%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU430+3 : 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 : n003.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 05:12:19 PM UTC 2026
% Result : Theorem 204.64s 167.95s
% Output : CNFRefutation 204.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 130 ( 53 unt; 0 def)
% Number of atoms : 302 ( 113 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 304 ( 132 ~; 103 |; 44 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-2 aty)
% Number of variables : 216 ( 19 sgn 118 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,axiom,
! [X1,X2] :
( ~ ( ~ r1_xboole_0(X1,X2)
& ! [X3] : ~ r2_hidden(X3,k3_xboole_0(X1,X2)) )
& ~ ( ? [X3] : r2_hidden(X3,k3_xboole_0(X1,X2))
& r1_xboole_0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',t4_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k3_xboole_0) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
=> k3_xboole_0(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t28_xboole_1) ).
fof(t79_xboole_1,axiom,
! [X1,X2] : r1_xboole_0(k4_xboole_0(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t79_xboole_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(t83_xboole_1,axiom,
! [X1,X2] :
( r1_xboole_0(X1,X2)
<=> k4_xboole_0(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t83_xboole_1) ).
fof(t30_relset_2,conjecture,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) )
& ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',fc1_subset_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = k1_zfmisc_1(X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> r1_tarski(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',d1_zfmisc_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( r1_xboole_0(X1,X2)
<=> k3_xboole_0(X1,X2) = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d7_xboole_0) ).
fof(t3_xboole_0,axiom,
! [X1,X2] :
( ~ ( ~ r1_xboole_0(X1,X2)
& ! [X3] :
~ ( r2_hidden(X3,X1)
& r2_hidden(X3,X2) ) )
& ~ ( ? [X3] :
( r2_hidden(X3,X1)
& r2_hidden(X3,X2) )
& r1_xboole_0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',t3_xboole_0) ).
fof(t91_orders_1,axiom,
! [X1] :
( ~ ( ? [X2] :
( X2 != k1_xboole_0
& r2_hidden(X2,X1) )
& k3_tarski(X1) = k1_xboole_0 )
& ~ ( k3_tarski(X1) != k1_xboole_0
& ! [X2] :
~ ( X2 != k1_xboole_0
& r2_hidden(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+59.ax',t91_orders_1) ).
fof(t51_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(k3_xboole_0(X1,X2),k4_xboole_0(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t51_xboole_1) ).
fof(t93_zfmisc_1,axiom,
! [X1,X2] : k3_tarski(k2_tarski(X1,X2)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t93_zfmisc_1) ).
fof(t39_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t39_xboole_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> k5_setfam_1(X1,X2) = k3_tarski(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+8.ax',redefinition_k5_setfam_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d1_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t2_boole) ).
fof(t100_zfmisc_1,axiom,
! [X1] : r1_tarski(X1,k1_zfmisc_1(k3_tarski(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t100_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( r1_tarski(X1,X2)
& r1_tarski(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d10_xboole_0) ).
fof(t63_subset_1,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(k1_tarski(X1),k1_zfmisc_1(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',t63_subset_1) ).
fof(t69_enumset1,axiom,
! [X1] : k2_tarski(X1,X1) = k1_tarski(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+5.ax',t69_enumset1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+1.ax',reflexivity_r1_tarski) ).
fof(t1_zfmisc_1,axiom,
k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t1_zfmisc_1) ).
fof(t99_zfmisc_1,axiom,
! [X1] : k3_tarski(k1_zfmisc_1(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t99_zfmisc_1) ).
fof(c_0_26,plain,
! [X1,X2] :
( ~ ( ~ r1_xboole_0(X1,X2)
& ! [X3] : ~ r2_hidden(X3,k3_xboole_0(X1,X2)) )
& ~ ( ? [X3] : r2_hidden(X3,k3_xboole_0(X1,X2))
& r1_xboole_0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_27,plain,
! [X1782,X1783,X1785,X1786,X1787] :
( ( r1_xboole_0(X1782,X1783)
| r2_hidden(esk55_2(X1782,X1783),k3_xboole_0(X1782,X1783)) )
& ( ~ r2_hidden(X1787,k3_xboole_0(X1785,X1786))
| ~ r1_xboole_0(X1785,X1786) ) ),
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_26])])])])]) ).
fof(c_0_28,plain,
! [X2780,X2781] : k3_xboole_0(X2780,X2781) = k3_xboole_0(X2781,X2780),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_29,plain,
( ~ r2_hidden(X1,k3_xboole_0(X2,X3))
| ~ r1_xboole_0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_31,plain,
! [X2806,X2807] :
( ~ r1_tarski(X2806,X2807)
| k3_xboole_0(X2806,X2807) = X2806 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
cnf(c_0_32,plain,
( ~ r1_xboole_0(X1,X2)
| ~ r2_hidden(X3,k3_xboole_0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( k3_xboole_0(X1,X2) = X1
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_34,plain,
! [X1837,X1838] : r1_xboole_0(k4_xboole_0(X1837,X1838),X1838),
inference(variable_rename,[status(thm)],[t79_xboole_1]) ).
cnf(c_0_35,plain,
( ~ r1_xboole_0(X1,X2)
| ~ r1_tarski(X2,X1)
| ~ r2_hidden(X3,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
r1_xboole_0(k4_xboole_0(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_37,plain,
! [X1599,X1600] :
( ( ~ m1_subset_1(X1599,k1_zfmisc_1(X1600))
| r1_tarski(X1599,X1600) )
& ( ~ r1_tarski(X1599,X1600)
| m1_subset_1(X1599,k1_zfmisc_1(X1600)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_38,plain,
( ~ r1_tarski(X1,k4_xboole_0(X2,X1))
| ~ r2_hidden(X3,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_40,plain,
! [X1847,X1848] :
( ( ~ r1_xboole_0(X1847,X1848)
| k4_xboole_0(X1847,X1848) = X1847 )
& ( k4_xboole_0(X1847,X1848) != X1847
| r1_xboole_0(X1847,X1848) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(c_0_41,negated_conjecture,
~ ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
inference(assume_negation,[status(cth)],[t30_relset_2]) ).
fof(c_0_42,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) )
& ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_43,plain,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_44,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(k4_xboole_0(X2,X1)))
| ~ r2_hidden(X3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( k4_xboole_0(X1,X2) = X1
| ~ r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_46,negated_conjecture,
! [X1400] :
( m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
& ( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| ~ r2_hidden(X1400,esk2_0)
| X1400 = k1_xboole_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])]) ).
fof(c_0_47,plain,
! [X1582,X1583,X1584,X1585,X1586,X1587] :
( ( ~ r2_hidden(X1584,X1583)
| r1_tarski(X1584,X1582)
| X1583 != k1_zfmisc_1(X1582) )
& ( ~ r1_tarski(X1585,X1582)
| r2_hidden(X1585,X1583)
| X1583 != k1_zfmisc_1(X1582) )
& ( ~ r2_hidden(esk31_2(X1586,X1587),X1587)
| ~ r1_tarski(esk31_2(X1586,X1587),X1586)
| X1587 = k1_zfmisc_1(X1586) )
& ( r2_hidden(esk31_2(X1586,X1587),X1587)
| r1_tarski(esk31_2(X1586,X1587),X1586)
| X1587 = k1_zfmisc_1(X1586) ) ),
inference(distribute,[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)],[d1_zfmisc_1])])])])])]) ).
fof(c_0_48,plain,
! [X1469,X1470] :
( ( ~ m1_subset_1(X1470,X1469)
| r2_hidden(X1470,X1469)
| v1_xboole_0(X1469) )
& ( ~ r2_hidden(X1470,X1469)
| m1_subset_1(X1470,X1469)
| v1_xboole_0(X1469) )
& ( ~ m1_subset_1(X1470,X1469)
| v1_xboole_0(X1470)
| ~ v1_xboole_0(X1469) )
& ( ~ v1_xboole_0(X1470)
| m1_subset_1(X1470,X1469)
| ~ v1_xboole_0(X1469) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
fof(c_0_49,plain,
! [X1560] : ~ v1_xboole_0(k1_zfmisc_1(X1560)),
inference(variable_rename,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_xboole_0(X2,X1)
| ~ r2_hidden(X3,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_52,plain,
! [X1774,X1775] :
( ( ~ r1_xboole_0(X1774,X1775)
| k3_xboole_0(X1774,X1775) = k1_xboole_0 )
& ( k3_xboole_0(X1774,X1775) != k1_xboole_0
| r1_xboole_0(X1774,X1775) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_53,plain,
( r1_tarski(X1,X3)
| ~ r2_hidden(X1,X2)
| X2 != k1_zfmisc_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( ~ r1_xboole_0(k1_zfmisc_1(esk1_0),esk2_0)
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( r1_xboole_0(X1,X2)
| k3_xboole_0(X1,X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
( r1_tarski(X1,X2)
| ~ r2_hidden(X1,k1_zfmisc_1(X2)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_59,negated_conjecture,
r2_hidden(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_55]) ).
fof(c_0_60,plain,
! [X1,X2] :
( ~ ( ~ r1_xboole_0(X1,X2)
& ! [X3] :
~ ( r2_hidden(X3,X1)
& r2_hidden(X3,X2) ) )
& ~ ( ? [X3] :
( r2_hidden(X3,X1)
& r2_hidden(X3,X2) )
& r1_xboole_0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
fof(c_0_61,plain,
! [X1733,X1734,X1735] :
( ( X1734 = k1_xboole_0
| ~ r2_hidden(X1734,X1733)
| k3_tarski(X1733) != k1_xboole_0 )
& ( esk51_1(X1735) != k1_xboole_0
| k3_tarski(X1735) = k1_xboole_0 )
& ( r2_hidden(esk51_1(X1735),X1735)
| k3_tarski(X1735) = k1_xboole_0 ) ),
inference(distribute,[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)],[t91_orders_1])])])])])]) ).
cnf(c_0_62,negated_conjecture,
( k3_xboole_0(esk2_0,k1_zfmisc_1(esk1_0)) != k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_30]) ).
cnf(c_0_63,negated_conjecture,
r1_tarski(esk2_0,k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_64,plain,
! [X1776,X1777,X1779,X1780,X1781] :
( ( r2_hidden(esk54_2(X1776,X1777),X1776)
| r1_xboole_0(X1776,X1777) )
& ( r2_hidden(esk54_2(X1776,X1777),X1777)
| r1_xboole_0(X1776,X1777) )
& ( ~ r2_hidden(X1781,X1779)
| ~ r2_hidden(X1781,X1780)
| ~ r1_xboole_0(X1779,X1780) ) ),
inference(distribute,[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_60])])])])])]) ).
fof(c_0_65,plain,
! [X2676,X2677] : k2_xboole_0(k3_xboole_0(X2676,X2677),k4_xboole_0(X2676,X2677)) = X2676,
inference(variable_rename,[status(thm)],[t51_xboole_1]) ).
fof(c_0_66,plain,
! [X1699,X1700] : k3_tarski(k2_tarski(X1699,X1700)) = k2_xboole_0(X1699,X1700),
inference(variable_rename,[status(thm)],[t93_zfmisc_1]) ).
fof(c_0_67,plain,
! [X2656,X2657] : k2_xboole_0(X2656,k4_xboole_0(X2657,X2656)) = k2_xboole_0(X2656,X2657),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_68,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| X1 = k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_69,plain,
( r2_hidden(esk51_1(X1),X1)
| k3_tarski(X1) = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
( k3_tarski(X1) = k1_xboole_0
| esk51_1(X1) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_71,plain,
! [X1512,X1513] :
( ~ m1_subset_1(X1513,k1_zfmisc_1(k1_zfmisc_1(X1512)))
| k5_setfam_1(X1512,X1513) = k3_tarski(X1513) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(c_0_72,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_73,negated_conjecture,
( esk2_0 != k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_33]),c_0_63])]) ).
cnf(c_0_74,plain,
( r2_hidden(esk54_2(X1,X2),X1)
| r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,plain,
k2_xboole_0(k3_xboole_0(X1,X2),k4_xboole_0(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,plain,
k3_tarski(k2_tarski(X1,X2)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_77,plain,
! [X2783] : k3_xboole_0(X2783,k1_xboole_0) = k1_xboole_0,
inference(variable_rename,[status(thm)],[t2_boole]) ).
cnf(c_0_78,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_79,plain,
! [X1714] : r1_tarski(X1714,k1_zfmisc_1(k3_tarski(X1714))),
inference(variable_rename,[status(thm)],[t100_zfmisc_1]) ).
cnf(c_0_80,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| k3_tarski(esk2_0) = k1_xboole_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_81,plain,
( k5_setfam_1(X2,X1) = k3_tarski(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_82,plain,
! [X1401,X1402,X1403] :
( ( X1401 != k1_xboole_0
| ~ r2_hidden(X1402,X1401) )
& ( r2_hidden(esk4_1(X1403),X1403)
| X1403 = k1_xboole_0 ) ),
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_72])])])])]) ).
cnf(c_0_83,plain,
( k3_xboole_0(X1,X2) = k1_xboole_0
| ~ r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_84,negated_conjecture,
( r1_xboole_0(esk2_0,X1)
| esk2_0 != k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_85,plain,
k3_tarski(k2_tarski(k3_xboole_0(X1,X2),k4_xboole_0(X1,X2))) = X1,
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_86,plain,
k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_87,plain,
k3_tarski(k2_tarski(X1,k4_xboole_0(X2,X1))) = k3_tarski(k2_tarski(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_76]),c_0_76]) ).
fof(c_0_88,plain,
! [X1577,X1578] :
( ( r1_tarski(X1577,X1578)
| X1577 != X1578 )
& ( r1_tarski(X1578,X1577)
| X1577 != X1578 )
& ( ~ r1_tarski(X1577,X1578)
| ~ r1_tarski(X1578,X1577)
| X1577 = X1578 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_89,plain,
r1_tarski(X1,k1_zfmisc_1(k3_tarski(X1))),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_90,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| k5_setfam_1(X1,esk2_0) = k1_xboole_0
| ~ m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(X1))) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
fof(c_0_91,plain,
! [X2417,X2418] :
( ~ r2_hidden(X2417,X2418)
| m1_subset_1(k1_tarski(X2417),k1_zfmisc_1(X2418)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_subset_1])]) ).
fof(c_0_92,plain,
! [X2478] : k2_tarski(X2478,X2478) = k1_tarski(X2478),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
cnf(c_0_93,plain,
( X1 = k1_xboole_0
| ~ r2_hidden(X1,X2)
| k3_tarski(X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_94,plain,
( r2_hidden(esk4_1(X1),X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_95,negated_conjecture,
( k3_xboole_0(esk2_0,X1) = k1_xboole_0
| esk2_0 != k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_96,plain,
k3_tarski(k2_tarski(k1_xboole_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
fof(c_0_97,plain,
! [X1576] : r1_tarski(X1576,X1576),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_98,plain,
( X1 = X2
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_99,plain,
( r1_tarski(X1,k1_zfmisc_1(k5_setfam_1(X2,X1)))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(spm,[status(thm)],[c_0_89,c_0_81]) ).
cnf(c_0_100,negated_conjecture,
k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_90,c_0_51]) ).
cnf(c_0_101,plain,
( m1_subset_1(k1_tarski(X1),k1_zfmisc_1(X2))
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_102,plain,
k2_tarski(X1,X1) = k1_tarski(X1),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_103,plain,
k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
cnf(c_0_104,plain,
( esk4_1(X1) = k1_xboole_0
| X1 = k1_xboole_0
| k3_tarski(X1) != k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_105,negated_conjecture,
( k4_xboole_0(esk2_0,X1) = esk2_0
| esk2_0 != k1_xboole_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_95]),c_0_96]) ).
cnf(c_0_106,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_107,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_108,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_109,plain,
( X1 = X2
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_39]) ).
cnf(c_0_110,negated_conjecture,
r1_tarski(esk2_0,k1_zfmisc_1(k1_xboole_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_51])]) ).
cnf(c_0_111,plain,
( m1_subset_1(k2_tarski(X1,X1),k1_zfmisc_1(X2))
| ~ r2_hidden(X1,X2) ),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_112,plain,
k1_zfmisc_1(k1_xboole_0) = k2_tarski(k1_xboole_0,k1_xboole_0),
inference(rw,[status(thm)],[c_0_103,c_0_102]) ).
cnf(c_0_113,plain,
( X1 = k1_xboole_0
| r2_hidden(k1_xboole_0,X1)
| k3_tarski(X1) != k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_94,c_0_104]) ).
cnf(c_0_114,negated_conjecture,
( esk2_0 != k1_xboole_0
| ~ m1_subset_1(X1,k1_zfmisc_1(esk2_0))
| ~ r2_hidden(X2,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_105]) ).
cnf(c_0_115,negated_conjecture,
r2_hidden(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_100])]) ).
cnf(c_0_116,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_117,negated_conjecture,
( k1_zfmisc_1(k1_xboole_0) = esk2_0
| ~ m1_subset_1(k1_zfmisc_1(k1_xboole_0),k1_zfmisc_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_118,plain,
( m1_subset_1(k1_zfmisc_1(k1_xboole_0),k1_zfmisc_1(X1))
| ~ r2_hidden(k1_xboole_0,X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,plain,
( X1 = k1_xboole_0
| r2_hidden(k1_xboole_0,X1)
| k5_setfam_1(X2,X1) != k1_xboole_0
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(spm,[status(thm)],[c_0_113,c_0_81]) ).
cnf(c_0_120,negated_conjecture,
esk2_0 != k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]) ).
cnf(c_0_121,negated_conjecture,
( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_122,plain,
! [X1713] : k3_tarski(k1_zfmisc_1(X1713)) = X1713,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
cnf(c_0_123,negated_conjecture,
( k1_zfmisc_1(k1_xboole_0) = esk2_0
| ~ r2_hidden(k1_xboole_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_124,negated_conjecture,
r2_hidden(k1_xboole_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_100]),c_0_51])]),c_0_120]) ).
cnf(c_0_125,negated_conjecture,
esk3_0 != k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_100])]) ).
cnf(c_0_126,plain,
k3_tarski(k1_zfmisc_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_127,negated_conjecture,
k1_zfmisc_1(k1_xboole_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_128,negated_conjecture,
k3_tarski(esk2_0) != k1_xboole_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_115]),c_0_125]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU430+3 : 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
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 03:12:29 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 204.64/167.95 % Version : CSE_E---1.7
% 204.64/167.95 % Problem : theBenchmark.p
% 204.64/167.95 % SZS status Theorem for theBenchmark.p
% 204.64/167.95 % SZS output start CNFRefutation
% See solution above
% 204.94/168.24 % Total time : 156.805s
%------------------------------------------------------------------------------