%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU169+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 : n018.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 05:10:54 PM UTC 2026
% Result : Theorem 0.26s 1.61s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 41)
% 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(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(l3_subset_1,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_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(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
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_15,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_16,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_17,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_18,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
inference(assume_negation,[status(cth)],[l3_subset_1]) ).
fof(i_0_19,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_20,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_21,plain,
! [X33,X34,X35,X36,X37,X38] :
( ( ~ in(X35,X34)
| subset(X35,X33)
| X34 != powerset(X33) )
& ( ~ subset(X36,X33)
| in(X36,X34)
| X34 != powerset(X33) )
& ( ~ in(esk1_2(X37,X38),X38)
| ~ subset(esk1_2(X37,X38),X37)
| X38 = powerset(X37) )
& ( in(esk1_2(X37,X38),X38)
| subset(esk1_2(X37,X38),X37)
| X38 = powerset(X37) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_zfmisc_1])])])])])]) ).
fof(i_0_22,plain,
! [X42,X43,X44,X45,X46] :
( ( ~ subset(X42,X43)
| ~ in(X44,X42)
| in(X44,X43) )
& ( in(esk2_2(X45,X46),X45)
| subset(X45,X46) )
& ( ~ in(esk2_2(X45,X46),X46)
| subset(X45,X46) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(i_0_23,plain,
! [X31,X32] :
( ~ in(X31,X32)
| ~ in(X32,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])]) ).
fof(i_0_24,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_16])])]) ).
fof(i_0_25,plain,
! [X54] :
( ( element(esk7_1(X54),powerset(X54))
| empty(X54) )
& ( ~ empty(esk7_1(X54))
| empty(X54) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_17])])])]) ).
fof(i_0_26,plain,
! [X60,X61] :
( ~ in(X60,X61)
| ~ empty(X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_27,plain,
! [X48] : element(esk3_1(X48),X48),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_28,negated_conjecture,
( element(esk5_0,powerset(esk4_0))
& in(esk6_0,esk5_0)
& ~ in(esk6_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])])]) ).
fof(i_0_29,plain,
! [X50] : ~ empty(powerset(X50)),
inference(variable_rename,[status(thm)],[i_0_19]) ).
fof(i_0_30,plain,
! [X62,X63] :
( ~ empty(X62)
| X62 = X63
| ~ empty(X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_31,plain,
! [X58] : subset(X58,X58),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_32,plain,
! [X59] :
( ~ empty(X59)
| X59 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_33,plain,
~ empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_20])]) ).
fof(i_0_34,plain,
empty(esk8_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_35,plain,
( X2 = powerset(X1)
| ~ in(esk1_2(X1,X2),X2)
| ~ subset(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_36,plain,
( in(esk1_2(X1,X2),X2)
| subset(esk1_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_37,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_38,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_39,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_41,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_42,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_43,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_44,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_45,plain,
( empty(X1)
| ~ element(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_46,plain,
( element(esk7_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_47,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_48,plain,
( element(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_49,plain,
( empty(X1)
| ~ empty(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_50,plain,
element(esk3_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_51,negated_conjecture,
~ in(esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_52,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_53,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_54,negated_conjecture,
element(esk5_0,powerset(esk4_0)),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_55,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_56,negated_conjecture,
in(esk6_0,esk5_0),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_57,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_58,plain,
~ empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_59,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_60,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_61,axiom,
X1 = X1 ).
cnf(i_0_62,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_63,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_64,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_66,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_67,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_68,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_69,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_70,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_71,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_61_001,axiom,
X1 = X1 ).
cnf(i_0_62_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_63_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_64_004,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_65_005,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_66_006,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_67_007,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_68_008,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_69_009,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_70_010,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_71_011,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_72,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[40]) ).
cnf(i_0_73,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[41]) ).
cnf(i_0_74,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_55,i_0_73]) ).
cnf(i_0_75,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_76,plain,
~ in(esk5_0,esk6_0),
inference(scs_inference,[],[i_0_56,i_0_55,i_0_73,i_0_42]) ).
cnf(i_0_77,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_78,plain,
~ in(X1,esk8_0),
inference(scs_inference,[],[i_0_56,i_0_55,i_0_59,i_0_73,i_0_42,i_0_47]) ).
cnf(i_0_79,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_80,plain,
~ subset(esk5_0,esk4_0),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_59,i_0_73,i_0_42,i_0_47,i_0_38]) ).
cnf(i_0_81,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_82,plain,
in(esk3_1(esk9_0),esk9_0),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_58,i_0_59,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44]) ).
cnf(i_0_83,plain,
element(esk3_1(X1),X1),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_84,plain,
( empty(X1)
| ~ element(X2,X1)
| in(X2,X1) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_85,plain,
~ element(esk9_0,esk8_0),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_58,i_0_59,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45]) ).
cnf(i_0_86,plain,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_87,plain,
esk5_0 != esk4_0,
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_58,i_0_59,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66]) ).
cnf(i_0_88,plain,
esk3_1(esk8_0) != esk9_0,
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69]) ).
cnf(i_0_89,plain,
element(esk3_1(X1),X1),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_90,plain,
element(X1,powerset(X1)),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_52,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69,i_0_43]) ).
cnf(i_0_91,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_92,plain,
( empty(X1)
| ~ in(X2,X1)
| element(X2,X1) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_93,plain,
element(esk8_0,esk8_0),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_52,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69,i_0_43,i_0_48]) ).
cnf(i_0_94,plain,
( ~ empty(X1)
| ~ empty(X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_95,plain,
esk4_0 != esk5_0,
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_52,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69,i_0_43,i_0_48,i_0_67]) ).
cnf(i_0_96,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_97,plain,
esk8_0 != esk9_0,
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_52,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69,i_0_43,i_0_48,i_0_67,i_0_71]) ).
cnf(i_0_98,plain,
subset(esk8_0,X1),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_52,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69,i_0_43,i_0_48,i_0_67,i_0_71,i_0_39]) ).
cnf(i_0_99,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_100,plain,
( X1 != esk6_0
| ~ in(X1,esk4_0) ),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_52,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69,i_0_43,i_0_48,i_0_67,i_0_71,i_0_39,i_0_65]) ).
cnf(i_0_101,plain,
( X1 != esk8_0
| ~ element(esk9_0,X1) ),
inference(scs_inference,[],[i_0_51,i_0_56,i_0_55,i_0_50,i_0_83,i_0_58,i_0_59,i_0_52,i_0_73,i_0_42,i_0_47,i_0_38,i_0_44,i_0_45,i_0_66,i_0_69,i_0_43,i_0_48,i_0_67,i_0_71,i_0_39,i_0_65,i_0_70]) ).
cnf(i_0_102,plain,
~ in(esk6_0,esk4_0),
inference(equality_inference,[],[100]) ).
cnf(i_0_103,plain,
~ element(esk9_0,esk8_0),
inference(equality_inference,[],[101]) ).
cnf(i_0_104,plain,
powerset(esk9_0) != esk8_0,
inference(scs_inference,[],[i_0_90,i_0_101]) ).
cnf(i_0_105,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_106,plain,
in(esk8_0,powerset(X1)),
inference(scs_inference,[],[i_0_90,i_0_98,i_0_101,i_0_73]) ).
cnf(i_0_107,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_108,plain,
~ in(powerset(X1),X1),
inference(scs_inference,[],[i_0_74,i_0_90,i_0_98,i_0_101,i_0_73,i_0_42]) ).
cnf(i_0_109,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_110,plain,
~ in(X1,empty_set),
inference(scs_inference,[],[i_0_74,i_0_90,i_0_98,i_0_60,i_0_101,i_0_73,i_0_42,i_0_47]) ).
cnf(i_0_111,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_112,plain,
in(esk5_0,powerset(esk4_0)),
inference(scs_inference,[],[i_0_54,i_0_74,i_0_90,i_0_98,i_0_60,i_0_52,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44]) ).
cnf(i_0_113,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_114,plain,
( empty(X1)
| ~ element(X2,X1)
| in(X2,X1) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_115,plain,
~ element(powerset(X1),empty_set),
inference(scs_inference,[],[i_0_54,i_0_74,i_0_90,i_0_98,i_0_60,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45]) ).
cnf(i_0_116,plain,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_117,plain,
element(empty_set,empty_set),
inference(scs_inference,[],[i_0_54,i_0_74,i_0_90,i_0_98,i_0_60,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48]) ).
cnf(i_0_118,plain,
( ~ empty(X1)
| ~ empty(X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_119,plain,
~ subset(powerset(esk6_0),esk4_0),
inference(scs_inference,[],[i_0_51,i_0_54,i_0_74,i_0_90,i_0_98,i_0_60,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48,i_0_38]) ).
cnf(i_0_120,plain,
in(X1,powerset(X1)),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_121,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_122,plain,
esk5_0 != esk8_0,
inference(scs_inference,[],[i_0_51,i_0_54,i_0_56,i_0_74,i_0_90,i_0_78,i_0_98,i_0_60,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48,i_0_38,i_0_66]) ).
cnf(i_0_123,plain,
~ in(X1,esk8_0),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_124,plain,
esk3_1(empty_set) != powerset(X1),
inference(scs_inference,[],[i_0_51,i_0_54,i_0_56,i_0_74,i_0_90,i_0_78,i_0_98,i_0_60,i_0_50,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48,i_0_38,i_0_66,i_0_69]) ).
cnf(i_0_125,plain,
element(esk3_1(X1),X1),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_126,plain,
esk8_0 != esk5_0,
inference(scs_inference,[],[i_0_51,i_0_54,i_0_56,i_0_74,i_0_80,i_0_90,i_0_78,i_0_98,i_0_60,i_0_50,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48,i_0_38,i_0_66,i_0_69,i_0_67]) ).
cnf(i_0_127,plain,
subset(esk8_0,X1),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_128,plain,
powerset(powerset(X1)) != empty_set,
inference(scs_inference,[],[i_0_51,i_0_54,i_0_56,i_0_74,i_0_80,i_0_90,i_0_105,i_0_78,i_0_98,i_0_60,i_0_50,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48,i_0_38,i_0_66,i_0_69,i_0_67,i_0_70]) ).
cnf(i_0_129,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_130,plain,
empty_set != powerset(X1),
inference(scs_inference,[],[i_0_51,i_0_54,i_0_56,i_0_74,i_0_80,i_0_90,i_0_105,i_0_78,i_0_98,i_0_60,i_0_50,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48,i_0_38,i_0_66,i_0_69,i_0_67,i_0_70,i_0_71]) ).
cnf(i_0_131,plain,
$false,
inference(scs_inference,[],[i_0_51,i_0_54,i_0_56,i_0_74,i_0_80,i_0_90,i_0_105,i_0_78,i_0_98,i_0_60,i_0_50,i_0_52,i_0_113,i_0_101,i_0_73,i_0_42,i_0_47,i_0_44,i_0_45,i_0_48,i_0_38,i_0_66,i_0_69,i_0_67,i_0_70,i_0_71,i_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU169+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
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:45:47 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.26/1.61 % Version : CSE_E---1.7
% 0.26/1.61 % Problem : theBenchmark.p
% 0.26/1.61 % SZS status Theorem for theBenchmark.p
% 0.26/1.61 % SZS output start CNFRefutation
% See solution above
% 0.45/1.81 % Total time : 1.270s
%------------------------------------------------------------------------------