%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU117+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 05:10:39 PM UTC 2026
% Result : Theorem 0.29s 1.62s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 79)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(rc4_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(rc3_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(t32_finsub_1,conjecture,
! [X1,X2] :
( element(X2,finite_subsets(X1))
=> element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
fof(fc2_finsub_1,axiom,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finsub_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(fc1_finsub_1,axiom,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc1_finset_1,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(rc1_finsub_1,axiom,
? [X1] :
( ~ empty(X1)
& cup_closed(X1)
& cap_closed(X1)
& diff_closed(X1)
& preboolean(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finsub_1) ).
fof(d5_finsub_1,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(cc2_finset_1,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(cc3_finsub_1,axiom,
! [X1,X2] :
( element(X2,finite_subsets(X1))
=> finite(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(rc2_finset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(cc2_finsub_1,axiom,
! [X1] :
( ( cup_closed(X1)
& diff_closed(X1) )
=> preboolean(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc1_finset_1,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(cc1_finsub_1,axiom,
! [X1] :
( preboolean(X1)
=> ( cup_closed(X1)
& diff_closed(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_32,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_33,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_34,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc4_finset_1]) ).
fof(i_0_35,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(i_0_36,negated_conjecture,
~ ! [X1,X2] :
( element(X2,finite_subsets(X1))
=> element(X2,powerset(X1)) ),
inference(assume_negation,[status(cth)],[t32_finsub_1]) ).
fof(i_0_37,plain,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_finsub_1]) ).
fof(i_0_38,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_39,plain,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_finsub_1]) ).
fof(i_0_40,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_41,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
fof(i_0_42,plain,
? [X1] :
( ~ empty(X1)
& cup_closed(X1)
& cap_closed(X1)
& diff_closed(X1)
& preboolean(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finsub_1]) ).
fof(i_0_43,plain,
! [X106,X107,X108,X109] :
( ( subset(X108,X106)
| ~ in(X108,X107)
| X107 != finite_subsets(X106)
| ~ preboolean(X107) )
& ( finite(X108)
| ~ in(X108,X107)
| X107 != finite_subsets(X106)
| ~ preboolean(X107) )
& ( ~ subset(X109,X106)
| ~ finite(X109)
| in(X109,X107)
| X107 != finite_subsets(X106)
| ~ preboolean(X107) )
& ( ~ in(esk13_2(X106,X107),X107)
| ~ subset(esk13_2(X106,X107),X106)
| ~ finite(esk13_2(X106,X107))
| X107 = finite_subsets(X106)
| ~ preboolean(X107) )
& ( subset(esk13_2(X106,X107),X106)
| in(esk13_2(X106,X107),X107)
| X107 = finite_subsets(X106)
| ~ preboolean(X107) )
& ( finite(esk13_2(X106,X107))
| in(esk13_2(X106,X107),X107)
| X107 = finite_subsets(X106)
| ~ preboolean(X107) ) ),
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)],[d5_finsub_1])])])])])]) ).
fof(i_0_44,plain,
! [X99,X100,X101] :
( ~ in(X99,X100)
| ~ element(X100,powerset(X101))
| element(X99,X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_45,plain,
! [X61,X62,X63] :
( ~ in(X61,X62)
| ~ element(X62,powerset(X63))
| ~ empty(X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_46,plain,
! [X97,X98] :
( ( ~ element(X97,powerset(X98))
| subset(X97,X98) )
& ( ~ subset(X97,X98)
| element(X97,powerset(X98)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_47,plain,
! [X68,X69] :
( ~ in(X68,X69)
| ~ in(X69,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_32])]) ).
fof(i_0_48,plain,
! [X79,X80] :
( ~ finite(X79)
| ~ element(X80,powerset(X79))
| finite(X80) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(i_0_49,plain,
! [X59,X60] :
( ~ element(X59,X60)
| empty(X60)
| in(X59,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_50,plain,
! [X95,X96] :
( ~ in(X95,X96)
| element(X95,X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_51,plain,
! [X76,X77] :
( ~ element(X77,finite_subsets(X76))
| finite(X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_finsub_1])]) ).
fof(i_0_52,plain,
! [X89] :
( ( element(esk7_1(X89),powerset(X89))
| empty(X89) )
& ( ~ empty(esk7_1(X89))
| empty(X89) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_33])])])]) ).
fof(i_0_53,plain,
! [X86] :
( ( element(esk6_1(X86),powerset(X86))
| empty(X86) )
& ( ~ empty(esk6_1(X86))
| empty(X86) )
& ( finite(esk6_1(X86))
| empty(X86) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_34])])])]) ).
fof(i_0_54,plain,
! [X84] :
( ( element(esk5_1(X84),powerset(X84))
| empty(X84) )
& ( ~ empty(esk5_1(X84))
| empty(X84) )
& ( finite(esk5_1(X84))
| empty(X84) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_35])])])]) ).
fof(i_0_55,plain,
! [X102,X103] :
( ~ in(X102,X103)
| ~ empty(X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_56,plain,
! [X91] :
( element(esk8_1(X91),powerset(X91))
& empty(esk8_1(X91)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_57,plain,
! [X82] :
( element(esk4_1(X82),powerset(X82))
& empty(esk4_1(X82))
& relation(esk4_1(X82))
& function(esk4_1(X82))
& one_to_one(esk4_1(X82))
& epsilon_transitive(esk4_1(X82))
& epsilon_connected(esk4_1(X82))
& ordinal(esk4_1(X82))
& natural(esk4_1(X82))
& finite(esk4_1(X82)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(i_0_58,negated_conjecture,
( element(esk12_0,finite_subsets(esk11_0))
& ~ element(esk12_0,powerset(esk11_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_36])])]) ).
fof(i_0_59,plain,
! [X70] : element(esk1_1(X70),X70),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_60,plain,
! [X57] :
( ~ cup_closed(X57)
| ~ diff_closed(X57)
| preboolean(X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finsub_1])]) ).
fof(i_0_61,plain,
! [X74] :
( ~ empty(finite_subsets(X74))
& cup_closed(finite_subsets(X74))
& diff_closed(finite_subsets(X74))
& preboolean(finite_subsets(X74)) ),
inference(variable_rename,[status(thm)],[i_0_37]) ).
fof(i_0_62,plain,
! [X88] : ~ empty(powerset(X88)),
inference(variable_rename,[status(thm)],[i_0_38]) ).
fof(i_0_63,plain,
! [X73] :
( ~ empty(powerset(X73))
& cup_closed(powerset(X73))
& diff_closed(powerset(X73))
& preboolean(powerset(X73)) ),
inference(variable_rename,[status(thm)],[i_0_39]) ).
fof(i_0_64,plain,
! [X65,X66] :
( ~ empty(X65)
| X65 = X66
| ~ empty(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_65,plain,
! [X67] : subset(X67,X67),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_66,plain,
! [X58] :
( ~ empty(X58)
| finite(X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_67,plain,
! [X75] :
( ( cup_closed(X75)
| ~ preboolean(X75) )
& ( diff_closed(X75)
| ~ preboolean(X75) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finsub_1])])]) ).
fof(i_0_68,plain,
! [X72] : preboolean(finite_subsets(X72)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(i_0_69,plain,
! [X64] :
( ~ empty(X64)
| X64 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_70,plain,
~ empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_40])]) ).
fof(i_0_71,plain,
( ~ empty(esk3_0)
& finite(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_41])]) ).
fof(i_0_72,plain,
( ~ empty(esk2_0)
& cup_closed(esk2_0)
& cap_closed(esk2_0)
& diff_closed(esk2_0)
& preboolean(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_42])]) ).
fof(i_0_73,plain,
empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_74,plain,
( X2 = finite_subsets(X1)
| ~ in(esk13_2(X1,X2),X2)
| ~ subset(esk13_2(X1,X2),X1)
| ~ finite(esk13_2(X1,X2))
| ~ preboolean(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_75,plain,
( subset(esk13_2(X1,X2),X1)
| in(esk13_2(X1,X2),X2)
| X2 = finite_subsets(X1)
| ~ preboolean(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_76,plain,
( finite(esk13_2(X1,X2))
| in(esk13_2(X1,X2),X2)
| X2 = finite_subsets(X1)
| ~ preboolean(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_77,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_78,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_79,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| ~ finite(X1)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_80,plain,
( subset(X1,X2)
| ~ in(X1,X3)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_81,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_82,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_83,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_84,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_85,plain,
( finite(X1)
| ~ in(X1,X2)
| X2 != finite_subsets(X3)
| ~ preboolean(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_86,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_87,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_88,plain,
( finite(X1)
| ~ element(X1,finite_subsets(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_89,plain,
( element(esk7_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_90,plain,
( element(esk6_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_91,plain,
( element(esk5_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_92,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_93,plain,
element(esk8_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_94,plain,
element(esk4_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_95,negated_conjecture,
~ element(esk12_0,powerset(esk11_0)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_96,plain,
( empty(X1)
| ~ empty(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_97,plain,
( empty(X1)
| ~ empty(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_98,plain,
( empty(X1)
| ~ empty(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_99,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_100,plain,
( preboolean(X1)
| ~ cup_closed(X1)
| ~ diff_closed(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_101,plain,
~ empty(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_102,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_103,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_104,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_105,negated_conjecture,
element(esk12_0,finite_subsets(esk11_0)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_106,plain,
( finite(esk6_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_107,plain,
( finite(esk5_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_108,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_109,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_110,plain,
( diff_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_111,plain,
( cup_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_112,plain,
natural(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_113,plain,
ordinal(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_114,plain,
epsilon_connected(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_115,plain,
epsilon_transitive(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_116,plain,
one_to_one(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_117,plain,
function(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_118,plain,
relation(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_119,plain,
finite(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_120,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_121,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_122,plain,
preboolean(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_123,plain,
diff_closed(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_124,plain,
diff_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_125,plain,
cup_closed(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_126,plain,
cup_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_127,plain,
empty(esk8_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_128,plain,
empty(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_129,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_130,plain,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_131,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_132,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_133,plain,
cap_closed(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_134,plain,
finite(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_135,plain,
preboolean(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_136,plain,
diff_closed(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_137,plain,
cup_closed(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_138,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_139,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_140,axiom,
X1 = X1 ).
cnf(i_0_141,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_142,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_143,axiom,
( X1 != X2
| finite_subsets(X1) = finite_subsets(X2) ) ).
cnf(i_0_144,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_145,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_146,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_147,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_148,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_149,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_150,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_151,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_152,axiom,
( X1 != X2
| ~ cap_closed(X1)
| cap_closed(X2) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| ~ preboolean(X1)
| preboolean(X2) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| ~ cup_closed(X1)
| cup_closed(X2) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| ~ diff_closed(X1)
| diff_closed(X2) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_140_001,axiom,
X1 = X1 ).
cnf(i_0_141_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_142_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_143_004,axiom,
( X1 != X2
| finite_subsets(X1) = finite_subsets(X2) ) ).
cnf(i_0_144_005,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_145_006,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_146_007,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_147_008,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_148_009,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_149_010,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_150_011,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_151_012,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_152_013,axiom,
( X1 != X2
| ~ cap_closed(X1)
| cap_closed(X2) ) ).
cnf(i_0_153_014,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_154_015,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_155_016,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_156_017,axiom,
( X1 != X2
| ~ preboolean(X1)
| preboolean(X2) ) ).
cnf(i_0_157_018,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_158_019,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_159_020,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_160_021,axiom,
( X1 != X2
| ~ cup_closed(X1)
| cup_closed(X2) ) ).
cnf(i_0_161_022,axiom,
( X1 != X2
| ~ diff_closed(X1)
| diff_closed(X2) ) ).
cnf(i_0_162_023,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_163,plain,
( ~ finite(X1)
| ~ preboolean(finite_subsets(X2))
| in(X1,finite_subsets(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[79]) ).
cnf(i_0_164,plain,
( ~ preboolean(finite_subsets(X1))
| subset(X2,X1)
| ~ in(X2,finite_subsets(X1)) ),
inference(equality_inference,[],[80]) ).
cnf(i_0_165,plain,
( ~ preboolean(finite_subsets(X1))
| finite(X2)
| ~ in(X2,finite_subsets(X1)) ),
inference(equality_inference,[],[85]) ).
cnf(i_0_166,plain,
~ subset(esk12_0,esk11_0),
inference(scs_inference,[],[i_0_95,i_0_84]) ).
cnf(i_0_167,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_168,plain,
finite(esk12_0),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_84,i_0_88]) ).
cnf(i_0_169,plain,
( ~ element(X1,finite_subsets(X2))
| finite(X1) ),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_170,plain,
subset(esk8_1(X1),X1),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_84,i_0_88,i_0_81]) ).
cnf(i_0_171,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_172,plain,
~ in(X1,esk9_0),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92]) ).
cnf(i_0_173,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_92]) ).
cnf(i_0_174,plain,
finite(esk9_0),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109]) ).
cnf(i_0_175,plain,
( ~ empty(X1)
| finite(X1) ),
inference(rename_variables,[],[i_0_109]) ).
cnf(i_0_176,plain,
~ in(esk12_0,esk8_1(powerset(esk11_0))),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109,i_0_77]) ).
cnf(i_0_177,plain,
element(esk8_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_178,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_179,plain,
~ in(X1,esk8_1(esk9_0)),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_177,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109,i_0_77,i_0_78]) ).
cnf(i_0_180,plain,
element(esk8_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_181,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_182,plain,
in(esk12_0,finite_subsets(esk11_0)),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_177,i_0_101,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109,i_0_77,i_0_78,i_0_86]) ).
cnf(i_0_183,plain,
~ empty(finite_subsets(X1)),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_184,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_185,plain,
esk8_1(esk11_0) != esk12_0,
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_177,i_0_180,i_0_101,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109,i_0_77,i_0_78,i_0_86,i_0_157]) ).
cnf(i_0_186,plain,
element(esk8_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_187,plain,
finite_subsets(esk11_0) != powerset(esk11_0),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_177,i_0_180,i_0_101,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109,i_0_77,i_0_78,i_0_86,i_0_157,i_0_158]) ).
cnf(i_0_188,plain,
finite(esk8_1(esk3_0)),
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_177,i_0_180,i_0_186,i_0_101,i_0_134,i_0_138,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109,i_0_77,i_0_78,i_0_86,i_0_157,i_0_158,i_0_83]) ).
cnf(i_0_189,plain,
element(esk8_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_190,plain,
( ~ element(X1,powerset(X2))
| finite(X1)
| ~ finite(X2) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_191,plain,
$false,
inference(scs_inference,[],[i_0_95,i_0_105,i_0_93,i_0_177,i_0_180,i_0_186,i_0_101,i_0_134,i_0_138,i_0_121,i_0_84,i_0_88,i_0_81,i_0_92,i_0_109,i_0_77,i_0_78,i_0_86,i_0_157,i_0_158,i_0_83,i_0_164]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU117+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:44:48 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.29/1.62 % Version : CSE_E---1.7
% 0.29/1.62 % Problem : theBenchmark.p
% 0.29/1.62 % SZS status Theorem for theBenchmark.p
% 0.29/1.62 % SZS output start CNFRefutation
% See solution above
% 0.39/1.72 % Total time : 1.272s
%------------------------------------------------------------------------------