%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU171+1 : 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 : n019.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 05:10:55 PM UTC 2026
% Result : Theorem 0.28s 1.62s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 51)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t50_subset_1,conjecture,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
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_19,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(i_0_20,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_subset_1])]) ).
fof(i_0_21,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_22,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(i_0_23,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_24,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_25,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_26,plain,
! [X42,X43,X44,X45,X46,X47,X48,X49] :
( ( in(X45,X42)
| ~ in(X45,X44)
| X44 != set_difference(X42,X43) )
& ( ~ in(X45,X43)
| ~ in(X45,X44)
| X44 != set_difference(X42,X43) )
& ( ~ in(X46,X42)
| in(X46,X43)
| in(X46,X44)
| X44 != set_difference(X42,X43) )
& ( ~ in(esk1_3(X47,X48,X49),X49)
| ~ in(esk1_3(X47,X48,X49),X47)
| in(esk1_3(X47,X48,X49),X48)
| X49 = set_difference(X47,X48) )
& ( in(esk1_3(X47,X48,X49),X47)
| in(esk1_3(X47,X48,X49),X49)
| X49 = set_difference(X47,X48) )
& ( ~ in(esk1_3(X47,X48,X49),X48)
| in(esk1_3(X47,X48,X49),X49)
| X49 = set_difference(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)],[i_0_19])])])])])]) ).
fof(i_0_27,plain,
! [X53,X54] :
( ~ element(X54,powerset(X53))
| element(subset_complement(X53,X54),powerset(X53)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(i_0_28,plain,
! [X58,X59] :
( ~ element(X59,powerset(X58))
| subset_complement(X58,subset_complement(X58,X59)) = X59 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
fof(i_0_29,plain,
! [X51,X52] :
( ~ element(X52,powerset(X51))
| subset_complement(X51,X52) = set_difference(X51,X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(i_0_30,negated_conjecture,
( esk7_0 != empty_set
& element(esk8_0,powerset(esk7_0))
& element(esk9_0,esk7_0)
& ~ in(esk9_0,esk8_0)
& ~ in(esk9_0,subset_complement(esk7_0,esk8_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_20])])]) ).
fof(i_0_31,plain,
! [X38,X39] :
( ~ in(X38,X39)
| ~ in(X39,X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_21])]) ).
fof(i_0_32,plain,
! [X40,X41] :
( ( ~ element(X41,X40)
| in(X41,X40)
| empty(X40) )
& ( ~ in(X41,X40)
| element(X41,X40)
| empty(X40) )
& ( ~ element(X41,X40)
| empty(X41)
| ~ empty(X40) )
& ( ~ empty(X41)
| element(X41,X40)
| ~ empty(X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_22])])]) ).
fof(i_0_33,plain,
! [X60] :
( ( element(esk3_1(X60),powerset(X60))
| empty(X60) )
& ( ~ empty(esk3_1(X60))
| empty(X60) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_23])])])]) ).
fof(i_0_34,plain,
! [X72,X73] :
( ~ in(X72,X73)
| ~ empty(X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_35,plain,
! [X63] :
( element(esk5_1(X63),powerset(X63))
& empty(esk5_1(X63)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_36,plain,
! [X55] : element(esk2_1(X55),X55),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_37,plain,
! [X57] : ~ empty(powerset(X57)),
inference(variable_rename,[status(thm)],[i_0_24]) ).
fof(i_0_38,plain,
! [X74,X75] :
( ~ empty(X74)
| X74 = X75
| ~ empty(X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_39,plain,
! [X66] : set_difference(X66,empty_set) = X66,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_40,plain,
! [X67] : set_difference(empty_set,X67) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_41,plain,
! [X71] :
( ~ empty(X71)
| X71 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_42,plain,
~ empty(esk6_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_25])]) ).
fof(i_0_43,plain,
empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_44,plain,
( in(esk1_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk1_3(X1,X2,X3),X3)
| ~ in(esk1_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_45,plain,
( in(esk1_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk1_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_46,plain,
( in(esk1_3(X1,X2,X3),X1)
| in(esk1_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_47,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_48,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_49,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_50,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_51,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_52,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_53,negated_conjecture,
~ in(esk9_0,subset_complement(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_54,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_55,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_56,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_57,plain,
( empty(X1)
| ~ element(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_58,plain,
( element(esk3_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_59,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_60,plain,
( element(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_61,plain,
element(esk5_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_62,plain,
( empty(X1)
| ~ empty(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_63,plain,
element(esk2_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_64,negated_conjecture,
~ in(esk9_0,esk8_0),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_65,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_66,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_67,negated_conjecture,
element(esk8_0,powerset(esk7_0)),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_68,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_69,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_70,negated_conjecture,
element(esk9_0,esk7_0),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_71,plain,
empty(esk5_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_72,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_73,plain,
~ empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_74,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_75,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_76,negated_conjecture,
esk7_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_77,axiom,
X1 = X1 ).
cnf(i_0_78,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_79,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_80,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_81,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_82,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_83,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_84,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_85,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_86,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_87,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_88,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_77_001,axiom,
X1 = X1 ).
cnf(i_0_78_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_79_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_80_004,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_81_005,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_82_006,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_83_007,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_84_008,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_85_009,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_86_010,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_87_011,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_88_012,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_89,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[48]) ).
cnf(i_0_90,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[50]) ).
cnf(i_0_91,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[51]) ).
cnf(i_0_92,plain,
element(subset_complement(esk7_0,esk8_0),powerset(esk7_0)),
inference(scs_inference,[],[i_0_67,i_0_47]) ).
cnf(i_0_93,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_94,plain,
subset_complement(esk7_0,esk8_0) = set_difference(esk7_0,esk8_0),
inference(scs_inference,[],[i_0_67,i_0_47,i_0_52]) ).
cnf(i_0_95,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_96,plain,
~ in(esk9_0,set_difference(subset_complement(esk7_0,esk8_0),X1)),
inference(scs_inference,[],[i_0_53,i_0_67,i_0_47,i_0_52,i_0_91]) ).
cnf(i_0_97,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_98,plain,
~ in(X1,esk4_0),
inference(scs_inference,[],[i_0_53,i_0_67,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59]) ).
cnf(i_0_99,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_100,plain,
~ empty(esk7_0),
inference(scs_inference,[],[i_0_53,i_0_76,i_0_67,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72]) ).
cnf(i_0_101,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_102,plain,
X1 = set_difference(X1,empty_set),
inference(scs_inference,[],[i_0_53,i_0_76,i_0_67,i_0_68,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78]) ).
cnf(i_0_103,plain,
in(esk2_1(esk6_0),esk6_0),
inference(scs_inference,[],[i_0_53,i_0_76,i_0_67,i_0_63,i_0_68,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56]) ).
cnf(i_0_104,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_105,plain,
( empty(X1)
| ~ element(X2,X1)
| in(X2,X1) ),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_106,plain,
~ element(esk6_0,esk4_0),
inference(scs_inference,[],[i_0_53,i_0_76,i_0_67,i_0_63,i_0_68,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57]) ).
cnf(i_0_107,plain,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_108,plain,
in(esk2_1(esk6_0),set_difference(esk6_0,esk4_0)),
inference(scs_inference,[],[i_0_53,i_0_76,i_0_67,i_0_63,i_0_68,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89]) ).
cnf(i_0_109,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_110,plain,
~ in(set_difference(esk9_0,empty_set),subset_complement(esk7_0,esk8_0)),
inference(scs_inference,[],[i_0_53,i_0_76,i_0_67,i_0_63,i_0_68,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84]) ).
cnf(i_0_111,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_112,plain,
~ in(esk9_0,set_difference(esk8_0,empty_set)),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85]) ).
cnf(i_0_113,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_114,plain,
~ element(set_difference(esk6_0,empty_set),esk4_0),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86]) ).
cnf(i_0_115,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_116,plain,
~ in(esk2_1(esk6_0),set_difference(set_difference(X1,esk6_0),empty_set)),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50]) ).
cnf(i_0_117,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_118,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_119,plain,
element(esk4_0,esk4_0),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60]) ).
cnf(i_0_120,plain,
( ~ empty(X1)
| ~ empty(X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_60]) ).
cnf(i_0_121,plain,
esk7_0 != set_difference(empty_set,empty_set),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79]) ).
cnf(i_0_122,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_123,plain,
~ element(esk6_0,set_difference(esk4_0,empty_set)),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_122,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79,i_0_87]) ).
cnf(i_0_124,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_125,plain,
esk4_0 != esk6_0,
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_122,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79,i_0_87,i_0_88]) ).
cnf(i_0_126,plain,
~ in(esk9_0,esk7_0),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_122,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79,i_0_87,i_0_88,i_0_48]) ).
cnf(i_0_127,plain,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_128,plain,
~ in(esk6_0,esk2_1(esk6_0)),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_122,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79,i_0_87,i_0_88,i_0_48,i_0_54]) ).
cnf(i_0_129,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_130,plain,
~ in(esk2_1(esk6_0),set_difference(X1,esk6_0)),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_122,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79,i_0_87,i_0_88,i_0_48,i_0_54,i_0_90]) ).
cnf(i_0_131,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_132,plain,
( in(X1,esk9_0)
| ~ in(X1,esk9_0) ),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_122,i_0_73,i_0_74,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79,i_0_87,i_0_88,i_0_48,i_0_54,i_0_90,i_0_51]) ).
cnf(i_0_133,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_134,plain,
( ~ in(X1,esk9_0)
| ~ in(esk1_3(empty_set,empty_set,esk7_0),empty_set)
| in(esk1_3(empty_set,empty_set,esk7_0),empty_set) ),
inference(scs_inference,[],[i_0_53,i_0_64,i_0_76,i_0_67,i_0_63,i_0_68,i_0_111,i_0_113,i_0_115,i_0_117,i_0_122,i_0_73,i_0_74,i_0_65,i_0_47,i_0_52,i_0_91,i_0_59,i_0_72,i_0_78,i_0_56,i_0_57,i_0_89,i_0_84,i_0_85,i_0_86,i_0_50,i_0_60,i_0_79,i_0_87,i_0_88,i_0_48,i_0_54,i_0_90,i_0_51,i_0_45,i_0_46,i_0_44]) ).
cnf(i_0_135,plain,
element(subset_complement(esk7_0,subset_complement(esk7_0,esk8_0)),powerset(esk7_0)),
inference(scs_inference,[],[i_0_92,i_0_47]) ).
cnf(i_0_136,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_137,plain,
subset_complement(esk7_0,subset_complement(esk7_0,esk8_0)) = set_difference(esk7_0,subset_complement(esk7_0,esk8_0)),
inference(scs_inference,[],[i_0_92,i_0_47,i_0_52]) ).
cnf(i_0_138,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_139,plain,
~ in(esk9_0,set_difference(esk8_0,X1)),
inference(scs_inference,[],[i_0_64,i_0_92,i_0_47,i_0_52,i_0_91]) ).
cnf(i_0_140,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_141,plain,
~ in(set_difference(esk6_0,esk4_0),esk2_1(esk6_0)),
inference(scs_inference,[],[i_0_64,i_0_92,i_0_108,i_0_47,i_0_52,i_0_91,i_0_54]) ).
cnf(i_0_142,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_143,plain,
~ in(X1,empty_set),
inference(scs_inference,[],[i_0_64,i_0_92,i_0_108,i_0_75,i_0_47,i_0_52,i_0_91,i_0_54,i_0_59]) ).
cnf(i_0_144,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_145,plain,
~ in(esk2_1(esk6_0),set_difference(X1,set_difference(esk6_0,esk4_0))),
inference(scs_inference,[],[i_0_64,i_0_92,i_0_108,i_0_75,i_0_47,i_0_52,i_0_91,i_0_54,i_0_59,i_0_90]) ).
cnf(i_0_146,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_147,plain,
set_difference(esk7_0,esk8_0) = subset_complement(esk7_0,esk8_0),
inference(scs_inference,[],[i_0_64,i_0_94,i_0_92,i_0_108,i_0_75,i_0_47,i_0_52,i_0_91,i_0_54,i_0_59,i_0_90,i_0_78]) ).
cnf(i_0_148,plain,
$false,
inference(scs_inference,[],[i_0_70,i_0_64,i_0_94,i_0_92,i_0_108,i_0_126,i_0_75,i_0_100,i_0_47,i_0_52,i_0_91,i_0_54,i_0_59,i_0_90,i_0_78,i_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU171+1 : 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 : n019.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 02:46:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.28/1.62 % Version : CSE_E---1.7
% 0.28/1.62 % Problem : theBenchmark.p
% 0.28/1.62 % SZS status Theorem for theBenchmark.p
% 0.28/1.62 % SZS output start CNFRefutation
% See solution above
% 0.49/1.86 % Total time : 1.271s
%------------------------------------------------------------------------------