46 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.46 % Preprocessing time : 0.002 s
% 0.12/0.46
% 0.12/0.46 % Proof found!
% 0.12/0.46 % SZS status Theorem
% 0.12/0.46 % SZS output start CNFRefutation
% See solution above
% 0.12/0.46 % Parsed axioms : 77
% 0.12/0.46 % Removed by relevancy pruning/SinE : 32
% 0.12/0.46 % Initial clauses : 98
% 0.12/0.46 % Removed in clause preprocessing : 1
% 0.12/0.46 % Initial clauses in saturation : 97
% 0.12/0.46 % Processed clauses : 357
% 0.12/0.46 % ...of these trivial : 0
% 0.12/0.46 % ...subsumed : 59
% 0.12/0.46 % ...remaining for further processing : 298
% 0.12/0.46 % Other redundant clauses eliminated : 2
% 0.12/0.46 % Clauses deleted for lack of memory : 0
% 0.12/0.46 % Backward-subsumed : 17
% 0.12/0.46 % Backward-rewritten : 3
% 0.12/0.46 % Generated clauses : 408
% 0.12/0.46 % ...of the previous two non-redundant : 393
% 0.12/0.46 % ...aggressively subsumed : 0
% 0.12/0.46 % Contextual simplify-reflections : 120
% 0.12/0.46 % Paramodulations : 398
% 0.12/0.46 % Factorizations : 0
% 0.12/0.46 % NegExts : 0
% 0.12/0.46 % Equation resolutions : 10
% 0.12/0.46 % Disequality decompositions : 0
% 0.12/0.46 % Total rewrite steps : 120
% 0.12/0.46 % ...of those cached : 104
% 0.12/0.46 % Propositional unsat checks : 0
% 0.12/0.46 % Propositional check models : 0
% 0.12/0.46 % Propositional check unsatisfiable : 0
% 0.12/0.46 % Propositional clauses : 0
% 0.12/0.46 % Propositional clauses after purity: 0
% 0.12/0.46 % Propositional unsat core size : 0
% 0.12/0.46 % Propositional preprocessing time : 0.000
% 0.12/0.46 % Propositional encoding time : 0.000
% 0.12/0.46 % Propositional solver time : 0.000
% 0.12/0.46 % Success case prop preproc time : 0.000
% 0.12/0.46 % Success case prop encoding time : 0.000
% 0.12/0.46 % Success case prop solver time : 0.000
% 0.12/0.46 % Current number of processed clauses : 276
% 0.12/0.46 % Positive orientable unit clauses : 41
% 0.12/0.46 % Positive unorientable unit clauses: 0
% 0.12/0.46 % Negative unit clauses : 7
% 0.12/0.46 % Non-unit-clauses : 228
% 0.12/0.46 % Current number of unprocessed clauses: 132
% 0.12/0.46 % ...number of literals in the above : 1814
% 0.12/0.46 % Current number of archived formulas : 0
% 0.12/0.46 % Current number of archived clauses : 20
% 0.12/0.46 % Clause-clause subsumption calls (NU) : 36069
% 0.12/0.46 % Rec. Clause-clause subsumption calls : 3221
% 0.12/0.46 % Non-unit clause-clause subsumptions : 193
% 0.12/0.46 % Unit Clause-clause subsumption calls : 154
% 0.12/0.46 % Rewrite failures with RHS unbound : 0
% 0.12/0.46 % BW rewrite match attempts : 2
% 0.12/0.46 % BW rewrite match successes : 2
% 0.12/0.46 % Condensation attempts : 0
% 0.12/0.46 % Condensation successes : 0
% 0.12/0.46 % Termbank termtop insertions : 22083
% 0.12/0.46 % Search garbage collected termcells : 1328
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.044 s
% 0.12/0.46 % System time : 0.005 s
% 0.12/0.46 % Total time : 0.049 s
% 0.12/0.46 % Maximum resident set size: 3968 pages
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.045 s
% 0.12/0.46 % System time : 0.010 s
% 0.12/0.46 % Total time : 0.055 s
% 0.12/0.46 % Maximum resident set size: 4608 pages
% 0.12/0.46 % E exiting
%------------------------------------------------------------------------------