%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU411+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 : n007.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 02:25:01 PM UTC 2026
% Result : Theorem 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 26 unt; 0 def)
% Number of atoms : 272 ( 17 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 308 ( 104 ~; 92 |; 85 &)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 106 ( 4 sgn 67 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t20_latsum_1,conjecture,
! [X1] :
( ( l1_orders_2(X1)
& v1_lattice3(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_orders_2(X2)
& v1_lattice3(X2)
& v1_yellow_0(X2)
& v4_orders_2(X2)
& v3_orders_2(X2)
& v2_orders_2(X2)
& ~ v3_struct_0(X2) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_latsum_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( v1_xboole_0(X3)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X3))
& r2_hidden(X1,X2) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( r2_hidden(X1,X2)
| v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(dt_k3_yellow_0,axiom,
! [X1] :
( l1_orders_2(X1)
=> m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
fof(d19_waybel_0,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( v12_waybel_0(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r1_orders_2(X1,X4,X3)
& r2_hidden(X3,X2) )
=> r2_hidden(X4,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_waybel_0) ).
fof(t44_yellow_0,axiom,
! [X1] :
( ( l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_orders_2(X1,k3_yellow_0(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
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(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k3_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( l1_orders_2(X1)
& v1_lattice3(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_orders_2(X2)
& v1_lattice3(X2)
& v1_yellow_0(X2)
& v4_orders_2(X2)
& v3_orders_2(X2)
& v2_orders_2(X2)
& ~ v3_struct_0(X2) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
inference(assume_negation,[status(cth)],[t20_latsum_1]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ( l1_orders_2(X1)
& v1_lattice3(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_orders_2(X2)
& v1_lattice3(X2)
& v1_yellow_0(X2)
& v4_orders_2(X2)
& v3_orders_2(X2)
& v2_orders_2(X2)
& ~ v3_struct_0(X2) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_15,negated_conjecture,
( ~ r2_hidden(k3_yellow_0(esk2_0),u1_struct_0(esk1_0))
& m1_subset_1(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),k1_zfmisc_1(u1_struct_0(esk2_0)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0)
& v1_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)))
& l1_orders_2(esk2_0)
& v1_lattice3(esk2_0)
& v1_yellow_0(esk2_0)
& v4_orders_2(esk2_0)
& v3_orders_2(esk2_0)
& v2_orders_2(esk2_0)
& ~ v3_struct_0(esk2_0)
& l1_orders_2(esk1_0)
& v1_lattice3(esk1_0)
& v1_yellow_0(esk1_0)
& v4_orders_2(esk1_0)
& v3_orders_2(esk1_0)
& v2_orders_2(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_14])])])]) ).
fof(c_0_16,plain,
! [X9,X10] : k3_xboole_0(X9,X10) = k3_xboole_0(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_17,plain,
! [X67,X68,X69] :
( ~ v1_xboole_0(X69)
| ~ m1_subset_1(X68,k1_zfmisc_1(X69))
| ~ r2_hidden(X67,X68) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
cnf(c_0_18,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_21,plain,
( ~ v1_xboole_0(X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)),k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_23,plain,
! [X17,X18,X19] :
( ( X19 = k1_xboole_0
| r2_hidden(esk5_1(X19),X19) )
& ( ~ r2_hidden(X18,X17)
| X17 != k1_xboole_0 ) ),
inference(fof_nnf,[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)],[c_0_20])])])])])]) ).
fof(c_0_24,plain,
! [X64,X65,X66] :
( m1_subset_1(X64,X66)
| ~ m1_subset_1(X65,k1_zfmisc_1(X66))
| ~ r2_hidden(X64,X65) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_25,plain,
! [X58,X59] :
( r2_hidden(X58,X59)
| v1_xboole_0(X59)
| ~ m1_subset_1(X58,X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_26,plain,
! [X34] : m1_subset_1(esk9_1(X34),X34),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_27,plain,
! [X30] :
( m1_subset_1(k3_yellow_0(X30),u1_struct_0(X30))
| ~ l1_orders_2(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_yellow_0])])]) ).
cnf(c_0_28,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk2_0))
| ~ r2_hidden(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( X1 = k1_xboole_0
| r2_hidden(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X11,X12,X13,X14] :
( ( ~ l1_orders_2(X11)
| ~ m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))
| v12_waybel_0(X12,X11)
| ~ r2_hidden(esk4_2(X11,X12),X12) )
& ( ~ l1_orders_2(X11)
| ~ m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))
| v12_waybel_0(X12,X11)
| r1_orders_2(X11,esk4_2(X11,X12),esk3_2(X11,X12)) )
& ( ~ l1_orders_2(X11)
| ~ m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))
| v12_waybel_0(X12,X11)
| r2_hidden(esk3_2(X11,X12),X12) )
& ( ~ l1_orders_2(X11)
| ~ m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))
| v12_waybel_0(X12,X11)
| m1_subset_1(esk4_2(X11,X12),u1_struct_0(X11)) )
& ( ~ l1_orders_2(X11)
| ~ m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))
| v12_waybel_0(X12,X11)
| m1_subset_1(esk3_2(X11,X12),u1_struct_0(X11)) )
& ( ~ l1_orders_2(X11)
| ~ m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))
| r2_hidden(X14,X12)
| ~ r1_orders_2(X11,X14,X13)
| ~ r2_hidden(X13,X12)
| ~ m1_subset_1(X14,u1_struct_0(X11))
| ~ m1_subset_1(X13,u1_struct_0(X11))
| ~ v12_waybel_0(X12,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d19_waybel_0])])])])])]) ).
fof(c_0_32,plain,
! [X1] :
( ( l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_orders_2(X1,k3_yellow_0(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[t44_yellow_0]) ).
cnf(c_0_33,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
( ~ l1_orders_2(X1)
| m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(rw,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_38,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk2_0))
| k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)) = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_40,plain,
( ~ l1_orders_2(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ r1_orders_2(X2,X4,X3)
| ~ r2_hidden(X3,X1)
| ~ m1_subset_1(X4,u1_struct_0(X2))
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ v12_waybel_0(X1,X2)
| r2_hidden(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_42,plain,
! [X62,X63] :
( r1_orders_2(X62,k3_yellow_0(X62),X63)
| ~ m1_subset_1(X63,u1_struct_0(X62))
| ~ l1_orders_2(X62)
| ~ v1_yellow_0(X62)
| ~ v4_orders_2(X62)
| v3_struct_0(X62) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
cnf(c_0_43,negated_conjecture,
( ~ r2_hidden(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))
| m1_subset_1(X1,u1_struct_0(esk2_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_44,plain,
( v1_xboole_0(X1)
| r2_hidden(esk9_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_45,plain,
! [X55,X56] :
( m1_subset_1(X55,X56)
| ~ r2_hidden(X55,X56) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_46,plain,
( ~ l1_orders_2(X1)
| v1_xboole_0(u1_struct_0(X1))
| r2_hidden(k3_yellow_0(X1),u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_47,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_48,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_49,plain,
( ~ l1_orders_2(X3)
| ~ v12_waybel_0(X2,X3)
| ~ m1_subset_1(X1,u1_struct_0(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X3)))
| ~ r2_hidden(X4,X2)
| ~ r1_orders_2(X3,X1,X4)
| r2_hidden(X1,X2) ),
inference(csr,[status(thm)],[c_0_40,c_0_33]) ).
cnf(c_0_50,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)),esk2_0),
inference(rw,[status(thm)],[c_0_41,c_0_19]) ).
cnf(c_0_51,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| r1_orders_2(X1,k3_yellow_0(X1),X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,negated_conjecture,
m1_subset_1(esk9_1(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_37]) ).
cnf(c_0_53,negated_conjecture,
v1_yellow_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_54,negated_conjecture,
v4_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_55,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_56,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,negated_conjecture,
r2_hidden(k3_yellow_0(esk2_0),u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
fof(c_0_58,plain,
! [X21,X22,X23,X24,X25,X26,X27,X28] :
( ( X28 = k3_xboole_0(X26,X27)
| r2_hidden(esk6_3(X26,X27,X28),X28)
| r2_hidden(esk6_3(X26,X27,X28),X27) )
& ( X28 = k3_xboole_0(X26,X27)
| r2_hidden(esk6_3(X26,X27,X28),X28)
| r2_hidden(esk6_3(X26,X27,X28),X26) )
& ( X28 = k3_xboole_0(X26,X27)
| ~ r2_hidden(esk6_3(X26,X27,X28),X27)
| ~ r2_hidden(esk6_3(X26,X27,X28),X26)
| ~ r2_hidden(esk6_3(X26,X27,X28),X28) )
& ( X23 != k3_xboole_0(X21,X22)
| r2_hidden(X25,X23)
| ~ r2_hidden(X25,X22)
| ~ r2_hidden(X25,X21) )
& ( X23 != k3_xboole_0(X21,X22)
| ~ r2_hidden(X24,X23)
| r2_hidden(X24,X22) )
& ( X23 != k3_xboole_0(X21,X22)
| ~ r2_hidden(X24,X23)
| r2_hidden(X24,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_xboole_0])])])])])])]) ).
cnf(c_0_59,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk2_0))
| ~ r2_hidden(X2,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))
| ~ r1_orders_2(esk2_0,X1,X2)
| r2_hidden(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_22]),c_0_50]),c_0_47])]) ).
cnf(c_0_60,negated_conjecture,
r1_orders_2(esk2_0,k3_yellow_0(esk2_0),esk9_1(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(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_51,c_0_52]),c_0_47]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_61,negated_conjecture,
m1_subset_1(k3_yellow_0(esk2_0),u1_struct_0(esk2_0)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
( X3 != k3_xboole_0(X4,X2)
| ~ r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( ~ r2_hidden(esk9_1(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))
| r2_hidden(k3_yellow_0(esk2_0),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_64,plain,
( ~ r2_hidden(X1,k3_xboole_0(X3,X2))
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_65,negated_conjecture,
r2_hidden(k3_yellow_0(esk2_0),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_44]),c_0_37]) ).
cnf(c_0_66,negated_conjecture,
~ r2_hidden(k3_yellow_0(esk2_0),u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU411+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 06:20:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.18/0.52 % Version: 3.5.1
% 0.18/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.52 % Starting sh5l with 300s (1) cores
% 0.18/0.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 368436 completed with status 0
% 0.18/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.52 % No SInE strategy applied
% 0.18/0.52 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.18/0.52 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.52 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.18/0.52 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.18/0.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 368445 completed with status 0
% 0.18/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.52 % No SInE strategy applied
% 0.18/0.52 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.18/0.52 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.52 % Preprocessing time : 0.002 s
% 0.18/0.52 % Presaturation interreduction done
% 0.18/0.52
% 0.18/0.52 % Proof found!
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 % SZS output start CNFRefutation
% See solution above
% 0.18/0.52 % Parsed axioms : 39
% 0.18/0.52 % Removed by relevancy pruning/SinE : 0
% 0.18/0.52 % Initial clauses : 75
% 0.18/0.52 % Removed in clause preprocessing : 6
% 0.18/0.52 % Initial clauses in saturation : 69
% 0.18/0.52 % Processed clauses : 874
% 0.18/0.52 % ...of these trivial : 3
% 0.18/0.52 % ...subsumed : 391
% 0.18/0.52 % ...remaining for further processing : 480
% 0.18/0.52 % Other redundant clauses eliminated : 4
% 0.18/0.52 % Clauses deleted for lack of memory : 0
% 0.18/0.52 % Backward-subsumed : 9
% 0.18/0.52 % Backward-rewritten : 19
% 0.18/0.52 % Generated clauses : 2567
% 0.18/0.52 % ...of the previous two non-redundant : 2401
% 0.18/0.52 % ...aggressively subsumed : 0
% 0.18/0.52 % Contextual simplify-reflections : 3
% 0.18/0.52 % Paramodulations : 2543
% 0.18/0.52 % Factorizations : 20
% 0.18/0.52 % NegExts : 0
% 0.18/0.52 % Equation resolutions : 4
% 0.18/0.52 % Disequality decompositions : 0
% 0.18/0.52 % Total rewrite steps : 717
% 0.18/0.52 % ...of those cached : 653
% 0.18/0.52 % Propositional unsat checks : 0
% 0.18/0.52 % Propositional check models : 0
% 0.18/0.52 % Propositional check unsatisfiable : 0
% 0.18/0.52 % Propositional clauses : 0
% 0.18/0.52 % Propositional clauses after purity: 0
% 0.18/0.52 % Propositional unsat core size : 0
% 0.18/0.52 % Propositional preprocessing time : 0.000
% 0.18/0.52 % Propositional encoding time : 0.000
% 0.18/0.52 % Propositional solver time : 0.000
% 0.18/0.52 % Success case prop preproc time : 0.000
% 0.18/0.52 % Success case prop encoding time : 0.000
% 0.18/0.52 % Success case prop solver time : 0.000
% 0.18/0.52 % Current number of processed clauses : 379
% 0.18/0.52 % Positive orientable unit clauses : 58
% 0.18/0.52 % Positive unorientable unit clauses: 1
% 0.18/0.52 % Negative unit clauses : 13
% 0.18/0.52 % Non-unit-clauses : 307
% 0.18/0.52 % Current number of unprocessed clauses: 1628
% 0.18/0.52 % ...number of literals in the above : 5960
% 0.18/0.52 % Current number of archived formulas : 0
% 0.18/0.52 % Current number of archived clauses : 97
% 0.18/0.52 % Clause-clause subsumption calls (NU) : 6081
% 0.18/0.52 % Rec. Clause-clause subsumption calls : 3174
% 0.18/0.52 % Non-unit clause-clause subsumptions : 288
% 0.18/0.52 % Unit Clause-clause subsumption calls : 164
% 0.18/0.52 % Rewrite failures with RHS unbound : 0
% 0.18/0.52 % BW rewrite match attempts : 28
% 0.18/0.52 % BW rewrite match successes : 16
% 0.18/0.52 % Condensation attempts : 0
% 0.18/0.52 % Condensation successes : 0
% 0.18/0.52 % Termbank termtop insertions : 43961
% 0.18/0.52 % Search garbage collected termcells : 1050
% 0.18/0.52
% 0.18/0.52 % -------------------------------------------------
% 0.18/0.52 % User time : 0.079 s
% 0.18/0.52 % System time : 0.007 s
% 0.18/0.52 % Total time : 0.086 s
% 0.18/0.52 % Maximum resident set size: 3620 pages
% 0.18/0.52
% 0.18/0.52 % -------------------------------------------------
% 0.18/0.52 % User time : 0.335 s
% 0.18/0.52 % System time : 0.030 s
% 0.18/0.52 % Total time : 0.365 s
% 0.18/0.52 % Maximum resident set size: 4864 pages
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------