%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU123+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 : n009.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 05:10:41 PM UTC 2026
% Result : Theorem 0.22s 1.62s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 51)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_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(t3_xboole_1,conjecture,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
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,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
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_21,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(i_0_22,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
fof(i_0_23,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_24,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_25,negated_conjecture,
~ ! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[t3_xboole_1]) ).
fof(i_0_26,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_27,plain,
! [X64,X65,X66,X67,X68,X69,X70,X71] :
( ( in(X67,X64)
| ~ in(X67,X66)
| X66 != set_intersection2(X64,X65) )
& ( in(X67,X65)
| ~ in(X67,X66)
| X66 != set_intersection2(X64,X65) )
& ( ~ in(X68,X64)
| ~ in(X68,X65)
| in(X68,X66)
| X66 != set_intersection2(X64,X65) )
& ( ~ in(esk3_3(X69,X70,X71),X71)
| ~ in(esk3_3(X69,X70,X71),X69)
| ~ in(esk3_3(X69,X70,X71),X70)
| X71 = set_intersection2(X69,X70) )
& ( in(esk3_3(X69,X70,X71),X69)
| in(esk3_3(X69,X70,X71),X71)
| X71 = set_intersection2(X69,X70) )
& ( in(esk3_3(X69,X70,X71),X70)
| in(esk3_3(X69,X70,X71),X71)
| X71 = set_intersection2(X69,X70) ) ),
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_xboole_0])])])])])]) ).
fof(i_0_28,lemma,
! [X92,X93,X95,X96,X97] :
( ( disjoint(X92,X93)
| in(esk8_2(X92,X93),set_intersection2(X92,X93)) )
& ( ~ in(X97,set_intersection2(X95,X96))
| ~ disjoint(X95,X96) ) ),
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_21])])])])]) ).
fof(i_0_29,plain,
! [X58,X59,X60,X61,X62] :
( ( ~ subset(X58,X59)
| ~ in(X60,X58)
| in(X60,X59) )
& ( in(esk2_2(X61,X62),X61)
| subset(X61,X62) )
& ( ~ in(esk2_2(X61,X62),X62)
| subset(X61,X62) ) ),
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_30,lemma,
! [X85,X86,X88,X89,X90] :
( ( in(esk6_2(X85,X86),X85)
| disjoint(X85,X86) )
& ( in(esk6_2(X85,X86),X86)
| disjoint(X85,X86) )
& ( ~ in(X90,X88)
| ~ in(X90,X89)
| ~ disjoint(X88,X89) ) ),
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)],[i_0_22])])])])])]) ).
fof(i_0_31,lemma,
! [X81,X82,X83] :
( ~ subset(X81,X82)
| ~ subset(X82,X83)
| subset(X81,X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_32,plain,
! [X52,X53] :
( ( subset(X52,X53)
| X52 != X53 )
& ( subset(X53,X52)
| X52 != X53 )
& ( ~ subset(X52,X53)
| ~ subset(X53,X52)
| X52 = X53 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_33,plain,
! [X48,X49] :
( ~ in(X48,X49)
| ~ in(X49,X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_23])]) ).
fof(i_0_34,plain,
! [X79,X80] :
( ~ disjoint(X79,X80)
| disjoint(X80,X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_35,plain,
! [X73,X74] :
( ( ~ disjoint(X73,X74)
| set_intersection2(X73,X74) = empty_set )
& ( set_intersection2(X73,X74) != empty_set
| disjoint(X73,X74) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_36,plain,
! [X99,X100] :
( ~ in(X99,X100)
| ~ empty(X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_37,plain,
! [X50,X51] : set_intersection2(X50,X51) = set_intersection2(X51,X50),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_38,plain,
! [X54,X55,X56] :
( ( X54 != empty_set
| ~ in(X55,X54) )
& ( in(esk1_1(X56),X56)
| X56 = 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_24])])])])]) ).
fof(i_0_39,plain,
! [X101,X102] :
( ~ empty(X101)
| X101 = X102
| ~ empty(X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_40,plain,
! [X75] : set_intersection2(X75,X75) = X75,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_41,plain,
! [X78] : subset(X78,X78),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_42,lemma,
! [X84] : subset(empty_set,X84),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_43,negated_conjecture,
( subset(esk7_0,empty_set)
& esk7_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_25])])]) ).
fof(i_0_44,plain,
! [X98] :
( ~ empty(X98)
| X98 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_45,plain,
~ empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_26])]) ).
fof(i_0_46,plain,
empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_47,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk3_3(X1,X2,X3),X3)
| ~ in(esk3_3(X1,X2,X3),X1)
| ~ in(esk3_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_48,plain,
( in(esk3_3(X1,X2,X3),X1)
| in(esk3_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_49,plain,
( in(esk3_3(X1,X2,X3),X2)
| in(esk3_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_50,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_51,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_52,lemma,
( disjoint(X1,X2)
| in(esk8_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_53,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_54,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_55,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_56,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_57,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_58,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_59,lemma,
( in(esk6_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_60,lemma,
( in(esk6_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_61,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_62,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_63,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_64,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_65,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_66,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_67,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_68,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_69,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_70,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_71,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_72,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_73,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_74,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_75,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_76,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_77,negated_conjecture,
subset(esk7_0,empty_set),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_78,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_79,plain,
~ empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_80,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_81,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_82,negated_conjecture,
esk7_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_83,axiom,
X1 = X1 ).
cnf(i_0_84,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_85,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_86,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_87,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_88,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_89,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_90,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_91,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_92,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_93,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_94,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_83_001,axiom,
X1 = X1 ).
cnf(i_0_84_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_85_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_86_004,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_87_005,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_88_006,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_89_007,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_90_008,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_91_009,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_92_010,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_93_011,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_94_012,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_95,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,X3) ),
inference(equality_inference,[],[51]) ).
cnf(i_0_96,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(equality_inference,[],[55]) ).
cnf(i_0_97,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(equality_inference,[],[56]) ).
cnf(i_0_98,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[69]) ).
cnf(i_0_99,plain,
subset(X1,X1),
inference(equality_inference,[],[71]) ).
cnf(i_0_100,plain,
subset(X1,X1),
inference(equality_inference,[],[72]) ).
cnf(i_0_101,plain,
$false,
inference(scs_inference,[],[i_0_82,i_0_77,i_0_76,i_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU123+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
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 5 02:43:41 EDT 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % start to proof: theBenchmark
% 0.22/1.62 % Version : CSE_E---1.7
% 0.22/1.62 % Problem : theBenchmark.p
% 0.22/1.62 % SZS status Theorem for theBenchmark.p
% 0.22/1.62 % SZS output start CNFRefutation
% See solution above
% 0.22/1.64 % Total time : 1.274s
%------------------------------------------------------------------------------