%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU164+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n018.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 05:10:53 PM UTC 2026
% Result : Theorem 114.76s 81.99s
% Output : CNFRefutation 115.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 94 ( 25 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 103 ( 36 ~; 50 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 65 ( 1 sgn 33 !; 1 ?)
% 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(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t99_zfmisc_1,conjecture,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_5,plain,
! [X220,X221,X222,X223,X224,X225] :
( ( ~ in(X222,X221)
| subset(X222,X220)
| X221 != powerset(X220) )
& ( ~ subset(X223,X220)
| in(X223,X221)
| X221 != powerset(X220) )
& ( ~ in(esk3_2(X224,X225),X225)
| ~ subset(esk3_2(X224,X225),X224)
| X225 = powerset(X224) )
& ( in(esk3_2(X224,X225),X225)
| subset(esk3_2(X224,X225),X224)
| X225 = powerset(X224) ) ),
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_6,plain,
! [X262,X263,X264,X265,X266] :
( ( ~ subset(X262,X263)
| ~ in(X264,X262)
| in(X264,X263) )
& ( in(esk11_2(X265,X266),X265)
| subset(X265,X266) )
& ( ~ in(esk11_2(X265,X266),X266)
| subset(X265,X266) ) ),
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])])])])])]) ).
fof(c_0_7,plain,
! [X277,X278,X279,X281,X282,X283,X284,X286] :
( ( in(X279,esk13_3(X277,X278,X279))
| ~ in(X279,X278)
| X278 != union(X277) )
& ( in(esk13_3(X277,X278,X279),X277)
| ~ in(X279,X278)
| X278 != union(X277) )
& ( ~ in(X281,X282)
| ~ in(X282,X277)
| in(X281,X278)
| X278 != union(X277) )
& ( ~ in(esk14_2(X283,X284),X284)
| ~ in(esk14_2(X283,X284),X286)
| ~ in(X286,X283)
| X284 = union(X283) )
& ( in(esk14_2(X283,X284),esk15_2(X283,X284))
| in(esk14_2(X283,X284),X284)
| X284 = union(X283) )
& ( in(esk15_2(X283,X284),X283)
| in(esk14_2(X283,X284),X284)
| X284 = union(X283) ) ),
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)],[d4_tarski])])])])])]) ).
cnf(c_0_8,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,plain,
! [X336] : subset(X336,X336),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_11,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( in(esk14_2(X1,X2),esk15_2(X1,X2))
| in(esk14_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( in(esk15_2(X1,X2),X1)
| in(esk14_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] : union(powerset(X1)) = X1,
inference(assume_negation,[status(cth)],[t99_zfmisc_1]) ).
cnf(c_0_18,plain,
( X1 = union(X2)
| in(esk14_2(X2,X1),X1)
| in(esk14_2(X2,X1),X3)
| ~ subset(esk15_2(X2,X1),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
( X1 = union(powerset(X2))
| subset(esk15_2(powerset(X2),X1),X2)
| in(esk14_2(powerset(X2),X1),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( X2 = union(X1)
| ~ in(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,plain,
in(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_22,negated_conjecture,
union(powerset(esk22_0)) != esk22_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_23,plain,
( X1 = union(powerset(X2))
| in(esk14_2(powerset(X2),X1),X1)
| in(esk14_2(powerset(X2),X1),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( X1 = union(powerset(X2))
| ~ in(esk14_2(powerset(X2),X1),X2)
| ~ in(esk14_2(powerset(X2),X1),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
union(powerset(esk22_0)) != esk22_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_23,c_0_24,c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU164+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n018.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 02:46:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 114.76/81.99 % Version : CSE_E---1.7
% 114.76/81.99 % Problem : theBenchmark.p
% 114.76/81.99 % SZS status Theorem for theBenchmark.p
% 114.76/81.99 % SZS output start CNFRefutation
% See solution above
% 115.05/82.29 % Total time : 69.999s
%------------------------------------------------------------------------------