%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET908+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 : n010.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 05:08:56 PM UTC 2026
% Result : Theorem 0.27s 1.61s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 40)
% Comments :
%------------------------------------------------------------------------------
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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t49_zfmisc_1,conjecture,
! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
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_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
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(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_12,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_13,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_14,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_15,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_16,negated_conjecture,
~ ! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
inference(assume_negation,[status(cth)],[t49_zfmisc_1]) ).
fof(i_0_17,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_18,plain,
! [X43,X44,X45,X46,X47,X48,X49,X50] :
( ( ~ in(X46,X45)
| in(X46,X43)
| in(X46,X44)
| X45 != set_union2(X43,X44) )
& ( ~ in(X47,X43)
| in(X47,X45)
| X45 != set_union2(X43,X44) )
& ( ~ in(X47,X44)
| in(X47,X45)
| X45 != set_union2(X43,X44) )
& ( ~ in(esk3_3(X48,X49,X50),X48)
| ~ in(esk3_3(X48,X49,X50),X50)
| X50 = set_union2(X48,X49) )
& ( ~ in(esk3_3(X48,X49,X50),X49)
| ~ in(esk3_3(X48,X49,X50),X50)
| X50 = set_union2(X48,X49) )
& ( in(esk3_3(X48,X49,X50),X50)
| in(esk3_3(X48,X49,X50),X48)
| in(esk3_3(X48,X49,X50),X49)
| X50 = set_union2(X48,X49) ) ),
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_19,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( ~ in(X34,X33)
| X34 = X32
| X33 != singleton(X32) )
& ( X35 != X32
| in(X35,X33)
| X33 != singleton(X32) )
& ( ~ in(esk1_2(X36,X37),X37)
| esk1_2(X36,X37) != X36
| X37 = singleton(X36) )
& ( in(esk1_2(X36,X37),X37)
| esk1_2(X36,X37) = X36
| X37 = singleton(X36) ) ),
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_tarski])])])])])]) ).
fof(i_0_20,plain,
! [X52,X53] :
( empty(X52)
| ~ empty(set_union2(X52,X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])]) ).
fof(i_0_21,plain,
! [X54,X55] :
( empty(X54)
| ~ empty(set_union2(X55,X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])]) ).
fof(i_0_22,plain,
! [X28,X29] :
( ~ in(X28,X29)
| ~ in(X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])]) ).
fof(i_0_23,plain,
! [X30,X31] : set_union2(X30,X31) = set_union2(X31,X30),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_24,plain,
! [X39,X40,X41] :
( ( X39 != empty_set
| ~ in(X40,X39) )
& ( in(esk2_1(X41),X41)
| X41 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])])])])]) ).
fof(i_0_25,negated_conjecture,
set_union2(singleton(esk6_0),esk7_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])])]) ).
fof(i_0_26,plain,
! [X56] : set_union2(X56,X56) = X56,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_27,plain,
~ empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_17])]) ).
fof(i_0_28,plain,
empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_29,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk3_3(X1,X2,X3),X1)
| ~ in(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_30,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk3_3(X1,X2,X3),X2)
| ~ in(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_31,plain,
( in(esk3_3(X1,X2,X3),X3)
| in(esk3_3(X1,X2,X3),X1)
| in(esk3_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_32,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_33,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_34,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_35,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_36,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_37,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_38,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_39,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_41,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_42,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_43,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_44,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_45,negated_conjecture,
set_union2(singleton(esk6_0),esk7_0) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_46,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_47,plain,
~ empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_48,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_49,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_50,axiom,
X1 = X1 ).
cnf(i_0_51,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_52,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_53,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_54,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_55,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_56,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_57,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_50_001,axiom,
X1 = X1 ).
cnf(i_0_51_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_52_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_53_004,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_54_005,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_55_006,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_56_007,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_57_008,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_58_009,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_59_010,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_60_011,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_61,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[33]) ).
cnf(i_0_62,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[34]) ).
cnf(i_0_63,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[35]) ).
cnf(i_0_64,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(equality_inference,[],[40]) ).
cnf(i_0_65,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[43]) ).
cnf(i_0_66,plain,
~ in(X1,set_union2(singleton(esk6_0),esk7_0)),
inference(scs_inference,[],[i_0_45,i_0_43]) ).
cnf(i_0_67,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_68,plain,
empty_set = set_union2(singleton(esk6_0),esk7_0),
inference(scs_inference,[],[i_0_45,i_0_43,i_0_51]) ).
cnf(i_0_69,plain,
in(set_union2(singleton(esk6_0),esk7_0),set_union2(singleton(empty_set),singleton(empty_set))),
inference(scs_inference,[],[i_0_45,i_0_46,i_0_43,i_0_51,i_0_42]) ).
cnf(i_0_70,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_71,plain,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_72,plain,
esk4_0 != esk5_0,
inference(scs_inference,[],[i_0_45,i_0_46,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60]) ).
cnf(i_0_73,plain,
~ in(X1,esk7_0),
inference(scs_inference,[],[i_0_45,i_0_46,i_0_41,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34]) ).
cnf(i_0_74,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_75,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_76,plain,
~ in(X1,singleton(esk6_0)),
inference(scs_inference,[],[i_0_45,i_0_46,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35]) ).
cnf(i_0_77,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_78,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_79,plain,
~ in(esk4_0,set_union2(singleton(esk5_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_45,i_0_46,i_0_70,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40]) ).
cnf(i_0_80,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_81,plain,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_82,plain,
in(set_union2(singleton(esk6_0),esk7_0),singleton(empty_set)),
inference(scs_inference,[],[i_0_45,i_0_46,i_0_70,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61]) ).
cnf(i_0_83,plain,
( ~ in(X1,set_union2(X2,X3))
| in(X1,X2)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_84,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33]) ).
cnf(i_0_85,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_86,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_87,plain,
in(set_union2(singleton(esk6_0),esk7_0),set_union2(singleton(empty_set),X1)),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33,i_0_62]) ).
cnf(i_0_88,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_89,plain,
in(set_union2(singleton(esk6_0),esk7_0),set_union2(X1,singleton(empty_set))),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33,i_0_62,i_0_63]) ).
cnf(i_0_90,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_91,plain,
esk4_0 != set_union2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_85,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33,i_0_62,i_0_63,i_0_52]) ).
cnf(i_0_92,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_93,plain,
~ in(set_union2(esk4_0,esk4_0),set_union2(singleton(esk5_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_85,i_0_92,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33,i_0_62,i_0_63,i_0_52,i_0_58]) ).
cnf(i_0_94,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_95,plain,
~ in(X1,set_union2(esk7_0,esk7_0)),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_85,i_0_92,i_0_94,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33,i_0_62,i_0_63,i_0_52,i_0_58,i_0_59]) ).
cnf(i_0_96,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_97,plain,
( in(esk3_3(esk5_0,esk5_0,esk4_0),esk4_0)
| in(esk3_3(esk5_0,esk5_0,esk4_0),esk5_0) ),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_85,i_0_92,i_0_94,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33,i_0_62,i_0_63,i_0_52,i_0_58,i_0_59,i_0_31]) ).
cnf(i_0_98,plain,
( X1 = set_union2(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(esk3_3(X2,X3,X1),X2)
| in(esk3_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_99,plain,
( ~ in(esk4_0,esk3_3(esk5_0,esk5_0,esk4_0))
| in(esk3_3(esk5_0,esk5_0,esk4_0),esk5_0) ),
inference(scs_inference,[],[i_0_45,i_0_65,i_0_46,i_0_70,i_0_80,i_0_85,i_0_92,i_0_94,i_0_41,i_0_74,i_0_47,i_0_48,i_0_43,i_0_51,i_0_42,i_0_60,i_0_34,i_0_35,i_0_40,i_0_61,i_0_33,i_0_62,i_0_63,i_0_52,i_0_58,i_0_59,i_0_31,i_0_39]) ).
cnf(i_0_100,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_101,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_46,i_0_43]) ).
cnf(i_0_102,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_103,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_104,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_46,i_0_102,i_0_43,i_0_51]) ).
cnf(i_0_105,plain,
set_union2(esk4_0,esk4_0) != esk5_0,
inference(scs_inference,[],[i_0_93,i_0_46,i_0_102,i_0_43,i_0_51,i_0_42]) ).
cnf(i_0_106,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_107,plain,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_108,plain,
~ in(set_union2(set_union2(esk4_0,esk4_0),set_union2(esk4_0,esk4_0)),set_union2(singleton(esk5_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_93,i_0_46,i_0_102,i_0_106,i_0_43,i_0_51,i_0_42,i_0_58]) ).
cnf(i_0_109,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_110,plain,
empty_set != esk5_0,
inference(scs_inference,[],[i_0_93,i_0_49,i_0_46,i_0_102,i_0_106,i_0_47,i_0_43,i_0_51,i_0_42,i_0_58,i_0_60]) ).
cnf(i_0_111,plain,
esk4_0 != set_union2(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_93,i_0_91,i_0_49,i_0_46,i_0_102,i_0_106,i_0_109,i_0_47,i_0_43,i_0_51,i_0_42,i_0_58,i_0_60,i_0_52]) ).
cnf(i_0_112,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_113,plain,
~ in(X1,set_union2(set_union2(esk7_0,esk7_0),set_union2(esk7_0,esk7_0))),
inference(scs_inference,[],[i_0_95,i_0_93,i_0_91,i_0_49,i_0_46,i_0_102,i_0_106,i_0_109,i_0_112,i_0_47,i_0_43,i_0_51,i_0_42,i_0_58,i_0_60,i_0_52,i_0_59]) ).
cnf(i_0_114,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_115,plain,
( in(X1,singleton(esk5_0))
| ~ in(X1,singleton(esk5_0)) ),
inference(scs_inference,[],[i_0_95,i_0_93,i_0_91,i_0_49,i_0_46,i_0_102,i_0_106,i_0_109,i_0_112,i_0_47,i_0_43,i_0_51,i_0_42,i_0_58,i_0_60,i_0_52,i_0_59,i_0_34]) ).
cnf(i_0_116,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_118,plain,
set_union2(set_union2(esk4_0,esk4_0),set_union2(esk4_0,esk4_0)) != esk5_0,
inference(scs_inference,[],[i_0_108,i_0_46,i_0_42]) ).
cnf(i_0_119,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_120,plain,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_121,plain,
~ in(set_union2(set_union2(esk4_0,esk4_0),set_union2(esk4_0,esk4_0)),singleton(esk5_0)),
inference(scs_inference,[],[i_0_104,i_0_108,i_0_46,i_0_42,i_0_59]) ).
cnf(i_0_122,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_123,plain,
~ in(set_union2(esk4_0,esk4_0),singleton(esk5_0)),
inference(scs_inference,[],[i_0_104,i_0_122,i_0_108,i_0_46,i_0_42,i_0_59,i_0_58]) ).
cnf(i_0_124,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_125,plain,
( in(esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0),esk4_0)
| in(esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0),set_union2(esk5_0,esk5_0)) ),
inference(scs_inference,[],[i_0_104,i_0_122,i_0_108,i_0_111,i_0_46,i_0_42,i_0_59,i_0_58,i_0_31]) ).
cnf(i_0_126,plain,
( X1 = set_union2(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(esk3_3(X2,X3,X1),X2)
| in(esk3_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_127,plain,
( ~ in(esk4_0,esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0))
| in(esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0),set_union2(esk5_0,esk5_0)) ),
inference(scs_inference,[],[i_0_104,i_0_122,i_0_108,i_0_111,i_0_46,i_0_42,i_0_59,i_0_58,i_0_31,i_0_39]) ).
cnf(i_0_128,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_129,plain,
( in(esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0),set_union2(esk4_0,X1))
| in(esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0),set_union2(esk5_0,esk5_0)) ),
inference(scs_inference,[],[i_0_104,i_0_122,i_0_108,i_0_111,i_0_46,i_0_42,i_0_59,i_0_58,i_0_31,i_0_39,i_0_62]) ).
cnf(i_0_130,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_131,plain,
( in(esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0),set_union2(X1,esk4_0))
| in(esk3_3(set_union2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0),esk4_0),set_union2(esk5_0,esk5_0)) ),
inference(scs_inference,[],[i_0_104,i_0_122,i_0_108,i_0_111,i_0_46,i_0_42,i_0_59,i_0_58,i_0_31,i_0_39,i_0_62,i_0_63]) ).
cnf(i_0_132,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_133,plain,
~ in(empty_set,set_union2(singleton(esk5_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_110,i_0_46,i_0_40]) ).
cnf(i_0_134,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_135,plain,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_136,plain,
empty_set != set_union2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_110,i_0_46,i_0_134,i_0_40,i_0_52]) ).
cnf(i_0_137,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_138,plain,
~ in(esk4_0,singleton(esk5_0)),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_104,i_0_46,i_0_134,i_0_40,i_0_52,i_0_58]) ).
cnf(i_0_139,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_140,plain,
~ in(X1,set_union2(singleton(esk6_0),singleton(esk6_0))),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_104,i_0_76,i_0_46,i_0_134,i_0_137,i_0_40,i_0_52,i_0_58,i_0_59]) ).
cnf(i_0_141,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_142,plain,
in(esk3_3(esk5_0,esk5_0,empty_set),esk5_0),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_104,i_0_65,i_0_76,i_0_46,i_0_134,i_0_137,i_0_40,i_0_52,i_0_58,i_0_59,i_0_31]) ).
cnf(i_0_143,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_144,plain,
( X1 = set_union2(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(esk3_3(X2,X3,X1),X2)
| in(esk3_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_145,plain,
~ in(esk5_0,esk3_3(esk5_0,esk5_0,empty_set)),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_104,i_0_65,i_0_76,i_0_46,i_0_134,i_0_137,i_0_40,i_0_52,i_0_58,i_0_59,i_0_31,i_0_39]) ).
cnf(i_0_146,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_147,plain,
in(esk3_3(esk5_0,esk5_0,empty_set),set_union2(esk5_0,X1)),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_104,i_0_65,i_0_76,i_0_46,i_0_134,i_0_137,i_0_40,i_0_52,i_0_58,i_0_59,i_0_31,i_0_39,i_0_62]) ).
cnf(i_0_148,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_149,plain,
in(esk3_3(esk5_0,esk5_0,empty_set),set_union2(X1,esk5_0)),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_104,i_0_65,i_0_76,i_0_46,i_0_134,i_0_137,i_0_40,i_0_52,i_0_58,i_0_59,i_0_31,i_0_39,i_0_62,i_0_63]) ).
cnf(i_0_150,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_151,plain,
~ in(set_union2(X1,esk5_0),esk3_3(esk5_0,esk5_0,empty_set)),
inference(scs_inference,[],[i_0_149,i_0_39]) ).
cnf(i_0_152,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_153,plain,
in(esk3_3(esk5_0,esk5_0,empty_set),set_union2(set_union2(X1,esk5_0),X2)),
inference(scs_inference,[],[i_0_149,i_0_39,i_0_62]) ).
cnf(i_0_154,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_155,plain,
in(esk3_3(esk5_0,esk5_0,empty_set),set_union2(X1,set_union2(X2,esk5_0))),
inference(scs_inference,[],[i_0_149,i_0_39,i_0_62,i_0_63]) ).
cnf(i_0_156,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_157,plain,
X1 != esk6_0,
inference(scs_inference,[],[i_0_140,i_0_149,i_0_46,i_0_39,i_0_62,i_0_63,i_0_42]) ).
cnf(i_0_158,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_159,plain,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_160,plain,
set_union2(esk4_0,esk4_0) != set_union2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_105,i_0_140,i_0_149,i_0_46,i_0_158,i_0_39,i_0_62,i_0_63,i_0_42,i_0_52]) ).
cnf(i_0_161,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_162,plain,
~ in(set_union2(singleton(esk6_0),esk7_0),set_union2(singleton(esk5_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_45,i_0_105,i_0_140,i_0_149,i_0_133,i_0_46,i_0_158,i_0_39,i_0_62,i_0_63,i_0_42,i_0_52,i_0_58]) ).
cnf(i_0_163,plain,
~ in(empty_set,singleton(esk5_0)),
inference(scs_inference,[],[i_0_45,i_0_105,i_0_140,i_0_104,i_0_149,i_0_133,i_0_46,i_0_158,i_0_39,i_0_62,i_0_63,i_0_42,i_0_52,i_0_58,i_0_59]) ).
cnf(i_0_164,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_165,plain,
$false,
inference(scs_inference,[],[i_0_45,i_0_105,i_0_140,i_0_104,i_0_164,i_0_149,i_0_133,i_0_46,i_0_158,i_0_39,i_0_62,i_0_63,i_0_42,i_0_52,i_0_58,i_0_59,i_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET908+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
% 0.14/0.32 % Computer : n010.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:39:21 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.27/1.61 % Version : CSE_E---1.7
% 0.27/1.61 % Problem : theBenchmark.p
% 0.27/1.61 % SZS status Theorem for theBenchmark.p
% 0.27/1.61 % SZS output start CNFRefutation
% See solution above
% 0.48/1.85 % Total time : 1.271s
%------------------------------------------------------------------------------