%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU174+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 : n028.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 05:10:56 PM UTC 2026
% Result : Theorem 0.55s 1.62s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 55)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
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(t46_setfam_1,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_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(d8_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
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(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(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(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
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(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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_24,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_25,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_26,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
inference(assume_negation,[status(cth)],[t46_setfam_1]) ).
fof(i_0_27,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_28,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_29,plain,
! [X60,X61,X62,X63] :
( ( ~ in(X63,X62)
| in(subset_complement(X60,X63),X61)
| ~ element(X63,powerset(X60))
| X62 != complements_of_subsets(X60,X61)
| ~ element(X62,powerset(powerset(X60)))
| ~ element(X61,powerset(powerset(X60))) )
& ( ~ in(subset_complement(X60,X63),X61)
| in(X63,X62)
| ~ element(X63,powerset(X60))
| X62 != complements_of_subsets(X60,X61)
| ~ element(X62,powerset(powerset(X60)))
| ~ element(X61,powerset(powerset(X60))) )
& ( element(esk2_3(X60,X61,X62),powerset(X60))
| X62 = complements_of_subsets(X60,X61)
| ~ element(X62,powerset(powerset(X60)))
| ~ element(X61,powerset(powerset(X60))) )
& ( ~ in(esk2_3(X60,X61,X62),X62)
| ~ in(subset_complement(X60,esk2_3(X60,X61,X62)),X61)
| X62 = complements_of_subsets(X60,X61)
| ~ element(X62,powerset(powerset(X60)))
| ~ element(X61,powerset(powerset(X60))) )
& ( in(esk2_3(X60,X61,X62),X62)
| in(subset_complement(X60,esk2_3(X60,X61,X62)),X61)
| X62 = complements_of_subsets(X60,X61)
| ~ element(X62,powerset(powerset(X60)))
| ~ element(X61,powerset(powerset(X60))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_setfam_1])])])])]) ).
fof(i_0_30,plain,
! [X67,X68] :
( ~ element(X68,powerset(powerset(X67)))
| element(complements_of_subsets(X67,X68),powerset(powerset(X67))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
fof(i_0_31,plain,
! [X74,X75] :
( ~ element(X75,powerset(powerset(X74)))
| complements_of_subsets(X74,complements_of_subsets(X74,X75)) = X75 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
fof(i_0_32,plain,
! [X65,X66] :
( ~ element(X66,powerset(X65))
| element(subset_complement(X65,X66),powerset(X65)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(i_0_33,plain,
! [X54,X55,X56,X57,X58] :
( ( ~ subset(X54,X55)
| ~ in(X56,X54)
| in(X56,X55) )
& ( in(esk1_2(X57,X58),X57)
| subset(X57,X58) )
& ( ~ in(esk1_2(X57,X58),X58)
| subset(X57,X58) ) ),
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_34,plain,
! [X72,X73] :
( ~ element(X73,powerset(X72))
| subset_complement(X72,subset_complement(X72,X73)) = X73 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
fof(i_0_35,plain,
! [X91,X92,X93] :
( ~ in(X91,X92)
| ~ element(X92,powerset(X93))
| element(X91,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_36,plain,
! [X94,X95,X96] :
( ~ in(X94,X95)
| ~ element(X95,powerset(X96))
| ~ empty(X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_37,plain,
! [X87,X88] :
( ( ~ element(X87,powerset(X88))
| subset(X87,X88) )
& ( ~ subset(X87,X88)
| element(X87,powerset(X88)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_38,plain,
! [X52,X53] :
( ~ in(X52,X53)
| ~ in(X53,X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_24])]) ).
fof(i_0_39,plain,
! [X85,X86] :
( ~ element(X85,X86)
| empty(X86)
| in(X85,X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_40,plain,
! [X83,X84] :
( ~ in(X83,X84)
| element(X83,X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_41,plain,
! [X76] :
( ( element(esk4_1(X76),powerset(X76))
| empty(X76) )
& ( ~ empty(esk4_1(X76))
| empty(X76) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_25])])])]) ).
fof(i_0_42,plain,
! [X98,X99] :
( ~ in(X98,X99)
| ~ empty(X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_43,plain,
! [X79] :
( element(esk6_1(X79),powerset(X79))
& empty(esk6_1(X79)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_44,negated_conjecture,
( element(esk9_0,powerset(powerset(esk8_0)))
& esk9_0 != empty_set
& complements_of_subsets(esk8_0,esk9_0) = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_26])])]) ).
fof(i_0_45,plain,
! [X69] : element(esk3_1(X69),X69),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_46,plain,
! [X71] : ~ empty(powerset(X71)),
inference(variable_rename,[status(thm)],[i_0_27]) ).
fof(i_0_47,plain,
! [X100,X101] :
( ~ empty(X100)
| X100 = X101
| ~ empty(X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_48,plain,
! [X82] : subset(X82,X82),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_49,plain,
! [X97] :
( ~ empty(X97)
| X97 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_50,plain,
~ empty(esk7_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_28])]) ).
fof(i_0_51,plain,
empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_52,plain,
( X3 = complements_of_subsets(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X3)
| ~ in(subset_complement(X1,esk2_3(X1,X2,X3)),X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_53,plain,
( in(esk2_3(X1,X2,X3),X3)
| in(subset_complement(X1,esk2_3(X1,X2,X3)),X2)
| X3 = complements_of_subsets(X1,X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_54,plain,
( element(esk2_3(X1,X2,X3),powerset(X1))
| X3 = complements_of_subsets(X1,X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_55,plain,
( in(X2,X4)
| ~ in(subset_complement(X1,X2),X3)
| ~ element(X2,powerset(X1))
| X4 != complements_of_subsets(X1,X3)
| ~ element(X4,powerset(powerset(X1)))
| ~ element(X3,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_56,plain,
( in(subset_complement(X3,X1),X4)
| ~ in(X1,X2)
| ~ element(X1,powerset(X3))
| X2 != complements_of_subsets(X3,X4)
| ~ element(X2,powerset(powerset(X3)))
| ~ element(X4,powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_57,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_58,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_59,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_60,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_61,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_62,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_63,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_64,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_65,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_66,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_67,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_68,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_69,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_70,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_71,plain,
( element(esk4_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_72,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_73,plain,
element(esk6_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_74,negated_conjecture,
element(esk9_0,powerset(powerset(esk8_0))),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_75,plain,
( empty(X1)
| ~ empty(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_76,plain,
element(esk3_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_77,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_78,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_79,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_80,negated_conjecture,
complements_of_subsets(esk8_0,esk9_0) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_81,plain,
empty(esk6_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_82,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_83,plain,
~ empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_84,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_85,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_86,negated_conjecture,
esk9_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_87,axiom,
X1 = X1 ).
cnf(i_0_88,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_89,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_90,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_91,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_92,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_93,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_94,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_95,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_96,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_97,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_98,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_99,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_100,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_87_001,axiom,
X1 = X1 ).
cnf(i_0_88_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_89_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_90_004,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_91_005,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_92_006,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_93_007,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_94_008,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_95_009,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_96_010,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_97_011,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_98_012,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_99_013,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_100_014,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_101,plain,
( in(X1,complements_of_subsets(X2,X3))
| ~ element(X1,powerset(X2))
| ~ in(subset_complement(X2,X1),X3)
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(equality_inference,[],[55]) ).
cnf(i_0_102,plain,
( ~ in(X1,complements_of_subsets(X2,X3))
| ~ element(X1,powerset(X2))
| in(subset_complement(X2,X1),X3)
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(equality_inference,[],[56]) ).
cnf(i_0_103,plain,
element(complements_of_subsets(esk8_0,esk9_0),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_74,i_0_57]) ).
cnf(i_0_104,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_105,plain,
complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)) = esk9_0,
inference(scs_inference,[],[i_0_74,i_0_57,i_0_58]) ).
cnf(i_0_106,plain,
( ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_107,plain,
element(subset_complement(powerset(esk8_0),esk9_0),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_74,i_0_57,i_0_58,i_0_59]) ).
cnf(i_0_108,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_109,plain,
subset(esk9_0,powerset(esk8_0)),
inference(scs_inference,[],[i_0_74,i_0_57,i_0_58,i_0_59,i_0_66]) ).
cnf(i_0_110,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_111,plain,
empty_set = complements_of_subsets(esk8_0,esk9_0),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88]) ).
cnf(i_0_112,plain,
~ in(X1,esk5_0),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_84,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72]) ).
cnf(i_0_113,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_114,plain,
~ empty(esk9_0),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_84,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82]) ).
cnf(i_0_115,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_116,plain,
~ in(X1,esk6_1(esk5_0)),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_84,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63]) ).
cnf(i_0_117,plain,
element(esk6_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_118,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_119,plain,
in(esk9_0,powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69]) ).
cnf(i_0_120,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_121,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_122,plain,
esk9_0 != complements_of_subsets(esk8_0,esk9_0),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89]) ).
cnf(i_0_123,plain,
powerset(powerset(esk8_0)) != esk5_0,
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95]) ).
cnf(i_0_124,plain,
~ subset(powerset(powerset(esk8_0)),esk5_0),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64]) ).
cnf(i_0_125,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_126,plain,
esk5_0 != esk7_0,
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100]) ).
cnf(i_0_127,plain,
element(esk2_3(esk8_0,esk9_0,esk9_0),powerset(esk8_0)),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54]) ).
cnf(i_0_128,plain,
( ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X1 = complements_of_subsets(X2,X3)
| element(esk2_3(X2,X3,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_129,plain,
subset(esk6_1(esk5_0),X1),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54,i_0_65]) ).
cnf(i_0_130,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_131,plain,
~ in(powerset(powerset(esk8_0)),esk9_0),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54,i_0_65,i_0_67]) ).
cnf(i_0_132,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_133,plain,
( element(X1,powerset(esk8_0))
| ~ in(X1,esk9_0) ),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54,i_0_65,i_0_67,i_0_62]) ).
cnf(i_0_134,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_135,plain,
esk5_0 != powerset(powerset(esk8_0)),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_79,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54,i_0_65,i_0_67,i_0_62,i_0_98]) ).
cnf(i_0_136,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_79]) ).
cnf(i_0_137,plain,
( X1 != powerset(powerset(esk8_0))
| ~ in(X1,esk9_0) ),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_79,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54,i_0_65,i_0_67,i_0_62,i_0_98,i_0_94]) ).
cnf(i_0_138,plain,
( in(esk2_3(esk8_0,esk9_0,esk9_0),esk9_0)
| in(subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0)),esk9_0) ),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_79,i_0_73,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54,i_0_65,i_0_67,i_0_62,i_0_98,i_0_94,i_0_53]) ).
cnf(i_0_139,plain,
( ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| in(subset_complement(X2,esk2_3(X2,X3,X1)),X3)
| X1 = complements_of_subsets(X2,X3)
| in(esk2_3(X2,X3,X1),X1) ),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_140,plain,
element(esk6_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_141,plain,
element(esk6_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_142,plain,
( ~ in(esk9_0,complements_of_subsets(powerset(esk8_0),esk6_1(powerset(powerset(esk8_0)))))
| ~ element(complements_of_subsets(powerset(esk8_0),esk6_1(powerset(powerset(esk8_0)))),powerset(powerset(powerset(esk8_0))))
| in(esk9_0,complements_of_subsets(powerset(esk8_0),esk6_1(powerset(powerset(esk8_0))))) ),
inference(scs_inference,[],[i_0_74,i_0_86,i_0_80,i_0_79,i_0_73,i_0_117,i_0_140,i_0_83,i_0_84,i_0_77,i_0_57,i_0_58,i_0_59,i_0_66,i_0_88,i_0_72,i_0_82,i_0_63,i_0_69,i_0_89,i_0_95,i_0_64,i_0_100,i_0_54,i_0_65,i_0_67,i_0_98,i_0_101,i_0_102]) ).
cnf(i_0_143,plain,
~ in(powerset(powerset(esk8_0)),esk9_0),
inference(equality_inference,[],[137]) ).
cnf(i_0_144,plain,
element(complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_103,i_0_57]) ).
cnf(i_0_145,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_146,plain,
element(subset_complement(powerset(esk8_0),complements_of_subsets(esk8_0,esk9_0)),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_103,i_0_57,i_0_59]) ).
cnf(i_0_147,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_148,plain,
subset(complements_of_subsets(esk8_0,esk9_0),powerset(esk8_0)),
inference(scs_inference,[],[i_0_103,i_0_57,i_0_59,i_0_66]) ).
cnf(i_0_149,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_150,plain,
subset(esk5_0,X1),
inference(scs_inference,[],[i_0_103,i_0_112,i_0_57,i_0_59,i_0_66,i_0_65]) ).
cnf(i_0_151,plain,
~ in(X1,esk5_0),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_152,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_153,plain,
~ in(X1,empty_set),
inference(scs_inference,[],[i_0_103,i_0_112,i_0_85,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72]) ).
cnf(i_0_154,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_155,plain,
esk9_0 = complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_103,i_0_105,i_0_112,i_0_85,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88]) ).
cnf(i_0_156,plain,
~ in(X1,esk3_1(powerset(empty_set))),
inference(scs_inference,[],[i_0_103,i_0_105,i_0_112,i_0_76,i_0_85,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63]) ).
cnf(i_0_157,plain,
element(esk3_1(X1),X1),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_158,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_159,plain,
in(complements_of_subsets(esk8_0,esk9_0),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_103,i_0_105,i_0_112,i_0_76,i_0_85,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69]) ).
cnf(i_0_160,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_161,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_162,plain,
~ subset(powerset(powerset(esk8_0)),esk6_1(esk5_0)),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_119,i_0_105,i_0_112,i_0_76,i_0_85,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64]) ).
cnf(i_0_163,plain,
~ in(X1,esk6_1(esk5_0)),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_164,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_165,plain,
powerset(powerset(esk8_0)) != esk6_1(esk5_0),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_112,i_0_76,i_0_85,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95]) ).
cnf(i_0_166,plain,
~ in(X1,esk6_1(esk5_0)),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_167,plain,
esk6_1(esk5_0) != powerset(powerset(esk8_0)),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98]) ).
cnf(i_0_168,plain,
subset(esk6_1(esk5_0),X1),
inference(rename_variables,[],[i_0_129]) ).
cnf(i_0_169,plain,
empty_set != esk9_0,
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_114,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98,i_0_100]) ).
cnf(i_0_170,plain,
~ in(powerset(powerset(esk8_0)),complements_of_subsets(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_114,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98,i_0_100,i_0_67]) ).
cnf(i_0_171,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_172,plain,
( element(X1,powerset(esk8_0))
| ~ in(X1,complements_of_subsets(esk8_0,esk9_0)) ),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_114,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98,i_0_100,i_0_67,i_0_62]) ).
cnf(i_0_173,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_174,plain,
empty_set != complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_114,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98,i_0_100,i_0_67,i_0_62,i_0_89]) ).
cnf(i_0_175,plain,
( X1 != powerset(powerset(esk8_0))
| ~ in(X1,complements_of_subsets(esk8_0,esk9_0)) ),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_114,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98,i_0_100,i_0_67,i_0_62,i_0_89,i_0_94]) ).
cnf(i_0_176,plain,
( complements_of_subsets(esk8_0,esk9_0) = complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))
| element(esk2_3(esk8_0,complements_of_subsets(esk8_0,esk9_0),complements_of_subsets(esk8_0,esk9_0)),powerset(esk8_0)) ),
inference(scs_inference,[],[i_0_103,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_114,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98,i_0_100,i_0_67,i_0_62,i_0_89,i_0_94,i_0_54]) ).
cnf(i_0_177,plain,
( ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X1 = complements_of_subsets(X2,X3)
| element(esk2_3(X2,X3,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_178,plain,
( ~ in(subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0)),esk9_0)
| in(esk2_3(esk8_0,esk9_0,esk9_0),complements_of_subsets(esk8_0,esk9_0)) ),
inference(scs_inference,[],[i_0_74,i_0_103,i_0_127,i_0_116,i_0_163,i_0_119,i_0_105,i_0_129,i_0_112,i_0_76,i_0_124,i_0_85,i_0_114,i_0_77,i_0_57,i_0_59,i_0_66,i_0_65,i_0_72,i_0_88,i_0_63,i_0_69,i_0_64,i_0_95,i_0_98,i_0_100,i_0_67,i_0_62,i_0_89,i_0_94,i_0_54,i_0_53,i_0_101]) ).
cnf(i_0_179,plain,
( ~ element(X1,powerset(X2))
| ~ in(subset_complement(X2,X1),X3)
| ~ element(X3,powerset(powerset(X2)))
| in(X1,complements_of_subsets(X2,X3))
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_180,plain,
~ in(powerset(powerset(esk8_0)),complements_of_subsets(esk8_0,esk9_0)),
inference(equality_inference,[],[175]) ).
cnf(i_0_181,plain,
~ in(X1,esk6_1(X2)),
inference(scs_inference,[],[i_0_81,i_0_72]) ).
cnf(i_0_182,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_183,plain,
element(subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0)),powerset(esk8_0)),
inference(scs_inference,[],[i_0_127,i_0_81,i_0_72,i_0_59]) ).
cnf(i_0_184,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_185,plain,
subset(subset_complement(powerset(esk8_0),esk9_0),powerset(esk8_0)),
inference(scs_inference,[],[i_0_107,i_0_127,i_0_81,i_0_72,i_0_59,i_0_66]) ).
cnf(i_0_186,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_187,plain,
subset(esk3_1(powerset(empty_set)),X1),
inference(scs_inference,[],[i_0_107,i_0_156,i_0_127,i_0_81,i_0_72,i_0_59,i_0_66,i_0_65]) ).
cnf(i_0_188,plain,
~ in(X1,esk3_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_189,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_190,plain,
in(subset_complement(powerset(esk8_0),esk9_0),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_107,i_0_156,i_0_127,i_0_81,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69]) ).
cnf(i_0_191,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_192,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_193,plain,
~ subset(powerset(powerset(esk8_0)),esk3_1(powerset(empty_set))),
inference(scs_inference,[],[i_0_119,i_0_107,i_0_156,i_0_188,i_0_127,i_0_81,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64]) ).
cnf(i_0_194,plain,
~ in(X1,esk3_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_195,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_196,plain,
powerset(powerset(esk8_0)) != esk3_1(powerset(empty_set)),
inference(scs_inference,[],[i_0_119,i_0_107,i_0_156,i_0_188,i_0_194,i_0_127,i_0_81,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64,i_0_95]) ).
cnf(i_0_197,plain,
~ in(X1,esk3_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_198,plain,
esk6_1(X1) != esk7_0,
inference(scs_inference,[],[i_0_119,i_0_107,i_0_156,i_0_188,i_0_194,i_0_127,i_0_81,i_0_83,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64,i_0_95,i_0_100]) ).
cnf(i_0_199,plain,
~ in(powerset(powerset(esk8_0)),subset_complement(powerset(esk8_0),esk9_0)),
inference(scs_inference,[],[i_0_119,i_0_107,i_0_156,i_0_188,i_0_194,i_0_127,i_0_81,i_0_83,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64,i_0_95,i_0_100,i_0_67]) ).
cnf(i_0_200,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_201,plain,
( element(X1,powerset(esk8_0))
| ~ in(X1,subset_complement(powerset(esk8_0),esk9_0)) ),
inference(scs_inference,[],[i_0_119,i_0_107,i_0_156,i_0_188,i_0_194,i_0_127,i_0_81,i_0_83,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64,i_0_95,i_0_100,i_0_67,i_0_62]) ).
cnf(i_0_202,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_203,plain,
( ~ empty(esk8_0)
| ~ in(X1,esk2_3(esk8_0,esk9_0,esk9_0)) ),
inference(scs_inference,[],[i_0_119,i_0_107,i_0_156,i_0_188,i_0_194,i_0_127,i_0_81,i_0_83,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64,i_0_95,i_0_100,i_0_67,i_0_62,i_0_63]) ).
cnf(i_0_204,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_205,plain,
( X1 != powerset(powerset(esk8_0))
| ~ in(X1,subset_complement(powerset(esk8_0),esk9_0)) ),
inference(scs_inference,[],[i_0_119,i_0_107,i_0_156,i_0_188,i_0_194,i_0_127,i_0_81,i_0_83,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64,i_0_95,i_0_100,i_0_67,i_0_62,i_0_63,i_0_94]) ).
cnf(i_0_206,plain,
~ in(X1,esk3_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_207,plain,
( ~ element(X1,powerset(X2))
| in(subset_complement(X2,X1),X3)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(X1,complements_of_subsets(X2,X3))
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_102]) ).
cnf(i_0_208,plain,
( ~ in(subset_complement(esk8_0,esk6_1(esk8_0)),esk9_0)
| in(esk6_1(esk8_0),complements_of_subsets(esk8_0,esk9_0)) ),
inference(scs_inference,[],[i_0_74,i_0_119,i_0_107,i_0_156,i_0_188,i_0_194,i_0_197,i_0_127,i_0_103,i_0_81,i_0_73,i_0_83,i_0_77,i_0_72,i_0_59,i_0_66,i_0_65,i_0_69,i_0_64,i_0_95,i_0_100,i_0_67,i_0_62,i_0_63,i_0_94,i_0_102,i_0_101]) ).
cnf(i_0_209,plain,
element(esk6_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_210,plain,
( ~ element(X1,powerset(X2))
| ~ in(subset_complement(X2,X1),X3)
| ~ element(X3,powerset(powerset(X2)))
| in(X1,complements_of_subsets(X2,X3))
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_211,plain,
~ in(powerset(powerset(esk8_0)),subset_complement(powerset(esk8_0),esk9_0)),
inference(equality_inference,[],[205]) ).
cnf(i_0_212,plain,
subset(esk6_1(X1),X2),
inference(scs_inference,[],[i_0_181,i_0_65]) ).
cnf(i_0_213,plain,
~ in(X1,esk6_1(X2)),
inference(rename_variables,[],[i_0_181]) ).
cnf(i_0_214,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_215,plain,
element(subset_complement(X1,esk6_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_73,i_0_181,i_0_65,i_0_59]) ).
cnf(i_0_216,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_217,plain,
subset(complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)),powerset(esk8_0)),
inference(scs_inference,[],[i_0_144,i_0_73,i_0_181,i_0_65,i_0_59,i_0_66]) ).
cnf(i_0_218,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_219,plain,
in(complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_144,i_0_73,i_0_181,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69]) ).
cnf(i_0_220,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_221,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_222,plain,
esk3_1(powerset(empty_set)) != powerset(powerset(esk8_0)),
inference(scs_inference,[],[i_0_144,i_0_124,i_0_73,i_0_181,i_0_187,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69,i_0_98]) ).
cnf(i_0_223,plain,
subset(esk3_1(powerset(empty_set)),X1),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_224,plain,
~ in(powerset(powerset(esk8_0)),complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))),
inference(scs_inference,[],[i_0_105,i_0_144,i_0_124,i_0_131,i_0_73,i_0_181,i_0_187,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69,i_0_98,i_0_95]) ).
cnf(i_0_225,plain,
esk6_1(X1) != esk9_0,
inference(scs_inference,[],[i_0_105,i_0_144,i_0_124,i_0_131,i_0_73,i_0_181,i_0_187,i_0_114,i_0_81,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69,i_0_98,i_0_95,i_0_100]) ).
cnf(i_0_226,plain,
( element(X1,powerset(esk8_0))
| ~ in(X1,complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))) ),
inference(scs_inference,[],[i_0_105,i_0_144,i_0_124,i_0_131,i_0_73,i_0_181,i_0_187,i_0_114,i_0_81,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69,i_0_98,i_0_95,i_0_100,i_0_62]) ).
cnf(i_0_227,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_228,plain,
( ~ empty(esk8_0)
| ~ in(X1,subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0))) ),
inference(scs_inference,[],[i_0_105,i_0_144,i_0_183,i_0_124,i_0_131,i_0_73,i_0_181,i_0_187,i_0_114,i_0_81,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69,i_0_98,i_0_95,i_0_100,i_0_62,i_0_63]) ).
cnf(i_0_229,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_230,plain,
( X1 != powerset(powerset(esk8_0))
| ~ in(X1,complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))) ),
inference(scs_inference,[],[i_0_105,i_0_144,i_0_183,i_0_124,i_0_131,i_0_73,i_0_181,i_0_187,i_0_114,i_0_81,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69,i_0_98,i_0_95,i_0_100,i_0_62,i_0_63,i_0_94]) ).
cnf(i_0_231,plain,
( ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| in(subset_complement(X2,esk2_3(X2,X3,X1)),X3)
| X1 = complements_of_subsets(X2,X3)
| in(esk2_3(X2,X3,X1),X1) ),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_232,plain,
element(esk6_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_233,plain,
~ in(X1,esk6_1(X2)),
inference(rename_variables,[],[i_0_181]) ).
cnf(i_0_234,plain,
( ~ in(esk2_3(esk8_0,complements_of_subsets(esk8_0,esk9_0),complements_of_subsets(esk8_0,esk9_0)),complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)))
| esk6_1(powerset(esk8_0)) != complements_of_subsets(esk8_0,esk9_0)
| complements_of_subsets(esk8_0,esk9_0) = complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))
| in(esk2_3(esk8_0,complements_of_subsets(esk8_0,esk9_0),complements_of_subsets(esk8_0,esk9_0)),complements_of_subsets(esk8_0,esk9_0))
| ~ in(subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0)),esk9_0) ),
inference(scs_inference,[],[i_0_74,i_0_105,i_0_103,i_0_144,i_0_127,i_0_183,i_0_124,i_0_131,i_0_73,i_0_181,i_0_213,i_0_187,i_0_114,i_0_81,i_0_77,i_0_65,i_0_59,i_0_66,i_0_69,i_0_98,i_0_95,i_0_100,i_0_62,i_0_53,i_0_101,i_0_55]) ).
cnf(i_0_235,plain,
~ in(powerset(powerset(esk8_0)),complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))),
inference(equality_inference,[],[230]) ).
cnf(i_0_236,plain,
subset(empty_set,X1),
inference(scs_inference,[],[i_0_153,i_0_65]) ).
cnf(i_0_237,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_238,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_239,plain,
subset(esk2_3(esk8_0,esk9_0,esk9_0),esk8_0),
inference(scs_inference,[],[i_0_127,i_0_153,i_0_65,i_0_66]) ).
cnf(i_0_240,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_241,plain,
~ in(X1,subset_complement(esk5_0,esk6_1(esk5_0))),
inference(scs_inference,[],[i_0_127,i_0_215,i_0_84,i_0_153,i_0_65,i_0_66,i_0_63]) ).
cnf(i_0_242,plain,
element(subset_complement(X1,esk6_1(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_215]) ).
cnf(i_0_243,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_244,plain,
in(esk2_3(esk8_0,esk9_0,esk9_0),powerset(esk8_0)),
inference(scs_inference,[],[i_0_127,i_0_215,i_0_84,i_0_153,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69]) ).
cnf(i_0_245,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_246,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_247,plain,
esk6_1(X1) != powerset(powerset(esk8_0)),
inference(scs_inference,[],[i_0_127,i_0_215,i_0_124,i_0_84,i_0_212,i_0_153,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98]) ).
cnf(i_0_248,plain,
subset(esk6_1(X1),X2),
inference(rename_variables,[],[i_0_212]) ).
cnf(i_0_249,plain,
empty_set != esk7_0,
inference(scs_inference,[],[i_0_127,i_0_215,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100]) ).
cnf(i_0_250,plain,
~ in(X1,complements_of_subsets(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_80,i_0_127,i_0_215,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95]) ).
cnf(i_0_251,plain,
~ in(subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0)),esk9_0),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101]) ).
cnf(i_0_252,plain,
( ~ element(X1,powerset(X2))
| ~ in(subset_complement(X2,X1),X3)
| ~ element(X3,powerset(powerset(X2)))
| in(X1,complements_of_subsets(X2,X3))
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_253,plain,
in(esk2_3(esk8_0,esk9_0,esk9_0),esk9_0),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138]) ).
cnf(i_0_254,plain,
element(esk2_3(esk8_0,esk9_0,esk9_0),esk9_0),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138,i_0_70]) ).
cnf(i_0_255,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_256,plain,
~ in(powerset(esk8_0),esk2_3(esk8_0,esk9_0,esk9_0)),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138,i_0_70,i_0_67]) ).
cnf(i_0_257,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_258,plain,
~ subset(powerset(esk8_0),esk3_1(powerset(empty_set))),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_156,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138,i_0_70,i_0_67,i_0_64]) ).
cnf(i_0_259,plain,
~ in(X1,esk3_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_260,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_261,plain,
( element(X1,esk8_0)
| ~ in(X1,esk2_3(esk8_0,esk9_0,esk9_0)) ),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_156,i_0_124,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138,i_0_70,i_0_67,i_0_64,i_0_62]) ).
cnf(i_0_262,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_263,plain,
esk2_3(esk8_0,esk9_0,esk9_0) != powerset(powerset(esk8_0)),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_156,i_0_124,i_0_131,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138,i_0_70,i_0_67,i_0_64,i_0_62,i_0_94]) ).
cnf(i_0_264,plain,
powerset(esk8_0) != esk3_1(powerset(empty_set)),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_156,i_0_124,i_0_131,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_79,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138,i_0_70,i_0_67,i_0_64,i_0_62,i_0_94,i_0_99]) ).
cnf(i_0_265,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_79]) ).
cnf(i_0_266,plain,
~ in(X1,esk3_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_267,plain,
( ~ element(X1,powerset(X2))
| in(subset_complement(X2,X1),X3)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(X1,complements_of_subsets(X2,X3))
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_102]) ).
cnf(i_0_268,plain,
( complements_of_subsets(esk8_0,esk9_0) = complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))
| in(esk2_3(esk8_0,complements_of_subsets(esk8_0,esk9_0),complements_of_subsets(esk8_0,esk9_0)),complements_of_subsets(esk8_0,esk9_0))
| in(subset_complement(esk8_0,esk2_3(esk8_0,complements_of_subsets(esk8_0,esk9_0),complements_of_subsets(esk8_0,esk9_0))),complements_of_subsets(esk8_0,esk9_0)) ),
inference(scs_inference,[],[i_0_74,i_0_80,i_0_103,i_0_127,i_0_215,i_0_156,i_0_259,i_0_124,i_0_131,i_0_84,i_0_85,i_0_212,i_0_153,i_0_237,i_0_79,i_0_83,i_0_77,i_0_65,i_0_66,i_0_63,i_0_69,i_0_98,i_0_100,i_0_95,i_0_101,i_0_138,i_0_70,i_0_67,i_0_64,i_0_94,i_0_99,i_0_53]) ).
cnf(i_0_269,plain,
~ in(subset_complement(esk8_0,esk6_1(esk8_0)),esk9_0),
inference(scs_inference,[],[i_0_250,i_0_208]) ).
cnf(i_0_270,plain,
~ in(esk9_0,esk2_3(esk8_0,esk9_0,esk9_0)),
inference(scs_inference,[],[i_0_253,i_0_67]) ).
cnf(i_0_271,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_272,plain,
subset(complements_of_subsets(esk8_0,esk9_0),X1),
inference(scs_inference,[],[i_0_250,i_0_253,i_0_67,i_0_65]) ).
cnf(i_0_273,plain,
~ in(X1,complements_of_subsets(esk8_0,esk9_0)),
inference(rename_variables,[],[i_0_250]) ).
cnf(i_0_274,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_275,plain,
subset(subset_complement(powerset(esk8_0),complements_of_subsets(esk8_0,esk9_0)),powerset(esk8_0)),
inference(scs_inference,[],[i_0_146,i_0_250,i_0_253,i_0_67,i_0_65,i_0_66]) ).
cnf(i_0_276,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_277,plain,
~ subset(powerset(powerset(esk8_0)),complements_of_subsets(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_119,i_0_146,i_0_250,i_0_273,i_0_253,i_0_67,i_0_65,i_0_66,i_0_64]) ).
cnf(i_0_278,plain,
~ in(X1,complements_of_subsets(esk8_0,esk9_0)),
inference(rename_variables,[],[i_0_250]) ).
cnf(i_0_279,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_280,plain,
in(subset_complement(powerset(esk8_0),complements_of_subsets(esk8_0,esk9_0)),powerset(powerset(esk8_0))),
inference(scs_inference,[],[i_0_119,i_0_146,i_0_250,i_0_273,i_0_253,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69]) ).
cnf(i_0_281,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_282,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_283,plain,
esk5_0 != powerset(esk8_0),
inference(scs_inference,[],[i_0_119,i_0_146,i_0_250,i_0_273,i_0_253,i_0_258,i_0_150,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98]) ).
cnf(i_0_284,plain,
subset(esk5_0,X1),
inference(rename_variables,[],[i_0_150]) ).
cnf(i_0_285,plain,
esk5_0 != esk9_0,
inference(scs_inference,[],[i_0_119,i_0_146,i_0_250,i_0_273,i_0_253,i_0_84,i_0_258,i_0_150,i_0_114,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98,i_0_100]) ).
cnf(i_0_286,plain,
~ in(subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0)),complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))),
inference(scs_inference,[],[i_0_105,i_0_119,i_0_146,i_0_250,i_0_273,i_0_253,i_0_251,i_0_84,i_0_258,i_0_150,i_0_114,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98,i_0_100,i_0_95]) ).
cnf(i_0_287,plain,
esk2_3(esk8_0,esk9_0,esk9_0) != subset_complement(esk8_0,esk2_3(esk8_0,esk9_0,esk9_0)),
inference(scs_inference,[],[i_0_105,i_0_119,i_0_146,i_0_250,i_0_273,i_0_253,i_0_251,i_0_84,i_0_258,i_0_150,i_0_114,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98,i_0_100,i_0_95,i_0_94]) ).
cnf(i_0_288,plain,
~ in(esk2_3(esk8_0,esk9_0,esk9_0),complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))),
inference(scs_inference,[],[i_0_103,i_0_105,i_0_119,i_0_127,i_0_146,i_0_144,i_0_250,i_0_273,i_0_278,i_0_253,i_0_251,i_0_84,i_0_258,i_0_150,i_0_114,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98,i_0_100,i_0_95,i_0_94,i_0_102]) ).
cnf(i_0_289,plain,
~ in(X1,complements_of_subsets(esk8_0,esk9_0)),
inference(rename_variables,[],[i_0_250]) ).
cnf(i_0_290,plain,
( ~ element(X1,powerset(X2))
| in(subset_complement(X2,X1),X3)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(X1,complements_of_subsets(X2,X3))
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_102]) ).
cnf(i_0_291,plain,
~ subset(powerset(powerset(esk8_0)),empty_set),
inference(scs_inference,[],[i_0_111,i_0_103,i_0_105,i_0_119,i_0_127,i_0_146,i_0_144,i_0_250,i_0_273,i_0_278,i_0_253,i_0_251,i_0_84,i_0_258,i_0_150,i_0_114,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98,i_0_100,i_0_95,i_0_94,i_0_102,i_0_99]) ).
cnf(i_0_292,plain,
( element(X1,powerset(esk8_0))
| ~ in(X1,subset_complement(powerset(esk8_0),complements_of_subsets(esk8_0,esk9_0))) ),
inference(scs_inference,[],[i_0_111,i_0_103,i_0_105,i_0_119,i_0_127,i_0_146,i_0_144,i_0_250,i_0_273,i_0_278,i_0_253,i_0_251,i_0_84,i_0_258,i_0_150,i_0_114,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98,i_0_100,i_0_95,i_0_94,i_0_102,i_0_99,i_0_62]) ).
cnf(i_0_293,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_294,plain,
( ~ empty(esk8_0)
| ~ in(powerset(powerset(esk8_0)),subset_complement(powerset(esk8_0),complements_of_subsets(esk8_0,esk9_0))) ),
inference(scs_inference,[],[i_0_111,i_0_103,i_0_105,i_0_119,i_0_127,i_0_146,i_0_144,i_0_250,i_0_273,i_0_278,i_0_253,i_0_251,i_0_84,i_0_258,i_0_150,i_0_114,i_0_77,i_0_67,i_0_65,i_0_66,i_0_64,i_0_69,i_0_98,i_0_100,i_0_95,i_0_94,i_0_102,i_0_99,i_0_62,i_0_63]) ).
cnf(i_0_295,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_296,plain,
~ in(X1,complements_of_subsets(esk8_0,esk9_0)),
inference(rename_variables,[],[i_0_250]) ).
cnf(i_0_297,plain,
~ in(X1,complements_of_subsets(esk8_0,esk9_0)),
inference(rename_variables,[],[i_0_250]) ).
cnf(i_0_299,plain,
( complements_of_subsets(esk8_0,esk9_0) = complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0))
| in(esk2_3(esk8_0,complements_of_subsets(esk8_0,esk9_0),complements_of_subsets(esk8_0,esk9_0)),complements_of_subsets(esk8_0,esk9_0)) ),
inference(scs_inference,[],[i_0_250,i_0_268]) ).
cnf(i_0_300,plain,
complements_of_subsets(esk8_0,esk9_0) = complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_250,i_0_299]) ).
cnf(i_0_301,plain,
~ in(X1,complements_of_subsets(esk8_0,esk9_0)),
inference(rename_variables,[],[i_0_250]) ).
cnf(i_0_302,plain,
~ in(powerset(powerset(esk8_0)),subset_complement(powerset(esk8_0),complements_of_subsets(esk8_0,esk9_0))),
inference(scs_inference,[],[i_0_280,i_0_250,i_0_299,i_0_67]) ).
cnf(i_0_303,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_304,plain,
subset(subset_complement(esk5_0,esk6_1(esk5_0)),X1),
inference(scs_inference,[],[i_0_280,i_0_241,i_0_250,i_0_299,i_0_67,i_0_65]) ).
cnf(i_0_305,plain,
~ in(X1,subset_complement(esk5_0,esk6_1(esk5_0))),
inference(rename_variables,[],[i_0_241]) ).
cnf(i_0_306,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_307,plain,
subset(subset_complement(X1,esk6_1(X1)),X1),
inference(scs_inference,[],[i_0_280,i_0_241,i_0_215,i_0_250,i_0_299,i_0_67,i_0_65,i_0_66]) ).
cnf(i_0_308,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_309,plain,
complements_of_subsets(esk8_0,complements_of_subsets(esk8_0,esk9_0)) = complements_of_subsets(esk8_0,esk9_0),
inference(scs_inference,[],[i_0_280,i_0_241,i_0_215,i_0_250,i_0_299,i_0_67,i_0_65,i_0_66,i_0_88]) ).
cnf(i_0_310,plain,
~ subset(powerset(powerset(esk8_0)),subset_complement(esk5_0,esk6_1(esk5_0))),
inference(scs_inference,[],[i_0_119,i_0_280,i_0_241,i_0_305,i_0_215,i_0_250,i_0_299,i_0_67,i_0_65,i_0_66,i_0_88,i_0_64]) ).
cnf(i_0_311,plain,
~ in(X1,subset_complement(esk5_0,esk6_1(esk5_0))),
inference(rename_variables,[],[i_0_241]) ).
cnf(i_0_312,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_313,plain,
in(subset_complement(X1,esk6_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_119,i_0_280,i_0_241,i_0_305,i_0_215,i_0_250,i_0_77,i_0_299,i_0_67,i_0_65,i_0_66,i_0_88,i_0_64,i_0_69]) ).
cnf(i_0_314,plain,
element(subset_complement(X1,esk6_1(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_215]) ).
cnf(i_0_315,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_316,plain,
$false,
inference(scs_inference,[],[i_0_111,i_0_119,i_0_174,i_0_280,i_0_241,i_0_305,i_0_215,i_0_250,i_0_77,i_0_299,i_0_67,i_0_65,i_0_66,i_0_88,i_0_64,i_0_69,i_0_89]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU174+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.13 % 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
% 0.17/0.33 % Computer : n028.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 02:46:46 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 0.55/1.62 % Version : CSE_E---1.7
% 0.55/1.62 % Problem : theBenchmark.p
% 0.55/1.62 % SZS status Theorem for theBenchmark.p
% 0.55/1.62 % SZS output start CNFRefutation
% See solution above
% 1.07/2.13 % Total time : 1.272s
%------------------------------------------------------------------------------