%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET938+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 05:09:00 PM UTC 2026
% Result : Theorem 2.06s 1.94s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 119 ( 22 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 121 ( 47 ~; 58 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 105 ( 7 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_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(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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t86_zfmisc_1,conjecture,
! [X1,X2] : subset(set_union2(powerset(set_difference(X1,X2)),powerset(set_difference(X2,X1))),powerset(symmetric_difference(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_zfmisc_1) ).
fof(d6_xboole_0,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
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(c_0_6,plain,
! [X41,X42,X43,X44,X45,X46] :
( ( ~ in(X43,X42)
| subset(X43,X41)
| X42 != powerset(X41) )
& ( ~ subset(X44,X41)
| in(X44,X42)
| X42 != powerset(X41) )
& ( ~ in(esk1_2(X45,X46),X46)
| ~ subset(esk1_2(X45,X46),X45)
| X46 = powerset(X45) )
& ( in(esk1_2(X45,X46),X46)
| subset(esk1_2(X45,X46),X45)
| X46 = powerset(X45) ) ),
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_7,plain,
! [X57,X58,X59,X60,X61] :
( ( ~ subset(X57,X58)
| ~ in(X59,X57)
| in(X59,X58) )
& ( in(esk3_2(X60,X61),X60)
| subset(X60,X61) )
& ( ~ in(esk3_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_8,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,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(esk2_3(X53,X54,X55),X53)
| ~ in(esk2_3(X53,X54,X55),X55)
| X55 = set_union2(X53,X54) )
& ( ~ in(esk2_3(X53,X54,X55),X54)
| ~ in(esk2_3(X53,X54,X55),X55)
| X55 = set_union2(X53,X54) )
& ( in(esk2_3(X53,X54,X55),X55)
| in(esk2_3(X53,X54,X55),X53)
| in(esk2_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_11,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( in(esk3_2(X1,X2),X1)
| in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2] : subset(set_union2(powerset(set_difference(X1,X2)),powerset(set_difference(X2,X1))),powerset(symmetric_difference(X1,X2))),
inference(assume_negation,[status(cth)],[t86_zfmisc_1]) ).
cnf(c_0_20,plain,
( in(X1,powerset(X2))
| ~ in(esk3_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_21,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( in(powerset(X1),powerset(X2))
| in(X3,X1)
| ~ in(X3,esk3_2(powerset(X1),X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,negated_conjecture,
~ subset(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(symmetric_difference(esk6_0,esk7_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_24,plain,
! [X63,X64] : symmetric_difference(X63,X64) = set_union2(set_difference(X63,X64),set_difference(X64,X63)),
inference(variable_rename,[status(thm)],[d6_xboole_0]) ).
cnf(c_0_25,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(esk3_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( in(esk3_2(esk3_2(powerset(X1),X2),X3),X1)
| in(esk3_2(powerset(X1),X2),powerset(X3))
| in(powerset(X1),powerset(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
~ subset(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(symmetric_difference(esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( in(esk3_2(powerset(X1),X2),powerset(set_union2(X3,X1)))
| in(powerset(X1),powerset(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X37,X38] : set_union2(X37,X38) = set_union2(X38,X37),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_31,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,negated_conjecture,
~ subset(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
in(powerset(X1),powerset(powerset(set_union2(X2,X1)))),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_34,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0)))),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_37,negated_conjecture,
~ in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_38,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(X1,powerset(X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_39,plain,
in(powerset(X1),powerset(powerset(set_union2(X1,X2)))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk7_0,esk6_0)))
| in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk6_0,esk7_0))) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
~ in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk7_0,esk6_0))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk6_0,esk7_0))),
inference(sr,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET938+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:40:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.06/1.94 % Version : CSE_E---1.7
% 2.06/1.94 % Problem : theBenchmark.p
% 2.06/1.94 % SZS status Theorem for theBenchmark.p
% 2.06/1.94 % SZS output start CNFRefutation
% See solution above
% 2.06/1.95 % Total time : 1.368s
%------------------------------------------------------------------------------