%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU412+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 : n016.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 02:25:02 PM UTC 2026
% Result : Theorem 200.26s 29.79s
% Output : CNFRefutation 200.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 90 ( 23 unt; 0 def)
% Number of atoms : 304 ( 30 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 356 ( 142 ~; 139 |; 52 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-6 aty)
% Number of variables : 163 ( 9 sgn 92 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [X1] :
( l1_orders_2(X1)
=> m2_relset_1(u1_orders_2(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
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(t22_latsum_1,conjecture,
! [X1,X2,X3] :
( l1_orders_2(X3)
=> ! [X4] :
( l1_orders_2(X4)
=> ~ ( ~ ( r2_hidden(X2,k4_xboole_0(u1_struct_0(X4),u1_struct_0(X3)))
& r2_hidden(X1,k4_xboole_0(u1_struct_0(X3),u1_struct_0(X4))) )
& ~ ( r2_hidden(X2,u1_struct_0(X4))
& r2_hidden(X1,u1_struct_0(X4)) )
& ~ ( r2_hidden(X2,u1_struct_0(X3))
& r2_hidden(X1,u1_struct_0(X3)) )
& m1_subset_1(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)),k1_zfmisc_1(u1_struct_0(X3)))
& v13_waybel_0(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)),X3)
& r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X3,X4))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_latsum_1) ).
fof(dt_k1_latsum_1,axiom,
! [X1,X2] :
( ( l1_orders_2(X2)
& l1_orders_2(X1) )
=> ( l1_orders_2(k1_latsum_1(X1,X2))
& v1_orders_2(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
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(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(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( r2_hidden(k4_tarski(X1,X2),k2_zfmisc_1(X3,X4))
<=> ( r2_hidden(X2,X4)
& r2_hidden(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
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(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(d2_latsum_1,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3] :
( ( l1_orders_2(X3)
& v1_orders_2(X3) )
=> ( X3 = k1_latsum_1(X1,X2)
<=> ( u1_orders_2(X3) = k2_xboole_0(k2_xboole_0(u1_orders_2(X1),u1_orders_2(X2)),k7_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X2),u1_struct_0(X2),u1_orders_2(X1),u1_orders_2(X2)))
& u1_struct_0(X3) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t17_latsum_1,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3,X4] :
( ( r2_hidden(X3,u1_struct_0(X2))
& r2_hidden(k4_tarski(X3,X4),u1_orders_2(k1_latsum_1(X1,X2)))
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X1)))
& v13_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X1) )
=> r2_hidden(X4,u1_struct_0(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_latsum_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(c_0_14,plain,
! [X103,X104,X105] :
( m1_subset_1(X105,k1_zfmisc_1(k2_zfmisc_1(X103,X104)))
| ~ m2_relset_1(X105,X103,X104) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])])]) ).
fof(c_0_15,plain,
! [X30] :
( m2_relset_1(u1_orders_2(X30),u1_struct_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_u1_orders_2])])]) ).
fof(c_0_16,plain,
! [X33,X34,X35] :
( m1_subset_1(X33,X35)
| ~ m1_subset_1(X34,k1_zfmisc_1(X35))
| ~ r2_hidden(X33,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
cnf(c_0_17,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( ~ l1_orders_2(X1)
| m2_relset_1(u1_orders_2(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3] :
( l1_orders_2(X3)
=> ! [X4] :
( l1_orders_2(X4)
=> ~ ( ~ ( r2_hidden(X2,k4_xboole_0(u1_struct_0(X4),u1_struct_0(X3)))
& r2_hidden(X1,k4_xboole_0(u1_struct_0(X3),u1_struct_0(X4))) )
& ~ ( r2_hidden(X2,u1_struct_0(X4))
& r2_hidden(X1,u1_struct_0(X4)) )
& ~ ( r2_hidden(X2,u1_struct_0(X3))
& r2_hidden(X1,u1_struct_0(X3)) )
& m1_subset_1(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)),k1_zfmisc_1(u1_struct_0(X3)))
& v13_waybel_0(k3_xboole_0(u1_struct_0(X3),u1_struct_0(X4)),X3)
& r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X3,X4))) ) ) ),
inference(assume_negation,[status(cth)],[t22_latsum_1]) ).
cnf(c_0_20,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_16]) ).
cnf(c_0_21,plain,
( ~ l1_orders_2(X1)
| m1_subset_1(u1_orders_2(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,negated_conjecture,
( ( ~ r2_hidden(esk2_0,k4_xboole_0(u1_struct_0(esk4_0),u1_struct_0(esk3_0)))
| ~ r2_hidden(esk1_0,k4_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0))) )
& ( ~ r2_hidden(esk2_0,u1_struct_0(esk4_0))
| ~ r2_hidden(esk1_0,u1_struct_0(esk4_0)) )
& ( ~ r2_hidden(esk2_0,u1_struct_0(esk3_0))
| ~ r2_hidden(esk1_0,u1_struct_0(esk3_0)) )
& m1_subset_1(k3_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0)),k1_zfmisc_1(u1_struct_0(esk3_0)))
& v13_waybel_0(k3_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0)),esk3_0)
& r2_hidden(k4_tarski(esk1_0,esk2_0),u1_orders_2(k1_latsum_1(esk3_0,esk4_0)))
& l1_orders_2(esk4_0)
& l1_orders_2(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_23,plain,
( ~ l1_orders_2(X2)
| ~ r2_hidden(X1,u1_orders_2(X2))
| m1_subset_1(X1,k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
r2_hidden(k4_tarski(esk1_0,esk2_0),u1_orders_2(k1_latsum_1(esk3_0,esk4_0))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X50,X51] :
( ( ~ l1_orders_2(X51)
| ~ l1_orders_2(X50)
| l1_orders_2(k1_latsum_1(X50,X51)) )
& ( ~ l1_orders_2(X51)
| ~ l1_orders_2(X50)
| v1_orders_2(k1_latsum_1(X50,X51)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_latsum_1])])])]) ).
fof(c_0_26,plain,
! [X15,X16] :
( r2_hidden(X15,X16)
| v1_xboole_0(X16)
| ~ m1_subset_1(X15,X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_27,negated_conjecture,
( ~ l1_orders_2(k1_latsum_1(esk3_0,esk4_0))
| m1_subset_1(k4_tarski(esk1_0,esk2_0),k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| l1_orders_2(k1_latsum_1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
l1_orders_2(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
l1_orders_2(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X36,X37,X38] :
( ~ v1_xboole_0(X38)
| ~ m1_subset_1(X37,k1_zfmisc_1(X38))
| ~ r2_hidden(X36,X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
fof(c_0_32,plain,
! [X52,X53,X54,X55] :
( ( r2_hidden(k4_tarski(X52,X53),k2_zfmisc_1(X54,X55))
| ~ r2_hidden(X53,X55)
| ~ r2_hidden(X52,X54) )
& ( ~ r2_hidden(k4_tarski(X52,X53),k2_zfmisc_1(X54,X55))
| r2_hidden(X53,X55) )
& ( ~ r2_hidden(k4_tarski(X52,X53),k2_zfmisc_1(X54,X55))
| r2_hidden(X52,X54) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])])]) ).
cnf(c_0_33,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
m1_subset_1(k4_tarski(esk1_0,esk2_0),k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_35,plain,
( ~ v1_xboole_0(X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
( ~ r2_hidden(k4_tarski(X3,X1),k2_zfmisc_1(X4,X2))
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( r2_hidden(k4_tarski(esk1_0,esk2_0),k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0))))
| v1_xboole_0(k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( ~ l1_orders_2(X1)
| ~ r2_hidden(X2,u1_orders_2(X1))
| ~ v1_xboole_0(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_39,negated_conjecture,
( r2_hidden(esk2_0,u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))
| v1_xboole_0(k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_40,plain,
! [X31] : m1_subset_1(esk6_1(X31),X31),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_41,plain,
! [X17,X18] :
( ~ v1_xboole_0(X18)
| ~ r2_hidden(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_42,negated_conjecture,
( ~ l1_orders_2(k1_latsum_1(esk3_0,esk4_0))
| ~ r2_hidden(X1,u1_orders_2(k1_latsum_1(esk3_0,esk4_0)))
| r2_hidden(esk2_0,u1_struct_0(k1_latsum_1(esk3_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
m1_subset_1(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( ~ r2_hidden(X1,u1_orders_2(k1_latsum_1(esk3_0,esk4_0)))
| r2_hidden(esk2_0,u1_struct_0(k1_latsum_1(esk3_0,esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_46,plain,
( r2_hidden(esk6_1(X1),X1)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
~ v1_xboole_0(u1_orders_2(k1_latsum_1(esk3_0,esk4_0))),
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_48,plain,
( ~ r2_hidden(X3,X4)
| ~ r2_hidden(X1,X2)
| r2_hidden(k4_tarski(X1,X3),k2_zfmisc_1(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_49,negated_conjecture,
r2_hidden(esk2_0,u1_struct_0(k1_latsum_1(esk3_0,esk4_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( ~ r2_hidden(X1,X2)
| r2_hidden(k4_tarski(X1,esk2_0),k2_zfmisc_1(X2,u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,negated_conjecture,
r2_hidden(k4_tarski(esk2_0,esk2_0),k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
~ v1_xboole_0(k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))),
inference(spm,[status(thm)],[c_0_44,c_0_51]) ).
fof(c_0_53,plain,
! [X47,X48,X49] :
( ( ~ l1_orders_2(X47)
| ~ l1_orders_2(X48)
| ~ l1_orders_2(X49)
| ~ v1_orders_2(X49)
| X49 = k1_latsum_1(X47,X48)
| u1_orders_2(X49) != k2_xboole_0(k2_xboole_0(u1_orders_2(X47),u1_orders_2(X48)),k7_relset_1(u1_struct_0(X47),u1_struct_0(X47),u1_struct_0(X48),u1_struct_0(X48),u1_orders_2(X47),u1_orders_2(X48)))
| u1_struct_0(X49) != k2_xboole_0(u1_struct_0(X47),u1_struct_0(X48)) )
& ( ~ l1_orders_2(X47)
| ~ l1_orders_2(X48)
| ~ l1_orders_2(X49)
| ~ v1_orders_2(X49)
| X49 != k1_latsum_1(X47,X48)
| u1_orders_2(X49) = k2_xboole_0(k2_xboole_0(u1_orders_2(X47),u1_orders_2(X48)),k7_relset_1(u1_struct_0(X47),u1_struct_0(X47),u1_struct_0(X48),u1_struct_0(X48),u1_orders_2(X47),u1_orders_2(X48))) )
& ( ~ l1_orders_2(X47)
| ~ l1_orders_2(X48)
| ~ l1_orders_2(X49)
| ~ v1_orders_2(X49)
| X49 != k1_latsum_1(X47,X48)
| u1_struct_0(X49) = k2_xboole_0(u1_struct_0(X47),u1_struct_0(X48)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_latsum_1])])])])]) ).
fof(c_0_54,plain,
! [X75,X76,X77,X78,X79,X80,X81,X82] :
( ( X82 = k2_xboole_0(X80,X81)
| r2_hidden(esk11_3(X80,X81,X82),X81)
| r2_hidden(esk11_3(X80,X81,X82),X80)
| r2_hidden(esk11_3(X80,X81,X82),X82) )
& ( X82 = k2_xboole_0(X80,X81)
| ~ r2_hidden(esk11_3(X80,X81,X82),X82)
| ~ r2_hidden(esk11_3(X80,X81,X82),X81) )
& ( X82 = k2_xboole_0(X80,X81)
| ~ r2_hidden(esk11_3(X80,X81,X82),X82)
| ~ r2_hidden(esk11_3(X80,X81,X82),X80) )
& ( X77 != k2_xboole_0(X75,X76)
| r2_hidden(X79,X77)
| ~ r2_hidden(X79,X76) )
& ( X77 != k2_xboole_0(X75,X76)
| r2_hidden(X79,X77)
| ~ r2_hidden(X79,X75) )
& ( X77 != k2_xboole_0(X75,X76)
| r2_hidden(X78,X76)
| r2_hidden(X78,X75)
| ~ r2_hidden(X78,X77) ) ),
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)],[d2_xboole_0])])])])])])]) ).
cnf(c_0_55,plain,
( ~ r2_hidden(k4_tarski(X1,X3),k2_zfmisc_1(X2,X4))
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_56,negated_conjecture,
r2_hidden(k4_tarski(esk1_0,esk2_0),k2_zfmisc_1(u1_struct_0(k1_latsum_1(esk3_0,esk4_0)),u1_struct_0(k1_latsum_1(esk3_0,esk4_0)))),
inference(sr,[status(thm)],[c_0_37,c_0_52]) ).
cnf(c_0_57,plain,
( ~ l1_orders_2(X2)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X1)
| ~ v1_orders_2(X1)
| X1 != k1_latsum_1(X2,X3)
| u1_struct_0(X1) = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,plain,
( ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| v1_orders_2(k1_latsum_1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_59,plain,
! [X43,X44,X45,X46] :
( r2_hidden(X46,u1_struct_0(X44))
| ~ r2_hidden(X45,u1_struct_0(X44))
| ~ r2_hidden(k4_tarski(X45,X46),u1_orders_2(k1_latsum_1(X43,X44)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X43),u1_struct_0(X44)),k1_zfmisc_1(u1_struct_0(X43)))
| ~ v13_waybel_0(k3_xboole_0(u1_struct_0(X43),u1_struct_0(X44)),X43)
| ~ l1_orders_2(X44)
| ~ l1_orders_2(X43) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_latsum_1])])])]) ).
cnf(c_0_60,plain,
( X2 != k2_xboole_0(X3,X4)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
r2_hidden(esk1_0,u1_struct_0(k1_latsum_1(esk3_0,esk4_0))),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X2)
| u1_struct_0(k1_latsum_1(X1,X2)) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_57]),c_0_28]),c_0_58]) ).
cnf(c_0_63,plain,
( ~ r2_hidden(X3,u1_struct_0(X2))
| ~ r2_hidden(k4_tarski(X3,X4),u1_orders_2(k1_latsum_1(X1,X2)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v13_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X1)
| ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| r2_hidden(X4,u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,negated_conjecture,
v13_waybel_0(k3_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0)),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_65,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0)),k1_zfmisc_1(u1_struct_0(esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_66,plain,
( ~ r2_hidden(X1,k2_xboole_0(X3,X2))
| r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_67,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_29]),c_0_30])]) ).
cnf(c_0_68,negated_conjecture,
( ~ r2_hidden(X2,u1_struct_0(esk4_0))
| ~ r2_hidden(k4_tarski(X2,X1),u1_orders_2(k1_latsum_1(esk3_0,esk4_0)))
| r2_hidden(X1,u1_struct_0(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_29]),c_0_30])]) ).
cnf(c_0_69,negated_conjecture,
( r2_hidden(esk1_0,u1_struct_0(esk3_0))
| r2_hidden(esk1_0,u1_struct_0(esk4_0)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( ~ r2_hidden(esk2_0,u1_struct_0(esk4_0))
| ~ r2_hidden(esk1_0,u1_struct_0(esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_71,plain,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
cnf(c_0_72,negated_conjecture,
( ~ r2_hidden(k4_tarski(esk1_0,X1),u1_orders_2(k1_latsum_1(esk3_0,esk4_0)))
| r2_hidden(X1,u1_struct_0(esk4_0))
| r2_hidden(esk1_0,u1_struct_0(esk3_0)) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( ~ r2_hidden(esk2_0,u1_struct_0(esk4_0))
| r2_hidden(esk1_0,u1_struct_0(esk3_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_69]) ).
fof(c_0_74,plain,
! [X19,X20,X21,X22,X23,X24,X25,X26] :
( ( X26 = k4_xboole_0(X24,X25)
| r2_hidden(esk5_3(X24,X25,X26),X26)
| ~ r2_hidden(esk5_3(X24,X25,X26),X25) )
& ( X26 = k4_xboole_0(X24,X25)
| r2_hidden(esk5_3(X24,X25,X26),X26)
| r2_hidden(esk5_3(X24,X25,X26),X24) )
& ( X26 = k4_xboole_0(X24,X25)
| r2_hidden(esk5_3(X24,X25,X26),X25)
| ~ r2_hidden(esk5_3(X24,X25,X26),X24)
| ~ r2_hidden(esk5_3(X24,X25,X26),X26) )
& ( X21 != k4_xboole_0(X19,X20)
| r2_hidden(X23,X21)
| r2_hidden(X23,X20)
| ~ r2_hidden(X23,X19) )
& ( X21 != k4_xboole_0(X19,X20)
| ~ r2_hidden(X22,X21)
| ~ r2_hidden(X22,X20) )
& ( X21 != k4_xboole_0(X19,X20)
| ~ r2_hidden(X22,X21)
| r2_hidden(X22,X19) ) ),
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)],[c_0_71])])])])])])]) ).
cnf(c_0_75,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_62]),c_0_29]),c_0_30])]) ).
cnf(c_0_76,negated_conjecture,
( ~ r2_hidden(esk2_0,u1_struct_0(esk3_0))
| ~ r2_hidden(esk1_0,u1_struct_0(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_77,negated_conjecture,
r2_hidden(esk1_0,u1_struct_0(esk3_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_24]),c_0_73]) ).
cnf(c_0_78,plain,
( X4 != k4_xboole_0(X2,X3)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( r2_hidden(esk2_0,u1_struct_0(esk3_0))
| r2_hidden(esk2_0,u1_struct_0(esk4_0)) ),
inference(spm,[status(thm)],[c_0_66,c_0_75]) ).
cnf(c_0_80,negated_conjecture,
~ r2_hidden(esk2_0,u1_struct_0(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_81,plain,
( ~ r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_82,negated_conjecture,
r2_hidden(esk2_0,u1_struct_0(esk4_0)),
inference(sr,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(u1_struct_0(esk4_0),u1_struct_0(esk3_0)))
| ~ r2_hidden(esk1_0,k4_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_84,negated_conjecture,
( r2_hidden(esk1_0,X1)
| r2_hidden(esk1_0,k4_xboole_0(u1_struct_0(esk3_0),X1)) ),
inference(spm,[status(thm)],[c_0_81,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
~ r2_hidden(esk1_0,u1_struct_0(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_82])]) ).
cnf(c_0_86,negated_conjecture,
( r2_hidden(esk2_0,X1)
| r2_hidden(esk2_0,u1_struct_0(esk3_0))
| r2_hidden(esk2_0,k4_xboole_0(u1_struct_0(esk4_0),X1)) ),
inference(spm,[status(thm)],[c_0_81,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
~ r2_hidden(esk2_0,k4_xboole_0(u1_struct_0(esk4_0),u1_struct_0(esk3_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( r2_hidden(esk2_0,X1)
| r2_hidden(esk2_0,k4_xboole_0(u1_struct_0(esk4_0),X1)) ),
inference(sr,[status(thm)],[c_0_86,c_0_80]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU412+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 06:27:22 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 200.26/29.79 % Version: 3.5.1
% 200.26/29.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.26/29.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.26/29.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.26/29.79 % Starting new_bool_3 with 300s (1) cores
% 200.26/29.79 % Starting new_bool_1 with 300s (1) cores
% 200.26/29.79 % Starting sh5l with 300s (1) cores
% 200.26/29.79 % new_bool_1 with pid 1748986 completed with status 0
% 200.26/29.79 % Result found by new_bool_1
% 200.26/29.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.26/29.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.26/29.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.26/29.79 % Starting new_bool_3 with 300s (1) cores
% 200.26/29.79 % Starting new_bool_1 with 300s (1) cores
% 200.26/29.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 200.26/29.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 200.26/29.79 % Search class: FGHSM-FFMM32-MFFFFFNN
% 200.26/29.79 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 200.26/29.79 % Starting SubtermCWHack with 28s (1) cores
% 200.26/29.79 % SubtermCWHack with pid 1748989 completed with status 8
% 200.26/29.79 % Starting new_bool_1 with 31s (1) cores
% 200.26/29.79 % new_bool_1 with pid 1749071 completed with status 0
% 200.26/29.79 % Result found by new_bool_1
% 200.26/29.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.26/29.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.26/29.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.26/29.79 % Starting new_bool_3 with 300s (1) cores
% 200.26/29.79 % Starting new_bool_1 with 300s (1) cores
% 200.26/29.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 200.26/29.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 200.26/29.79 % Search class: FGHSM-FFMM32-MFFFFFNN
% 200.26/29.79 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 200.26/29.79 % Starting SubtermCWHack with 28s (1) cores
% 200.26/29.79 % SubtermCWHack with pid 1748989 completed with status 8
% 200.26/29.79 % Starting new_bool_1 with 31s (1) cores
% 200.26/29.79 % Preprocessing time : 0.003 s
% 200.26/29.79 % Presaturation interreduction done
% 200.26/29.79
% 200.26/29.79 % Proof found!
% 200.26/29.79 % SZS status Theorem
% 200.26/29.79 % SZS output start CNFRefutation
% See solution above
% 200.26/29.79 % Parsed axioms : 57
% 200.26/29.79 % Removed by relevancy pruning/SinE : 15
% 200.26/29.79 % Initial clauses : 67
% 200.26/29.79 % Removed in clause preprocessing : 0
% 200.26/29.79 % Initial clauses in saturation : 67
% 200.26/29.79 % Processed clauses : 3037
% 200.26/29.79 % ...of these trivial : 74
% 200.26/29.79 % ...subsumed : 2116
% 200.26/29.79 % ...remaining for further processing : 847
% 200.26/29.79 % Other redundant clauses eliminated : 48
% 200.26/29.79 % Clauses deleted for lack of memory : 0
% 200.26/29.79 % Backward-subsumed : 49
% 200.26/29.79 % Backward-rewritten : 49
% 200.26/29.79 % Generated clauses : 12650
% 200.26/29.79 % ...of the previous two non-redundant : 11869
% 200.26/29.79 % ...aggressively subsumed : 0
% 200.26/29.79 % Contextual simplify-reflections : 18
% 200.26/29.79 % Paramodulations : 12578
% 200.26/29.79 % Factorizations : 8
% 200.26/29.79 % NegExts : 0
% 200.26/29.79 % Equation resolutions : 50
% 200.26/29.79 % Disequality decompositions : 0
% 200.26/29.79 % Total rewrite steps : 1071
% 200.26/29.79 % ...of those cached : 927
% 200.26/29.79 % Propositional unsat checks : 0
% 200.26/29.79 % Propositional check models : 0
% 200.26/29.79 % Propositional check unsatisfiable : 0
% 200.26/29.79 % Propositional clauses : 0
% 200.26/29.79 % Propositional clauses after purity: 0
% 200.26/29.79 % Propositional unsat core size : 0
% 200.26/29.79 % Propositional preprocessing time : 0.000
% 200.26/29.79 % Propositional encoding time : 0.000
% 200.26/29.79 % Propositional solver time : 0.000
% 200.26/29.79 % Success case prop preproc time : 0.000
% 200.26/29.79 % Success case prop encoding time : 0.000
% 200.26/29.79 % Success case prop solver time : 0.000
% 200.26/29.79 % Current number of processed clauses : 660
% 200.26/29.79 % Positive orientable unit clauses : 96
% 200.26/29.79 % Positive unorientable unit clauses: 2
% 200.26/29.79 % Negative unit clauses : 104
% 200.26/29.79 % Non-unit-clauses : 458
% 200.26/29.79 % Current number of unprocessed clauses: 8607
% 200.26/29.79 % ...number of literals in the above : 34780
% 200.26/29.79 % Current number of archived formulas : 0
% 200.26/29.79 % Current number of archived clauses : 179
% 200.26/29.79 % Clause-clause subsumption calls (NU) : 42060
% 200.26/29.79 % Rec. Clause-clause subsumption calls : 24413
% 200.26/29.79 % Non-unit clause-clause subsumptions : 1383
% 200.26/29.79 % Unit Clause-clause subsumption calls : 4022
% 200.26/29.79 % Rewrite failures with RHS unbound : 0
% 200.26/29.79 % BW rewrite match attempts : 133
% 200.26/29.79 % BW rewrite match successes : 40
% 200.26/29.79 % Condensation attempts : 0
% 200.26/29.79 % Condensation successes : 0
% 200.26/29.79 % Termbank termtop insertions : 172262
% 200.26/29.79 % Search garbage collected termcells : 1040
% 200.26/29.79
% 200.26/29.79 % -------------------------------------------------
% 200.26/29.79 % User time : 27.663 s
% 200.26/29.79 % System time : 0.981 s
% 200.26/29.79 % Total time : 28.644 s
% 200.26/29.79 % Maximum resident set size: 3692 pages
% 200.26/29.79
% 200.26/29.79 % -------------------------------------------------
% 200.26/29.79 % User time : 27.665 s
% 200.26/29.79 % System time : 0.990 s
% 200.26/29.79 % Total time : 28.654 s
% 200.26/29.79 % Maximum resident set size: 4864 pages
% 200.26/29.79 % E exiting
%------------------------------------------------------------------------------