%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET935+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n022.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 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 16 unt; 0 def)
% Number of atoms : 121 ( 31 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 121 ( 43 ~; 56 |; 14 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 76 ( 3 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t82_zfmisc_1,conjecture,
! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_zfmisc_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
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(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(d9_xboole_0,axiom,
! [X1,X2] :
( inclusion_comparable(X1,X2)
<=> ( subset(X1,X2)
| subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(c_0_8,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58] :
( ( ~ in(X54,X53)
| in(X54,X51)
| in(X54,X52)
| X53 != set_union2(X51,X52) )
& ( ~ in(X55,X51)
| in(X55,X53)
| X53 != set_union2(X51,X52) )
& ( ~ in(X55,X52)
| in(X55,X53)
| X53 != set_union2(X51,X52) )
& ( ~ in(esk2_3(X56,X57,X58),X56)
| ~ in(esk2_3(X56,X57,X58),X58)
| X58 = set_union2(X56,X57) )
& ( ~ in(esk2_3(X56,X57,X58),X57)
| ~ in(esk2_3(X56,X57,X58),X58)
| X58 = set_union2(X56,X57) )
& ( in(esk2_3(X56,X57,X58),X58)
| in(esk2_3(X56,X57,X58),X56)
| in(esk2_3(X56,X57,X58),X57)
| X58 = set_union2(X56,X57) ) ),
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])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
inference(assume_negation,[status(cth)],[t82_zfmisc_1]) ).
cnf(c_0_10,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,negated_conjecture,
( set_union2(powerset(esk5_0),powerset(esk6_0)) = powerset(set_union2(esk5_0,esk6_0))
& ~ inclusion_comparable(esk5_0,esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_12,plain,
! [X44,X45,X46,X47,X48,X49] :
( ( ~ in(X46,X45)
| subset(X46,X44)
| X45 != powerset(X44) )
& ( ~ subset(X47,X44)
| in(X47,X45)
| X45 != powerset(X44) )
& ( ~ in(esk1_2(X48,X49),X49)
| ~ subset(esk1_2(X48,X49),X48)
| X49 = powerset(X48) )
& ( in(esk1_2(X48,X49),X49)
| subset(esk1_2(X48,X49),X48)
| X49 = powerset(X48) ) ),
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])])])])])]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
set_union2(powerset(esk5_0),powerset(esk6_0)) = powerset(set_union2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( in(X1,powerset(esk5_0))
| in(X1,powerset(esk6_0))
| ~ in(X1,powerset(set_union2(esk5_0,esk6_0))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X69] : subset(X69,X69),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_19,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,powerset(esk6_0))
| in(X1,powerset(esk5_0))
| ~ subset(X1,set_union2(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( in(set_union2(esk5_0,esk6_0),powerset(esk5_0))
| in(set_union2(esk5_0,esk6_0),powerset(esk6_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_24,plain,
! [X73,X74] : subset(X73,set_union2(X73,X74)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_25,plain,
! [X40,X41] : set_union2(X40,X41) = set_union2(X41,X40),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_26,plain,
! [X42,X43] :
( ( subset(X42,X43)
| X42 != X43 )
& ( subset(X43,X42)
| X42 != X43 )
& ( ~ subset(X42,X43)
| ~ subset(X43,X42)
| X42 = X43 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_27,negated_conjecture,
( subset(set_union2(esk5_0,esk6_0),esk6_0)
| in(set_union2(esk5_0,esk6_0),powerset(esk5_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( subset(set_union2(esk5_0,esk6_0),esk6_0)
| subset(set_union2(esk5_0,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_32,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X60,X61] :
( ( ~ inclusion_comparable(X60,X61)
| subset(X60,X61)
| subset(X61,X60) )
& ( ~ subset(X60,X61)
| inclusion_comparable(X60,X61) )
& ( ~ subset(X61,X60)
| inclusion_comparable(X60,X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_xboole_0])])]) ).
cnf(c_0_34,negated_conjecture,
( set_union2(esk5_0,esk6_0) = esk6_0
| subset(set_union2(esk5_0,esk6_0),esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
~ inclusion_comparable(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,plain,
( inclusion_comparable(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( set_union2(esk5_0,esk6_0) = esk6_0
| set_union2(esk5_0,esk6_0) = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_34]),c_0_28])]) ).
cnf(c_0_38,negated_conjecture,
~ subset(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( inclusion_comparable(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
set_union2(esk5_0,esk6_0) = esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_37]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
~ subset(esk6_0,esk5_0),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET935+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:40:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------