%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:23:58 PM UTC 2026
% Result : Theorem 48.88s 7.66s
% Output : CNFRefutation 48.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 135 ( 65 unt; 0 def)
% Number of atoms : 268 ( 101 equ)
% Maximal formula atoms : 20 ( 1 avg)
% Number of connectives : 227 ( 94 ~; 95 |; 19 &)
% ( 11 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 256 ( 19 sgn 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(l3_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(t8_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X3,X2)
& subset(X1,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(c_0_22,lemma,
! [X84,X85] :
( ( set_difference(X84,X85) = empty_set
| ~ subset(X84,X85) )
& ( subset(X84,X85)
| set_difference(X84,X85) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])]) ).
fof(c_0_23,lemma,
! [X115,X116,X117] :
( subset(set_difference(X115,X117),set_difference(X116,X117))
| ~ subset(X115,X116) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])])]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1) ) ),
inference(assume_negation,[status(cth)],[l3_zfmisc_1]) ).
fof(c_0_25,plain,
! [X13,X14] : set_intersection2(X13,X14) = set_intersection2(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_26,lemma,
! [X136,X137] : set_difference(X136,set_difference(X136,X137)) = set_intersection2(X136,X137),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
cnf(c_0_27,lemma,
( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,lemma,
( ~ subset(X1,X2)
| subset(set_difference(X1,X3),set_difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,negated_conjecture,
( ~ subset(esk8_0,set_difference(esk9_0,singleton(esk10_0)))
& ~ in(esk10_0,esk8_0)
& subset(esk8_0,esk9_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_30,lemma,
! [X154,X155] : subset(X154,set_union2(X154,X155)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_31,lemma,
! [X160,X161,X162] :
( subset(set_union2(X160,X162),X161)
| ~ subset(X162,X161)
| ~ subset(X160,X161) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])])]) ).
fof(c_0_32,lemma,
! [X102,X103,X104] :
( subset(X102,X104)
| ~ subset(X103,X104)
| ~ subset(X102,X103) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
fof(c_0_33,plain,
! [X46,X47,X48,X49,X50] :
( ( subset(X49,X50)
| ~ in(esk5_2(X49,X50),X50) )
& ( subset(X49,X50)
| in(esk5_2(X49,X50),X49) )
& ( in(X48,X47)
| ~ in(X48,X46)
| ~ subset(X46,X47) ) ),
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_tarski])])])])])])]) ).
fof(c_0_34,lemma,
! [X118,X119] : subset(set_difference(X118,X119),X118),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_35,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,lemma,
( ~ subset(X1,X3)
| set_difference(set_difference(X1,X2),set_difference(X3,X2)) = empty_set ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
subset(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_40,plain,
! [X124] : set_difference(X124,empty_set) = X124,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_41,lemma,
( ~ subset(X3,X2)
| ~ subset(X1,X2)
| subset(set_union2(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_42,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_43,lemma,
! [X150] : unordered_pair(X150,X150) = singleton(X150),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
cnf(c_0_44,lemma,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
( subset(X1,X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_48,negated_conjecture,
set_difference(set_difference(esk8_0,X1),set_difference(esk9_0,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_49,lemma,
set_difference(X1,set_union2(X1,X2)) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_50,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_51,lemma,
! [X94,X95] :
( set_union2(X94,X95) = X95
| ~ subset(X94,X95) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])]) ).
fof(c_0_52,lemma,
! [X132,X133] : set_difference(set_union2(X132,X133),X133) = set_difference(X132,X133),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(c_0_53,plain,
! [X11,X12] : set_union2(X11,X12) = set_union2(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_54,lemma,
( ~ subset(X1,X3)
| ~ subset(X2,X3)
| set_difference(set_union2(X1,X2),X3) = empty_set ),
inference(spm,[status(thm)],[c_0_27,c_0_41]) ).
fof(c_0_55,plain,
! [X61,X62,X63,X64,X65,X66,X67,X68] :
( ( X68 = set_difference(X66,X67)
| in(esk7_3(X66,X67,X68),X68)
| ~ in(esk7_3(X66,X67,X68),X67) )
& ( X68 = set_difference(X66,X67)
| in(esk7_3(X66,X67,X68),X68)
| in(esk7_3(X66,X67,X68),X66) )
& ( X68 = set_difference(X66,X67)
| in(esk7_3(X66,X67,X68),X67)
| ~ in(esk7_3(X66,X67,X68),X66)
| ~ in(esk7_3(X66,X67,X68),X68) )
& ( X63 != set_difference(X61,X62)
| in(X65,X63)
| in(X65,X62)
| ~ in(X65,X61) )
& ( X63 != set_difference(X61,X62)
| ~ in(X64,X63)
| ~ in(X64,X62) )
& ( X63 != set_difference(X61,X62)
| ~ in(X64,X63)
| in(X64,X61) ) ),
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_42])])])])])])]) ).
cnf(c_0_56,negated_conjecture,
~ subset(esk8_0,set_difference(esk9_0,singleton(esk10_0))),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_57,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_58,lemma,
( ~ subset(X1,X3)
| in(esk5_2(X3,X2),X3)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_59,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_60,lemma,
set_difference(esk8_0,set_union2(esk9_0,X1)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_61,lemma,
( ~ subset(X1,X2)
| set_union2(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,lemma,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_63,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,negated_conjecture,
( ~ subset(X1,esk9_0)
| set_difference(set_union2(X1,esk8_0),esk9_0) = empty_set ),
inference(spm,[status(thm)],[c_0_54,c_0_38]) ).
fof(c_0_66,lemma,
! [X108,X109] :
( set_intersection2(X108,X109) = X108
| ~ subset(X108,X109) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])]) ).
fof(c_0_67,lemma,
! [X82,X83] :
( ( subset(singleton(X82),X83)
| ~ in(X82,X83) )
& ( in(X82,X83)
| ~ subset(singleton(X82),X83) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])]) ).
fof(c_0_68,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( X22 = singleton(X21)
| esk1_2(X21,X22) = X21
| in(esk1_2(X21,X22),X22) )
& ( X22 = singleton(X21)
| esk1_2(X21,X22) != X21
| ~ in(esk1_2(X21,X22),X22) )
& ( X18 != singleton(X17)
| in(X20,X18)
| X20 != X17 )
& ( X18 != singleton(X17)
| X19 = X17
| ~ in(X19,X18) ) ),
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)],[d1_tarski])])])])])])]) ).
cnf(c_0_69,plain,
( X4 != set_difference(X2,X3)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,negated_conjecture,
~ subset(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_71,negated_conjecture,
( in(esk5_2(esk9_0,X1),esk9_0)
| subset(esk8_0,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_38]) ).
cnf(c_0_72,lemma,
subset(esk8_0,set_union2(esk9_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_50]) ).
cnf(c_0_73,lemma,
( set_difference(X1,X2) != empty_set
| set_union2(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_74,lemma,
set_difference(set_union2(X1,X2),X1) = set_difference(X2,X1),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_75,lemma,
set_difference(set_union2(esk8_0,set_difference(esk9_0,X1)),esk9_0) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_46]),c_0_64]) ).
cnf(c_0_76,lemma,
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,lemma,
( ~ in(X1,X2)
| subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_79,plain,
( ~ in(esk5_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_80,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_81,negated_conjecture,
in(esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),esk9_0),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_82,lemma,
( set_difference(esk9_0,X1) != empty_set
| subset(esk8_0,X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,lemma,
( ~ subset(set_union2(X2,X1),X3)
| subset(set_difference(X1,X2),set_difference(X3,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_74]) ).
cnf(c_0_84,lemma,
subset(set_union2(esk8_0,set_difference(esk9_0,X1)),esk9_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_75]),c_0_50]) ).
cnf(c_0_85,lemma,
( ~ subset(X1,X2)
| set_difference(X1,set_difference(X1,X2)) = X1 ),
inference(rw,[status(thm)],[c_0_76,c_0_36]) ).
cnf(c_0_86,lemma,
( ~ in(X1,X2)
| subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[c_0_77,c_0_57]) ).
cnf(c_0_87,plain,
( ~ in(X1,X2)
| X2 != unordered_pair(X3,X3)
| X1 = X3 ),
inference(rw,[status(thm)],[c_0_78,c_0_57]) ).
cnf(c_0_88,lemma,
( ~ in(esk5_2(X1,X2),X2)
| set_difference(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_27,c_0_79]) ).
cnf(c_0_89,negated_conjecture,
( in(esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),X1)
| in(esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),set_difference(esk9_0,X1)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,negated_conjecture,
set_difference(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))) != empty_set,
inference(spm,[status(thm)],[c_0_70,c_0_82]) ).
cnf(c_0_91,plain,
( X3 != set_difference(X4,X2)
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_92,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_93,lemma,
( ~ subset(X1,set_difference(X2,X3))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_94,lemma,
subset(set_difference(set_difference(esk9_0,X1),esk8_0),set_difference(esk9_0,esk8_0)),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_95,lemma,
( ~ in(X1,X2)
| set_difference(unordered_pair(X1,X1),set_difference(unordered_pair(X1,X1),X2)) = unordered_pair(X1,X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_96,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_97,lemma,
in(esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),unordered_pair(esk10_0,esk10_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_98,lemma,
( ~ subset(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_99,plain,
( ~ in(X1,X3)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_91]) ).
fof(c_0_100,plain,
! [X24,X25,X26] :
( ( X26 = empty_set
| in(esk2_1(X26),X26) )
& ( ~ in(X25,X24)
| X24 != empty_set ) ),
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_92])])])])])]) ).
cnf(c_0_101,lemma,
subset(set_difference(set_difference(esk9_0,X1),esk8_0),esk9_0),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_102,lemma,
set_difference(esk9_0,set_difference(esk9_0,unordered_pair(esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0)))))) = unordered_pair(esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))),esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_81]),c_0_47]) ).
cnf(c_0_103,lemma,
esk5_2(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))) = esk10_0,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,lemma,
( ~ subset(unordered_pair(X1,X1),X2)
| in(X1,X2) ),
inference(rw,[status(thm)],[c_0_98,c_0_57]) ).
cnf(c_0_105,plain,
( X3 != set_difference(X2,X4)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_106,plain,
( ~ in(X1,set_difference(X3,X2))
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(spm,[status(thm)],[c_0_99,c_0_47]) ).
cnf(c_0_107,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_108,lemma,
set_difference(set_difference(set_difference(esk9_0,X1),esk8_0),esk9_0) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_101]) ).
cnf(c_0_109,lemma,
set_difference(esk9_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))) = unordered_pair(esk10_0,esk10_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103]),c_0_103]),c_0_103]),c_0_103]) ).
cnf(c_0_110,negated_conjecture,
~ in(esk10_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_111,lemma,
( set_difference(unordered_pair(X1,X1),X2) != empty_set
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_104,c_0_62]) ).
cnf(c_0_112,plain,
( ~ in(X1,set_difference(X2,X3))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_105]) ).
fof(c_0_113,lemma,
! [X122,X123] : set_union2(X122,set_difference(X123,X122)) = set_union2(X122,X123),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_114,plain,
( ~ in(esk2_1(set_difference(X1,set_difference(X1,X2))),set_difference(X2,X1))
| set_difference(X1,set_difference(X1,X2)) = empty_set ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_115,lemma,
set_difference(set_difference(unordered_pair(esk10_0,esk10_0),esk8_0),esk9_0) = empty_set,
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,negated_conjecture,
set_difference(unordered_pair(esk10_0,esk10_0),esk8_0) != empty_set,
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_117,plain,
( in(esk2_1(set_difference(X1,X2)),X1)
| set_difference(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_112,c_0_107]) ).
cnf(c_0_118,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_119,lemma,
~ in(esk2_1(set_difference(unordered_pair(esk10_0,esk10_0),esk8_0)),set_difference(esk9_0,set_difference(unordered_pair(esk10_0,esk10_0),esk8_0))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_50]),c_0_50]),c_0_116]) ).
cnf(c_0_120,plain,
( set_difference(unordered_pair(X1,X1),X2) = empty_set
| esk2_1(set_difference(unordered_pair(X1,X1),X2)) = X1 ),
inference(spm,[status(thm)],[c_0_96,c_0_117]) ).
fof(c_0_121,plain,
! [X101] : set_union2(X101,empty_set) = X101,
inference(variable_rename,[status(thm)],[t1_boole]) ).
cnf(c_0_122,lemma,
set_difference(set_union2(X1,X2),set_difference(X2,X1)) = set_difference(X1,set_difference(X2,X1)),
inference(spm,[status(thm)],[c_0_63,c_0_118]) ).
cnf(c_0_123,lemma,
~ in(esk10_0,set_difference(esk9_0,set_difference(unordered_pair(esk10_0,esk10_0),esk8_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_116]) ).
cnf(c_0_124,negated_conjecture,
( in(esk10_0,X1)
| in(esk10_0,set_difference(esk9_0,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_103]),c_0_103]) ).
cnf(c_0_125,lemma,
set_difference(set_difference(X1,X2),X1) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_126,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_127,lemma,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_74]),c_0_122]),c_0_49]),c_0_50]) ).
cnf(c_0_128,lemma,
( ~ in(X1,X2)
| set_union2(unordered_pair(X1,X1),X2) = X2 ),
inference(spm,[status(thm)],[c_0_61,c_0_86]) ).
cnf(c_0_129,negated_conjecture,
in(esk10_0,set_difference(unordered_pair(esk10_0,esk10_0),esk8_0)),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_130,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_125]),c_0_126]) ).
cnf(c_0_131,lemma,
set_difference(esk8_0,set_difference(esk9_0,set_difference(X1,esk8_0))) = empty_set,
inference(spm,[status(thm)],[c_0_48,c_0_127]) ).
cnf(c_0_132,lemma,
set_difference(unordered_pair(esk10_0,esk10_0),esk8_0) = unordered_pair(esk10_0,esk10_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_133,negated_conjecture,
set_difference(esk8_0,set_difference(esk9_0,unordered_pair(esk10_0,esk10_0))) != empty_set,
inference(spm,[status(thm)],[c_0_70,c_0_62]) ).
cnf(c_0_134,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:52:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 48.88/7.66 % Version: 3.5.1
% 48.88/7.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 48.88/7.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.88/7.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 48.88/7.66 % Starting new_bool_3 with 300s (1) cores
% 48.88/7.66 % Starting new_bool_1 with 300s (1) cores
% 48.88/7.66 % Starting sh5l with 300s (1) cores
% 48.88/7.66 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 988615 completed with status 0
% 48.88/7.66 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 48.88/7.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 48.88/7.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.88/7.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 48.88/7.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.88/7.66 % No SInE strategy applied
% 48.88/7.66 % Search class: FGHSM-FFMS32-SFFFFFNN
% 48.88/7.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.88/7.66 % Starting SubtermCWHack with 136s (1) cores
% 48.88/7.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 48.88/7.66 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 48.88/7.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 48.88/7.66 % Starting new_bool_3 with 136s (1) cores
% 48.88/7.66 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with pid 988625 completed with status 0
% 48.88/7.66 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I
% 48.88/7.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 48.88/7.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.88/7.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 48.88/7.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.88/7.66 % No SInE strategy applied
% 48.88/7.66 % Search class: FGHSM-FFMS32-SFFFFFNN
% 48.88/7.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.88/7.66 % Starting SubtermCWHack with 136s (1) cores
% 48.88/7.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 48.88/7.66 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 48.88/7.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 48.88/7.66 % Preprocessing time : 0.004 s
% 48.88/7.66 % Presaturation interreduction done
% 48.88/7.66
% 48.88/7.66 % Proof found!
% 48.88/7.66 % SZS status Theorem
% 48.88/7.66 % SZS output start CNFRefutation
% See solution above
% 48.88/7.67 % Parsed axioms : 66
% 48.88/7.67 % Removed by relevancy pruning/SinE : 0
% 48.88/7.67 % Initial clauses : 107
% 48.88/7.67 % Removed in clause preprocessing : 8
% 48.88/7.67 % Initial clauses in saturation : 99
% 48.88/7.67 % Processed clauses : 35768
% 48.88/7.67 % ...of these trivial : 528
% 48.88/7.67 % ...subsumed : 31453
% 48.88/7.67 % ...remaining for further processing : 3787
% 48.88/7.67 % Other redundant clauses eliminated : 2326
% 48.88/7.67 % Clauses deleted for lack of memory : 0
% 48.88/7.67 % Backward-subsumed : 809
% 48.88/7.67 % Backward-rewritten : 130
% 48.88/7.67 % Generated clauses : 382588
% 48.88/7.67 % ...of the previous two non-redundant : 339932
% 48.88/7.67 % ...aggressively subsumed : 0
% 48.88/7.67 % Contextual simplify-reflections : 25
% 48.88/7.67 % Paramodulations : 379795
% 48.88/7.67 % Factorizations : 444
% 48.88/7.67 % NegExts : 0
% 48.88/7.67 % Equation resolutions : 2326
% 48.88/7.67 % Disequality decompositions : 0
% 48.88/7.67 % Total rewrite steps : 208874
% 48.88/7.67 % ...of those cached : 202133
% 48.88/7.67 % Propositional unsat checks : 0
% 48.88/7.67 % Propositional check models : 0
% 48.88/7.67 % Propositional check unsatisfiable : 0
% 48.88/7.67 % Propositional clauses : 0
% 48.88/7.67 % Propositional clauses after purity: 0
% 48.88/7.67 % Propositional unsat core size : 0
% 48.88/7.67 % Propositional preprocessing time : 0.000
% 48.88/7.67 % Propositional encoding time : 0.000
% 48.88/7.67 % Propositional solver time : 0.000
% 48.88/7.67 % Success case prop preproc time : 0.000
% 48.88/7.67 % Success case prop encoding time : 0.000
% 48.88/7.67 % Success case prop solver time : 0.000
% 48.88/7.67 % Current number of processed clauses : 2711
% 48.88/7.67 % Positive orientable unit clauses : 250
% 48.88/7.67 % Positive unorientable unit clauses: 3
% 48.88/7.67 % Negative unit clauses : 369
% 48.88/7.67 % Non-unit-clauses : 2089
% 48.88/7.67 % Current number of unprocessed clauses: 302657
% 48.88/7.67 % ...number of literals in the above : 1000518
% 48.88/7.67 % Current number of archived formulas : 0
% 48.88/7.67 % Current number of archived clauses : 1056
% 48.88/7.67 % Clause-clause subsumption calls (NU) : 600152
% 48.88/7.67 % Rec. Clause-clause subsumption calls : 392940
% 48.88/7.67 % Non-unit clause-clause subsumptions : 9533
% 48.88/7.67 % Unit Clause-clause subsumption calls : 55242
% 48.88/7.67 % Rewrite failures with RHS unbound : 0
% 48.88/7.67 % BW rewrite match attempts : 413
% 48.88/7.67 % BW rewrite match successes : 85
% 48.88/7.67 % Condensation attempts : 0
% 48.88/7.67 % Condensation successes : 0
% 48.88/7.67 % Termbank termtop insertions : 6019582
% 48.88/7.67 % Search garbage collected termcells : 1475
% 48.88/7.67
% 48.88/7.67 % -------------------------------------------------
% 48.88/7.67 % User time : 6.705 s
% 48.88/7.67 % System time : 0.244 s
% 48.88/7.67 % Total time : 6.950 s
% 48.88/7.67 % Maximum resident set size: 3940 pages
% 48.88/7.67
% 48.88/7.67 % -------------------------------------------------
% 48.88/7.67 % User time : 33.288 s
% 48.88/7.67 % System time : 1.122 s
% 48.88/7.67 % Total time : 34.411 s
% 48.88/7.67 % Maximum resident set size: 4864 pages
% 48.88/7.67 % E exiting
%------------------------------------------------------------------------------