%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU116+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 : n022.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 0.26s 1.61s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 75
% Syntax : Number of formulae : 177 ( 54 unt; 0 def)
% Number of atoms : 420 ( 56 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 424 ( 181 ~; 143 |; 79 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-1 aty)
% Number of variables : 264 ( 24 sgn 87 !; 16 ?)
% 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(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(t30_finsub_1,conjecture,
! [X1,X2] :
( element(X2,finite_subsets(X1))
=> finite(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_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(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_31,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_32,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_33,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc4_finset_1]) ).
fof(i_0_34,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(i_0_35,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_36,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_37,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_38,negated_conjecture,
~ ! [X1,X2] :
( element(X2,finite_subsets(X1))
=> finite(X2) ),
inference(assume_negation,[status(cth)],[t30_finsub_1]) ).
fof(i_0_39,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_40,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
fof(i_0_41,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_42,plain,
! [X59,X60,X61] :
( ~ in(X59,X60)
| ~ element(X60,powerset(X61))
| element(X59,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_43,plain,
! [X62,X63,X64] :
( ~ in(X62,X63)
| ~ element(X63,powerset(X64))
| ~ empty(X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_44,plain,
! [X76,X77] :
( ( ~ element(X76,powerset(X77))
| subset(X76,X77) )
& ( ~ subset(X76,X77)
| element(X76,powerset(X77)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_45,plain,
! [X55,X56] :
( ~ in(X55,X56)
| ~ in(X56,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_31])]) ).
fof(i_0_46,plain,
! [X71,X72] :
( ~ finite(X71)
| ~ element(X72,powerset(X71))
| finite(X72) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(i_0_47,plain,
! [X74,X75] :
( ~ element(X74,X75)
| empty(X75)
| in(X74,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_48,plain,
! [X57,X58] :
( ~ in(X57,X58)
| element(X57,X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_49,plain,
! [X85,X86] :
( ~ element(X86,finite_subsets(X85))
| finite(X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_finsub_1])]) ).
fof(i_0_50,plain,
! [X95] :
( ( element(esk7_1(X95),powerset(X95))
| empty(X95) )
& ( ~ empty(esk7_1(X95))
| empty(X95) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_32])])])]) ).
fof(i_0_51,plain,
! [X93] :
( ( element(esk6_1(X93),powerset(X93))
| empty(X93) )
& ( ~ empty(esk6_1(X93))
| empty(X93) )
& ( finite(esk6_1(X93))
| empty(X93) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_33])])])]) ).
fof(i_0_52,plain,
! [X91] :
( ( element(esk5_1(X91),powerset(X91))
| empty(X91) )
& ( ~ empty(esk5_1(X91))
| empty(X91) )
& ( finite(esk5_1(X91))
| empty(X91) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_34])])])]) ).
fof(i_0_53,plain,
! [X79,X80] :
( ~ in(X79,X80)
| ~ empty(X80) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_54,plain,
! [X97] :
( element(esk8_1(X97),powerset(X97))
& empty(esk8_1(X97)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_55,plain,
! [X89] :
( element(esk4_1(X89),powerset(X89))
& empty(esk4_1(X89))
& relation(esk4_1(X89))
& function(esk4_1(X89))
& one_to_one(esk4_1(X89))
& epsilon_transitive(esk4_1(X89))
& epsilon_connected(esk4_1(X89))
& ordinal(esk4_1(X89))
& natural(esk4_1(X89))
& finite(esk4_1(X89)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(i_0_56,plain,
! [X81] : element(esk1_1(X81),X81),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_57,plain,
! [X69] :
( ~ cup_closed(X69)
| ~ diff_closed(X69)
| preboolean(X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finsub_1])]) ).
fof(i_0_58,plain,
! [X84] :
( ~ empty(finite_subsets(X84))
& cup_closed(finite_subsets(X84))
& diff_closed(finite_subsets(X84))
& preboolean(finite_subsets(X84)) ),
inference(variable_rename,[status(thm)],[i_0_35]) ).
fof(i_0_59,plain,
! [X73] : ~ empty(powerset(X73)),
inference(variable_rename,[status(thm)],[i_0_36]) ).
fof(i_0_60,plain,
! [X67] :
( ~ empty(powerset(X67))
& cup_closed(powerset(X67))
& diff_closed(powerset(X67))
& preboolean(powerset(X67)) ),
inference(variable_rename,[status(thm)],[i_0_37]) ).
fof(i_0_61,plain,
! [X65,X66] :
( ~ empty(X65)
| X65 = X66
| ~ empty(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_62,negated_conjecture,
( element(esk12_0,finite_subsets(esk11_0))
& ~ finite(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_38])])]) ).
fof(i_0_63,plain,
! [X54] : subset(X54,X54),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_64,plain,
! [X70] :
( ~ empty(X70)
| finite(X70) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_65,plain,
! [X68] :
( ( cup_closed(X68)
| ~ preboolean(X68) )
& ( diff_closed(X68)
| ~ preboolean(X68) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finsub_1])])]) ).
fof(i_0_66,plain,
! [X83] : preboolean(finite_subsets(X83)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(i_0_67,plain,
! [X78] :
( ~ empty(X78)
| X78 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_68,plain,
~ empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_39])]) ).
fof(i_0_69,plain,
( ~ empty(esk3_0)
& finite(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_40])]) ).
fof(i_0_70,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_41])]) ).
fof(i_0_71,plain,
empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_72,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_73,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_74,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_75,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_76,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_77,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_78,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_79,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_80,plain,
( finite(X1)
| ~ element(X1,finite_subsets(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_81,plain,
( element(esk7_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_82,plain,
( element(esk6_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_83,plain,
( element(esk5_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_84,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_85,plain,
element(esk8_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_86,plain,
element(esk4_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_87,plain,
( empty(X1)
| ~ empty(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_88,plain,
( empty(X1)
| ~ empty(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_89,plain,
( empty(X1)
| ~ empty(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_90,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_91,plain,
( preboolean(X1)
| ~ cup_closed(X1)
| ~ diff_closed(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_92,plain,
~ empty(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_93,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_94,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_95,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_96,negated_conjecture,
element(esk12_0,finite_subsets(esk11_0)),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_97,plain,
( finite(esk6_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_98,plain,
( finite(esk5_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_99,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_100,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_101,plain,
( diff_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_102,plain,
( cup_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_103,plain,
natural(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_104,plain,
ordinal(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_105,plain,
epsilon_connected(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_106,plain,
epsilon_transitive(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_107,plain,
one_to_one(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_108,plain,
function(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_109,plain,
relation(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_110,plain,
finite(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_111,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_112,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_113,plain,
preboolean(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_114,plain,
diff_closed(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_115,plain,
diff_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_116,plain,
cup_closed(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_117,plain,
cup_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_118,plain,
empty(esk8_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_119,plain,
empty(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_120,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_121,negated_conjecture,
~ finite(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_122,plain,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_123,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_124,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_125,plain,
cap_closed(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_126,plain,
finite(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_127,plain,
preboolean(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_128,plain,
diff_closed(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_129,plain,
cup_closed(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_130,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_131,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_132,axiom,
X1 = X1 ).
cnf(i_0_133,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_134,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_135,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_136,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_137,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_138,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_139,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_140,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_141,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_142,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_143,axiom,
( X1 != X2
| ~ cap_closed(X1)
| cap_closed(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
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_147,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_148,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_149,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_150,axiom,
( X1 != X2
| ~ preboolean(X1)
| preboolean(X2) ) ).
cnf(i_0_151,axiom,
( X1 != X2
| ~ cup_closed(X1)
| cup_closed(X2) ) ).
cnf(i_0_152,axiom,
( X1 != X2
| ~ diff_closed(X1)
| diff_closed(X2) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_132_001,axiom,
X1 = X1 ).
cnf(i_0_133_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_134_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_135_004,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_136_005,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_137_006,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_138_007,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_139_008,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_140_009,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_141_010,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_142_011,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_143_012,axiom,
( X1 != X2
| ~ cap_closed(X1)
| cap_closed(X2) ) ).
cnf(i_0_144_013,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_145_014,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_146_015,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_147_016,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_148_017,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_149_018,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_150_019,axiom,
( X1 != X2
| ~ preboolean(X1)
| preboolean(X2) ) ).
cnf(i_0_151_020,axiom,
( X1 != X2
| ~ cup_closed(X1)
| cup_closed(X2) ) ).
cnf(i_0_152_021,axiom,
( X1 != X2
| ~ diff_closed(X1)
| diff_closed(X2) ) ).
cnf(i_0_153_022,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_154,plain,
$false,
inference(scs_inference,[],[i_0_121,i_0_96,i_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU116+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n022.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 02:44:06 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % 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
% 0.26/1.62 % Total time : 1.269s
%------------------------------------------------------------------------------