%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET934+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 : n004.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 147.27s 111.73s
% Output : CNFRefutation 149.37s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_72)
% Comments :
%------------------------------------------------------------------------------
fof(t81_zfmisc_1,conjecture,
! [X1,X2] : subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
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(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_14,negated_conjecture,
~ ! [X1,X2] : subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
inference(assume_negation,[status(cth)],[t81_zfmisc_1]) ).
fof(i_0_15,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_16,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_17,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_18,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_19,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54] :
( ( ~ in(X50,X49)
| in(X50,X47)
| in(X50,X48)
| X49 != set_union2(X47,X48) )
& ( ~ in(X51,X47)
| in(X51,X49)
| X49 != set_union2(X47,X48) )
& ( ~ in(X51,X48)
| in(X51,X49)
| X49 != set_union2(X47,X48) )
& ( ~ in(esk2_3(X52,X53,X54),X52)
| ~ in(esk2_3(X52,X53,X54),X54)
| X54 = set_union2(X52,X53) )
& ( ~ in(esk2_3(X52,X53,X54),X53)
| ~ in(esk2_3(X52,X53,X54),X54)
| X54 = set_union2(X52,X53) )
& ( in(esk2_3(X52,X53,X54),X54)
| in(esk2_3(X52,X53,X54),X52)
| in(esk2_3(X52,X53,X54),X53)
| X54 = set_union2(X52,X53) ) ),
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(i_0_20,negated_conjecture,
~ subset(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])])]) ).
fof(i_0_21,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ in(X42,X41)
| subset(X42,X40)
| X41 != powerset(X40) )
& ( ~ subset(X43,X40)
| in(X43,X41)
| X41 != powerset(X40) )
& ( ~ in(esk1_2(X44,X45),X45)
| ~ subset(esk1_2(X44,X45),X44)
| X45 = powerset(X44) )
& ( in(esk1_2(X44,X45),X45)
| subset(esk1_2(X44,X45),X44)
| X45 = powerset(X44) ) ),
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(i_0_22,plain,
! [X56,X57,X58,X59,X60] :
( ( ~ subset(X56,X57)
| ~ in(X58,X56)
| in(X58,X57) )
& ( in(esk3_2(X59,X60),X59)
| subset(X59,X60) )
& ( ~ in(esk3_2(X59,X60),X60)
| subset(X59,X60) ) ),
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(i_0_23,plain,
! [X70,X71,X72] :
( ~ subset(X70,X71)
| ~ subset(X71,X72)
| subset(X70,X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_24,plain,
! [X62,X63] :
( empty(X62)
| ~ empty(set_union2(X62,X63)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])]) ).
fof(i_0_25,plain,
! [X64,X65] :
( empty(X64)
| ~ empty(set_union2(X65,X64)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])]) ).
fof(i_0_26,plain,
! [X36,X37] :
( ~ in(X36,X37)
| ~ in(X37,X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_17])]) ).
fof(i_0_27,plain,
! [X73,X74] : subset(X73,set_union2(X73,X74)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_28,plain,
! [X38,X39] : set_union2(X38,X39) = set_union2(X39,X38),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_29,plain,
! [X66] : set_union2(X66,X66) = X66,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_30,plain,
! [X69] : subset(X69,X69),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_31,plain,
~ empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_18])]) ).
fof(i_0_32,plain,
empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_33,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_34,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X2)
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_35,plain,
( in(esk2_3(X1,X2,X3),X3)
| in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_36,negated_conjecture,
~ subset(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_37,plain,
( X2 = powerset(X1)
| ~ in(esk1_2(X1,X2),X2)
| ~ subset(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_38,plain,
( in(esk1_2(X1,X2),X2)
| subset(esk1_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_39,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_41,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_42,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_43,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_44,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_45,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_46,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_47,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_48,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_49,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_50,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_51,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_52,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_53,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_54,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_55,plain,
~ empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_56,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_57,axiom,
X1 = X1 ).
cnf(i_0_58,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_59,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_60,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_66,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_67,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_77,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_80,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_83,plain,
subset(X1,set_union2(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_93,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_96,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_101,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_114,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_128,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_130,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_144,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_168,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_172,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_178,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_181,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_186,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_191,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_194,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_197,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_200,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_207,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_211,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_213,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_214,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_215,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_219,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_247,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_250,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_256,plain,
subset(X1,set_union2(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_262,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_265,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_280,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_286,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_294,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_302,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_309,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_317,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_321,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_329,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_336,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_1710,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_1712,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_1720,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_1722,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_1725,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_1753,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_1755,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_1756,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_1768,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_1773,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_1777,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_1808,plain,
subset(X1,set_union2(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_1815,plain,
subset(X1,set_union2(X1,X2)),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_1936,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_2170,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_2225,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_2378,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_2418,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_2629,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_2698,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_2732,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_2900,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_2906,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_73,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_54,i_0_72]) ).
cnf(i_0_75,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_72,i_0_58]) ).
cnf(i_0_76,plain,
in(X1,set_union2(X2,powerset(X1))),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_72,i_0_58,i_0_41]) ).
cnf(i_0_79,plain,
in(X1,set_union2(powerset(X1),X2)),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_77,i_0_72,i_0_58,i_0_41,i_0_42]) ).
cnf(i_0_82,plain,
in(X1,set_union2(set_union2(X2,powerset(X1)),X3)),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_77,i_0_51,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44]) ).
cnf(i_0_85,plain,
esk4_0 != esk5_0,
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_77,i_0_51,i_0_55,i_0_56,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44,i_0_67]) ).
cnf(i_0_86,plain,
~ in(powerset(X1),X1),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_77,i_0_51,i_0_55,i_0_56,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44,i_0_67,i_0_50]) ).
cnf(i_0_88,plain,
in(X1,set_union2(set_union2(powerset(X1),X2),X3)),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_77,i_0_51,i_0_55,i_0_56,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44,i_0_67,i_0_50,i_0_69]) ).
cnf(i_0_90,plain,
in(X1,set_union2(X2,set_union2(X3,powerset(X1)))),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_77,i_0_51,i_0_55,i_0_56,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44,i_0_67,i_0_50,i_0_69,i_0_70]) ).
cnf(i_0_92,plain,
~ subset(powerset(set_union2(powerset(X1),powerset(X1))),X1),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_52,i_0_77,i_0_51,i_0_55,i_0_56,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44,i_0_67,i_0_50,i_0_69,i_0_70,i_0_49]) ).
cnf(i_0_95,plain,
esk4_0 != set_union2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_93,i_0_52,i_0_77,i_0_51,i_0_55,i_0_56,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44,i_0_67,i_0_50,i_0_69,i_0_70,i_0_49,i_0_59]) ).
cnf(i_0_99,plain,
~ subset(powerset(set_union2(powerset(X1),powerset(X1))),set_union2(X1,X1)),
inference(scs_inference,[],[i_0_54,i_0_53,i_0_93,i_0_96,i_0_52,i_0_77,i_0_51,i_0_55,i_0_56,i_0_72,i_0_58,i_0_41,i_0_42,i_0_44,i_0_67,i_0_50,i_0_69,i_0_70,i_0_49,i_0_59,i_0_35,i_0_66]) ).
cnf(i_0_104,plain,
~ in(powerset(set_union2(powerset(X1),powerset(X1))),set_union2(powerset(X1),powerset(X1))),
inference(equality_inference,[],[100]) ).
cnf(i_0_105,plain,
~ in(set_union2(X1,powerset(X2)),X2),
inference(scs_inference,[],[i_0_76,i_0_50]) ).
cnf(i_0_107,plain,
in(X1,set_union2(X2,set_union2(powerset(X1),X3))),
inference(scs_inference,[],[i_0_76,i_0_79,i_0_50,i_0_70]) ).
cnf(i_0_109,plain,
in(X1,powerset(set_union2(X1,X2))),
inference(scs_inference,[],[i_0_76,i_0_79,i_0_51,i_0_50,i_0_70,i_0_72]) ).
cnf(i_0_111,plain,
in(X1,set_union2(powerset(set_union2(X1,X2)),X3)),
inference(scs_inference,[],[i_0_76,i_0_79,i_0_51,i_0_50,i_0_70,i_0_72,i_0_69]) ).
cnf(i_0_113,plain,
~ subset(set_union2(powerset(esk7_0),powerset(esk6_0)),powerset(set_union2(esk6_0,esk7_0))),
inference(scs_inference,[],[i_0_36,i_0_76,i_0_79,i_0_52,i_0_51,i_0_50,i_0_70,i_0_72,i_0_69,i_0_65]) ).
cnf(i_0_115,plain,
~ in(powerset(set_union2(X1,X1)),X1),
inference(scs_inference,[],[i_0_36,i_0_75,i_0_86,i_0_76,i_0_79,i_0_52,i_0_51,i_0_50,i_0_70,i_0_72,i_0_69,i_0_65,i_0_64]) ).
cnf(i_0_116,plain,
~ in(powerset(X1),X1),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_118,plain,
~ in(powerset(X1),X1),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_121,plain,
~ in(powerset(X1),X1),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_124,plain,
in(X1,powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_131,plain,
~ in(powerset(X1),X1),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_132,plain,
~ in(powerset(X1),X1),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_137,plain,
~ in(set_union2(set_union2(X1,powerset(X2)),X3),X2),
inference(scs_inference,[],[i_0_82,i_0_50]) ).
cnf(i_0_145,plain,
~ in(set_union2(set_union2(powerset(X1),X2),X3),X1),
inference(scs_inference,[],[i_0_88,i_0_50]) ).
cnf(i_0_149,plain,
~ in(set_union2(X1,set_union2(X2,powerset(X3))),X3),
inference(scs_inference,[],[i_0_90,i_0_50]) ).
cnf(i_0_153,plain,
~ in(set_union2(powerset(X1),X2),X1),
inference(scs_inference,[],[i_0_79,i_0_50]) ).
cnf(i_0_166,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_210,plain,
in(X1,set_union2(X2,powerset(X1))),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_216,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_242,plain,
~ in(powerset(X1),set_union2(X1,X1)),
inference(scs_inference,[],[i_0_53,i_0_86,i_0_64]) ).
cnf(i_0_243,plain,
~ in(powerset(X1),X1),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_244,plain,
X1 != powerset(set_union2(X2,powerset(X1))),
inference(scs_inference,[],[i_0_53,i_0_82,i_0_86,i_0_64,i_0_63]) ).
cnf(i_0_245,plain,
in(X1,set_union2(set_union2(X2,powerset(X1)),X3)),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_246,plain,
set_union2(powerset(esk6_0),powerset(esk7_0)) != powerset(set_union2(esk6_0,esk7_0)),
inference(scs_inference,[],[i_0_53,i_0_36,i_0_82,i_0_54,i_0_86,i_0_64,i_0_63,i_0_66]) ).
cnf(i_0_248,plain,
X1 != set_union2(X2,powerset(powerset(X1))),
inference(scs_inference,[],[i_0_53,i_0_36,i_0_82,i_0_54,i_0_86,i_0_64,i_0_63,i_0_66,i_0_62]) ).
cnf(i_0_249,plain,
set_union2(X1,X1) != powerset(set_union2(powerset(X1),powerset(X1))),
inference(scs_inference,[],[i_0_53,i_0_36,i_0_99,i_0_82,i_0_54,i_0_247,i_0_86,i_0_64,i_0_63,i_0_66,i_0_62,i_0_65]) ).
cnf(i_0_259,plain,
in(X1,set_union2(X2,powerset(X1))),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_290,plain,
in(X1,powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_306,plain,
in(X1,powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_333,plain,
in(X1,powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_1721,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1724,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1729,plain,
in(X1,powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_1752,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1754,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1758,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1770,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1772,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1774,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1776,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1779,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1789,plain,
set_union2(X1,X2) = set_union2(set_union2(X1,X1),X2),
inference(scs_inference,[],[i_0_75,i_0_60]) ).
cnf(i_0_1790,plain,
~ empty(set_union2(esk5_0,X1)),
inference(scs_inference,[],[i_0_55,i_0_75,i_0_60,i_0_46]) ).
cnf(i_0_1792,plain,
~ empty(set_union2(X1,esk5_0)),
inference(scs_inference,[],[i_0_55,i_0_75,i_0_60,i_0_46,i_0_47]) ).
cnf(i_0_1818,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1820,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1822,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1824,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1890,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_1894,plain,
in(X1,powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_1961,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(c_0_62,plain,
( in(X1,X2)
| ~ subset(X1,X3)
| X2 != powerset(X3) ),
i_0_49 ).
cnf(c_0_63,plain,
( subset(X1,X2)
| ~ subset(X1,X3)
| ~ subset(X3,X2) ),
i_0_43 ).
cnf(c_0_64,plain,
subset(X1,set_union2(X1,X2)),
i_0_51 ).
cnf(c_0_65,plain,
set_union2(X1,X2) = set_union2(X2,X1),
i_0_52 ).
cnf(c_0_66,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
( subset(X1,set_union2(X2,X3))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
( subset(X1,X2)
| ~ in(X1,X3)
| X3 != powerset(X2) ),
i_0_48 ).
cnf(c_0_69,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,X4)
| X4 != set_union2(X2,X3) ),
i_0_40 ).
cnf(c_0_71,negated_conjecture,
~ subset(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),
i_0_36 ).
cnf(c_0_72,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
i_0_45 ).
cnf(c_0_73,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
i_0_39 ).
cnf(c_0_74,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_76,plain,
( subset(X1,set_union2(X2,X3))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_69]) ).
cnf(c_0_77,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_78,negated_conjecture,
in(esk3_2(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),set_union2(powerset(esk6_0),powerset(esk7_0))),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
~ in(esk3_2(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),powerset(set_union2(esk6_0,esk7_0))),
inference(spm,[status(thm)],[c_0_71,c_0_73]) ).
cnf(c_0_80,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_66,c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( in(esk3_2(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),powerset(esk7_0))
| in(esk3_2(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),powerset(esk6_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
~ in(esk3_2(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),powerset(esk6_0)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(X1,powerset(X3)) ),
inference(spm,[status(thm)],[c_0_81,c_0_75]) ).
cnf(c_0_85,negated_conjecture,
in(esk3_2(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),powerset(esk7_0)),
inference(sr,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_84]),c_0_85])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET934+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n004.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:40:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 147.27/111.73 % Version : CSE_E---1.7
% 147.27/111.73 % Problem : theBenchmark.p
% 147.27/111.73 % SZS status Theorem for theBenchmark.p
% 147.27/111.73 % SZS output start CNFRefutation
% See solution above
% 149.37/113.88 % Total time : 111.370s
%------------------------------------------------------------------------------