%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU135+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n017.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 05:10:44 PM UTC 2026
% Result : Theorem 28.76s 17.34s
% Output : CNFRefutation 28.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 121 ( 64 unt; 0 def)
% Number of atoms : 247 ( 63 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 202 ( 76 ~; 99 |; 18 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 329 ( 40 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t39_xboole_1,conjecture,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_12,plain,
! [X63,X64,X65,X66,X67,X68,X69,X70] :
( ( in(X66,X63)
| ~ in(X66,X65)
| X65 != set_difference(X63,X64) )
& ( ~ in(X66,X64)
| ~ in(X66,X65)
| X65 != set_difference(X63,X64) )
& ( ~ in(X67,X63)
| in(X67,X64)
| in(X67,X65)
| X65 != set_difference(X63,X64) )
& ( ~ in(esk3_3(X68,X69,X70),X70)
| ~ in(esk3_3(X68,X69,X70),X68)
| in(esk3_3(X68,X69,X70),X69)
| X70 = set_difference(X68,X69) )
& ( in(esk3_3(X68,X69,X70),X68)
| in(esk3_3(X68,X69,X70),X70)
| X70 = set_difference(X68,X69) )
& ( ~ in(esk3_3(X68,X69,X70),X69)
| in(esk3_3(X68,X69,X70),X70)
| X70 = set_difference(X68,X69) ) ),
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_11])])])])])]) ).
fof(c_0_13,plain,
! [X48,X49,X50,X51,X52,X53,X54,X55] :
( ( ~ in(X51,X50)
| in(X51,X48)
| in(X51,X49)
| X50 != set_union2(X48,X49) )
& ( ~ in(X52,X48)
| in(X52,X50)
| X50 != set_union2(X48,X49) )
& ( ~ in(X52,X49)
| in(X52,X50)
| X50 != set_union2(X48,X49) )
& ( ~ in(esk1_3(X53,X54,X55),X53)
| ~ in(esk1_3(X53,X54,X55),X55)
| X55 = set_union2(X53,X54) )
& ( ~ in(esk1_3(X53,X54,X55),X54)
| ~ in(esk1_3(X53,X54,X55),X55)
| X55 = set_union2(X53,X54) )
& ( in(esk1_3(X53,X54,X55),X55)
| in(esk1_3(X53,X54,X55),X53)
| in(esk1_3(X53,X54,X55),X54)
| X55 = set_union2(X53,X54) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X57,X58,X59,X60,X61] :
( ( ~ subset(X57,X58)
| ~ in(X59,X57)
| in(X59,X58) )
& ( in(esk2_2(X60,X61),X60)
| subset(X60,X61) )
& ( ~ in(esk2_2(X60,X61),X61)
| subset(X60,X61) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_16,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X44,X45] : set_union2(X44,X45) = set_union2(X45,X44),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X84] : set_difference(empty_set,X84) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( subset(set_difference(X1,X2),X3)
| in(esk2_2(set_difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( subset(set_difference(X1,X2),X3)
| ~ in(esk2_2(set_difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_31,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( subset(X1,set_difference(X2,X3))
| in(esk2_2(X1,set_difference(X2,X3)),X3)
| ~ in(esk2_2(X1,set_difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ in(X1,empty_set)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_34,plain,
( subset(set_difference(set_difference(X1,X2),X3),X4)
| ~ in(esk2_2(set_difference(set_difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_35,plain,
( subset(set_difference(X1,set_difference(X2,X3)),X4)
| in(esk2_2(set_difference(X1,set_difference(X2,X3)),X4),X3)
| ~ in(esk2_2(set_difference(X1,set_difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_36,plain,
( subset(set_difference(set_difference(X1,X2),X3),X4)
| in(esk2_2(set_difference(set_difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
fof(c_0_37,plain,
! [X46,X47] :
( ( subset(X46,X47)
| X46 != X47 )
& ( subset(X47,X46)
| X46 != X47 )
& ( ~ subset(X46,X47)
| ~ subset(X47,X46)
| X46 = X47 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_38,plain,
( subset(set_difference(X1,set_union2(X2,X3)),X4)
| ~ in(esk2_2(set_difference(X1,set_union2(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
( subset(X1,set_difference(X1,X2))
| in(esk2_2(X1,set_difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_40,plain,
( subset(empty_set,X1)
| ~ in(esk2_2(empty_set,X1),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_41,plain,
( subset(set_difference(set_difference(X1,set_union2(X2,X3)),X4),X5)
| ~ in(esk2_2(set_difference(set_difference(X1,set_union2(X2,X3)),X4),X5),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_42,plain,
( subset(set_difference(set_difference(X1,X2),set_difference(X1,X3)),X4)
| in(esk2_2(set_difference(set_difference(X1,X2),set_difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
subset(set_difference(X1,set_union2(X2,X3)),set_difference(set_difference(X1,set_union2(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
subset(set_difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_46,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_47,plain,
subset(set_difference(set_difference(X1,set_union2(X2,X3)),set_difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
set_difference(set_difference(X1,set_union2(X2,X3)),X2) = set_difference(X1,set_union2(X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_49,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_43,c_0_46]) ).
cnf(c_0_50,plain,
subset(set_difference(X1,set_union2(X2,set_difference(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_25]) ).
fof(c_0_51,plain,
! [X83] : set_difference(X83,empty_set) = X83,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_52,plain,
( subset(set_difference(set_difference(set_difference(X1,X2),X3),X4),X5)
| in(esk2_2(set_difference(set_difference(set_difference(X1,X2),X3),X4),X5),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_53,plain,
( subset(set_difference(X1,set_difference(X1,X2)),X3)
| in(esk2_2(set_difference(X1,set_difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_54,plain,
set_difference(X1,set_union2(X2,set_difference(X1,X2))) = empty_set,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,plain,
( subset(set_difference(set_difference(set_difference(X1,X2),X3),set_difference(X1,X4)),X5)
| in(esk2_2(set_difference(set_difference(set_difference(X1,X2),X3),set_difference(X1,X4)),X5),X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_52]) ).
cnf(c_0_57,plain,
subset(set_difference(set_difference(X1,X2),X3),set_difference(set_difference(set_difference(X1,X2),X3),X2)),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_58,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_59,plain,
( subset(X1,set_difference(X1,set_difference(X2,X3)))
| ~ in(esk2_2(X1,set_difference(X1,set_difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_60,plain,
( subset(X1,X2)
| in(esk2_2(X1,X2),set_union2(X3,set_difference(X1,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_55]) ).
cnf(c_0_61,plain,
subset(set_difference(set_difference(set_difference(X1,X2),X3),set_difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
cnf(c_0_62,plain,
set_difference(set_difference(set_difference(X1,X2),X3),X2) = set_difference(set_difference(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_57]),c_0_45])]) ).
cnf(c_0_63,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_58]) ).
fof(c_0_64,plain,
! [X86,X87] :
( ~ in(X86,X87)
| ~ empty(X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_65,plain,
subset(X1,set_difference(X1,set_difference(X2,set_union2(X3,set_difference(X1,X3))))),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,plain,
subset(set_difference(set_difference(X1,set_difference(X1,X2)),X2),X3),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_67,plain,
! [X80] : set_union2(X80,empty_set) = X80,
inference(variable_rename,[status(thm)],[t1_boole]) ).
cnf(c_0_68,plain,
( subset(set_difference(set_difference(set_union2(X1,X2),X3),X4),X5)
| in(esk2_2(set_difference(set_difference(set_union2(X1,X2),X3),X4),X5),X1)
| in(esk2_2(set_difference(set_difference(set_union2(X1,X2),X3),X4),X5),X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_36]) ).
cnf(c_0_69,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,plain,
subset(X1,set_difference(X1,set_difference(X2,X1))),
inference(spm,[status(thm)],[c_0_59,c_0_22]) ).
cnf(c_0_71,plain,
set_difference(X1,set_difference(X2,set_union2(X3,set_difference(X1,X3)))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_65]),c_0_45])]) ).
cnf(c_0_72,plain,
set_difference(set_difference(X1,set_difference(X1,X2)),X2) = empty_set,
inference(spm,[status(thm)],[c_0_49,c_0_66]) ).
cnf(c_0_73,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,plain,
( subset(set_difference(set_difference(set_union2(X1,X2),X3),X2),X4)
| in(esk2_2(set_difference(set_difference(set_union2(X1,X2),X3),X2),X4),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_68]) ).
cnf(c_0_75,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk2_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_76,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk2_2(X1,set_union2(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_77,plain,
( subset(set_difference(set_union2(X1,X2),X3),X4)
| in(esk2_2(set_difference(set_union2(X1,X2),X3),X4),X1)
| in(esk2_2(set_difference(set_union2(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_29]) ).
cnf(c_0_78,plain,
( subset(X1,set_difference(X1,X2))
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_39]) ).
cnf(c_0_79,plain,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_70]),c_0_45])]) ).
cnf(c_0_80,plain,
set_difference(set_difference(X1,set_difference(X1,X2)),set_difference(X3,X2)) = set_difference(X1,set_difference(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_81,plain,
subset(set_difference(set_difference(set_union2(X1,X2),X1),X2),X3),
inference(spm,[status(thm)],[c_0_34,c_0_74]) ).
cnf(c_0_82,plain,
( subset(set_union2(X1,X2),X3)
| in(esk2_2(set_union2(X1,X2),X3),X1)
| in(esk2_2(set_union2(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_22]) ).
cnf(c_0_83,plain,
( subset(X1,set_union2(X2,set_union2(X3,X4)))
| ~ in(esk2_2(X1,set_union2(X2,set_union2(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_75,c_0_24]) ).
cnf(c_0_84,plain,
( subset(set_difference(set_union2(X1,X2),X3),set_union2(X2,X4))
| in(esk2_2(set_difference(set_union2(X1,X2),X3),set_union2(X2,X4)),X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_85,plain,
subset(set_difference(X1,set_difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_26,c_0_53]) ).
cnf(c_0_86,plain,
( set_difference(X1,X2) = X1
| ~ empty(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_78]),c_0_45])]) ).
cnf(c_0_87,plain,
set_difference(set_difference(X1,X2),set_difference(X3,set_difference(X3,X2))) = set_difference(X1,X2),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_88,plain,
set_difference(set_difference(set_union2(X1,X2),X1),X2) = empty_set,
inference(spm,[status(thm)],[c_0_49,c_0_81]) ).
cnf(c_0_89,plain,
( subset(set_union2(X1,X2),X2)
| in(esk2_2(set_union2(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_82]) ).
cnf(c_0_90,plain,
set_difference(X1,set_difference(set_difference(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_79,c_0_62]) ).
cnf(c_0_91,plain,
subset(set_difference(set_union2(X1,X2),X3),set_union2(X2,set_union2(X4,X1))),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_92,plain,
( subset(X1,set_union2(X2,set_union2(X3,X4)))
| ~ in(esk2_2(X1,set_union2(X2,set_union2(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_75,c_0_31]) ).
cnf(c_0_93,plain,
( subset(X1,X2)
| ~ empty(set_difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,plain,
set_difference(set_union2(X1,set_difference(X2,set_difference(X2,X1))),X1) = empty_set,
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_96,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_75,c_0_22]) ).
cnf(c_0_97,plain,
subset(set_union2(X1,set_union2(X2,set_union2(X3,X1))),set_union2(X2,set_union2(X3,X1))),
inference(spm,[status(thm)],[c_0_83,c_0_89]) ).
cnf(c_0_98,plain,
set_difference(set_difference(X1,X2),set_difference(X2,X3)) = set_difference(X1,X2),
inference(spm,[status(thm)],[c_0_90,c_0_79]) ).
cnf(c_0_99,plain,
subset(set_union2(X1,X2),set_union2(X2,set_union2(X3,X1))),
inference(spm,[status(thm)],[c_0_91,c_0_55]) ).
cnf(c_0_100,plain,
subset(set_union2(X1,set_union2(X2,set_union2(X1,X3))),set_union2(X2,set_union2(X1,X3))),
inference(spm,[status(thm)],[c_0_92,c_0_89]) ).
cnf(c_0_101,plain,
subset(set_union2(X1,set_difference(X2,set_difference(X2,X1))),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_102,plain,
subset(X1,set_union2(X1,X2)),
inference(spm,[status(thm)],[c_0_96,c_0_25]) ).
cnf(c_0_103,plain,
set_union2(X1,set_union2(X2,set_union2(X3,X1))) = set_union2(X2,set_union2(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_97]),c_0_96])]) ).
cnf(c_0_104,plain,
set_difference(set_union2(X1,set_difference(X1,X2)),X1) = empty_set,
inference(spm,[status(thm)],[c_0_98,c_0_88]) ).
cnf(c_0_105,plain,
subset(set_union2(X1,X2),set_union2(X2,set_union2(X1,X3))),
inference(spm,[status(thm)],[c_0_99,c_0_25]) ).
cnf(c_0_106,plain,
set_union2(X1,set_union2(X2,set_union2(X1,X3))) = set_union2(X2,set_union2(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_100]),c_0_96])]) ).
cnf(c_0_107,plain,
set_union2(X1,set_difference(X2,set_difference(X2,X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_101]),c_0_102])]) ).
cnf(c_0_108,plain,
set_union2(X1,set_union2(set_union2(X2,X1),X3)) = set_union2(set_union2(X2,X1),X3),
inference(spm,[status(thm)],[c_0_103,c_0_25]) ).
cnf(c_0_109,plain,
subset(set_union2(X1,set_difference(X1,X2)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_104]),c_0_95])]) ).
fof(c_0_110,negated_conjecture,
~ ! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(assume_negation,[status(cth)],[t39_xboole_1]) ).
cnf(c_0_111,plain,
subset(set_union2(X1,X2),set_union2(X1,set_union2(X2,X3))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
set_union2(X1,set_union2(X2,set_difference(X1,X2))) = set_union2(X2,set_difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_54]),c_0_55]),c_0_25]) ).
cnf(c_0_113,plain,
subset(set_union2(X1,X2),set_union2(set_union2(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_99,c_0_108]) ).
cnf(c_0_114,plain,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_109]),c_0_102])]) ).
fof(c_0_115,negated_conjecture,
set_union2(esk6_0,set_difference(esk7_0,esk6_0)) != set_union2(esk6_0,esk7_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])])]) ).
cnf(c_0_116,plain,
subset(set_union2(X1,X2),set_union2(X2,set_difference(X1,X2))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,plain,
subset(set_union2(X1,set_difference(X2,X3)),set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
set_union2(esk6_0,set_difference(esk7_0,esk6_0)) != set_union2(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_119,plain,
set_union2(X1,set_difference(X2,X1)) = set_union2(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_116]),c_0_117])]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU135+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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 : n017.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 02:43:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 28.76/17.34 % Version : CSE_E---1.7
% 28.76/17.34 % Problem : theBenchmark.p
% 28.76/17.34 % SZS status Theorem for theBenchmark.p
% 28.76/17.34 % SZS output start CNFRefutation
% See solution above
% 28.86/17.48 % Total time : 12.395s
%------------------------------------------------------------------------------