%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU164+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 : n006.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 48.44s 28.14s
% Output : CNFRefutation 48.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 120 ( 28 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 138 ( 54 ~; 64 |; 12 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-3 aty)
% Number of variables : 90 ( 1 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
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(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(t99_zfmisc_1,conjecture,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_6,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ in(X39,X38)
| subset(X39,X37)
| X38 != powerset(X37) )
& ( ~ subset(X40,X37)
| in(X40,X38)
| X38 != powerset(X37) )
& ( ~ in(esk2_2(X41,X42),X42)
| ~ subset(esk2_2(X41,X42),X41)
| X42 = powerset(X41) )
& ( in(esk2_2(X41,X42),X42)
| subset(esk2_2(X41,X42),X41)
| X42 = powerset(X41) ) ),
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,
! [X50,X51,X52,X54,X55,X56,X57,X59] :
( ( in(X52,esk4_3(X50,X51,X52))
| ~ in(X52,X51)
| X51 != union(X50) )
& ( in(esk4_3(X50,X51,X52),X50)
| ~ in(X52,X51)
| X51 != union(X50) )
& ( ~ in(X54,X55)
| ~ in(X55,X50)
| in(X54,X51)
| X51 != union(X50) )
& ( ~ in(esk5_2(X56,X57),X57)
| ~ in(esk5_2(X56,X57),X59)
| ~ in(X59,X56)
| X57 = union(X56) )
& ( in(esk5_2(X56,X57),esk6_2(X56,X57))
| in(esk5_2(X56,X57),X57)
| X57 = union(X56) )
& ( in(esk6_2(X56,X57),X56)
| in(esk5_2(X56,X57),X57)
| X57 = union(X56) ) ),
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_6]) ).
cnf(c_0_9,plain,
( in(esk4_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X44,X45,X46,X47,X48] :
( ( ~ subset(X44,X45)
| ~ in(X46,X44)
| in(X46,X45) )
& ( in(esk3_2(X47,X48),X47)
| subset(X47,X48) )
& ( ~ in(esk3_2(X47,X48),X48)
| subset(X47,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)],[d3_tarski])])])])])]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(esk4_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( subset(esk4_3(powerset(X1),union(powerset(X1)),X2),X1)
| ~ in(X2,union(powerset(X1))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( in(X1,esk4_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( in(X1,union(X2))
| ~ in(X3,X2)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X63] : subset(X63,X63),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(X1,esk4_3(powerset(X2),union(powerset(X2)),X3))
| ~ in(X3,union(powerset(X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( in(X1,esk4_3(X2,union(X2),X1))
| ~ in(X1,union(X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X64,X65] :
( ( ~ in(esk7_2(X64,X65),X64)
| ~ in(esk7_2(X64,X65),X65)
| X64 = X65 )
& ( in(esk7_2(X64,X65),X64)
| in(esk7_2(X64,X65),X65)
| X64 = X65 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_24,plain,
( in(X1,union(powerset(X2)))
| ~ subset(X3,X2)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] : union(powerset(X1)) = X1,
inference(assume_negation,[status(cth)],[t99_zfmisc_1]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| ~ in(X1,union(powerset(X2))) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( in(esk7_2(X1,X2),X1)
| in(esk7_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ in(esk7_2(X1,X2),X1)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( in(X1,union(powerset(X2)))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_31,negated_conjecture,
union(powerset(esk8_0)) != esk8_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_32,plain,
( in(esk7_2(X1,union(powerset(X2))),X2)
| X1 = union(powerset(X2))
| in(esk7_2(X1,union(powerset(X2))),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( X1 = union(powerset(X2))
| ~ in(esk7_2(X1,union(powerset(X2))),X1)
| ~ in(esk7_2(X1,union(powerset(X2))),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
union(powerset(esk8_0)) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_32,c_0_33,c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU164+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.33 % Computer : n006.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 02:46:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 48.44/28.14 % Version : CSE_E---1.7
% 48.44/28.14 % Problem : theBenchmark.p
% 48.44/28.14 % SZS status Theorem for theBenchmark.p
% 48.44/28.14 % SZS output start CNFRefutation
% See solution above
% 48.61/28.32 % Total time : 21.417s
%------------------------------------------------------------------------------