%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU217+3 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:06 PM UTC 2026
% Result : Theorem 0.28s 1.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 68)
% 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(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(t35_funct_1,conjecture,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_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(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(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(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_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_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
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)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_34,negated_conjecture,
~ ! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[t35_funct_1]) ).
fof(i_0_35,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_36,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_37,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_38,plain,
! [X90,X91,X92] :
( ( relation_dom(X91) = X90
| X91 != identity_relation(X90)
| ~ relation(X91)
| ~ function(X91) )
& ( ~ in(X92,X90)
| apply(X91,X92) = X92
| X91 != identity_relation(X90)
| ~ relation(X91)
| ~ function(X91) )
& ( in(esk12_2(X90,X91),X90)
| relation_dom(X91) != X90
| X91 = identity_relation(X90)
| ~ relation(X91)
| ~ function(X91) )
& ( apply(X91,esk12_2(X90,X91)) != esk12_2(X90,X91)
| relation_dom(X91) != X90
| X91 = identity_relation(X90)
| ~ relation(X91)
| ~ function(X91) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(i_0_39,plain,
! [X61,X62,X63] :
( ~ in(X61,X62)
| ~ element(X62,powerset(X63))
| element(X61,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_40,plain,
! [X64,X65,X66] :
( ~ in(X64,X65)
| ~ element(X65,powerset(X66))
| ~ empty(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_41,plain,
! [X59,X60] :
( ( ~ element(X59,powerset(X60))
| subset(X59,X60) )
& ( ~ subset(X59,X60)
| element(X59,powerset(X60)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_42,plain,
! [X70,X71] :
( ~ in(X70,X71)
| ~ in(X71,X70) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_31])]) ).
fof(i_0_43,plain,
! [X57,X58] :
( ~ element(X57,X58)
| empty(X58)
| in(X57,X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_44,plain,
! [X84,X85] :
( ~ in(X84,X85)
| element(X84,X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_45,plain,
! [X75] :
( ( element(esk3_1(X75),powerset(X75))
| empty(X75) )
& ( ~ empty(esk3_1(X75))
| empty(X75) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_32])])])]) ).
fof(i_0_46,plain,
! [X86,X87] :
( ~ in(X86,X87)
| ~ empty(X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_47,plain,
! [X54] :
( empty(X54)
| ~ relation(X54)
| ~ empty(relation_dom(X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_33])]) ).
fof(i_0_48,plain,
! [X77] :
( element(esk4_1(X77),powerset(X77))
& empty(esk4_1(X77)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_49,negated_conjecture,
( in(esk11_0,esk10_0)
& apply(identity_relation(esk10_0),esk11_0) != esk11_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_34])])]) ).
fof(i_0_50,plain,
! [X50] : element(esk1_1(X50),X50),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_51,plain,
! [X55] :
( ( empty(relation_dom(X55))
| ~ empty(X55) )
& ( relation(relation_dom(X55))
| ~ empty(X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_52,plain,
! [X53] : ~ empty(powerset(X53)),
inference(variable_rename,[status(thm)],[i_0_35]) ).
fof(i_0_53,plain,
! [X68,X69] :
( ~ empty(X68)
| X68 = X69
| ~ empty(X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_54,plain,
! [X49] : subset(X49,X49),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_55,plain,
! [X52] :
( ~ empty(X52)
| function(X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_56,plain,
! [X56] :
( ~ empty(X56)
| relation(X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_57,plain,
! [X73] :
( relation(identity_relation(X73))
& function(identity_relation(X73)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(i_0_58,plain,
! [X72] : relation(identity_relation(X72)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(i_0_59,plain,
! [X67] :
( ~ empty(X67)
| X67 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_60,plain,
~ empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_36])]) ).
fof(i_0_61,plain,
( ~ empty(esk6_0)
& relation(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_37])]) ).
fof(i_0_62,plain,
( relation(esk2_0)
& function(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_63,plain,
( relation(esk7_0)
& relation_empty_yielding(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_64,plain,
( empty(esk5_0)
& relation(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_65,plain,
empty(esk8_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_66,plain,
( X1 = identity_relation(X2)
| apply(X1,esk12_2(X2,X1)) != esk12_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_67,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_68,plain,
( in(esk12_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_69,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_70,plain,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_71,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_72,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_73,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_74,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_75,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_76,plain,
( element(esk3_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_77,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_78,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_79,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_80,plain,
element(esk4_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_81,negated_conjecture,
apply(identity_relation(esk10_0),esk11_0) != esk11_0,
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_82,plain,
( empty(X1)
| ~ empty(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_83,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_84,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_85,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_86,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_87,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_88,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_89,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_90,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_91,negated_conjecture,
in(esk11_0,esk10_0),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_92,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_93,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_94,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_95,plain,
empty(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_96,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_97,plain,
~ empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_98,plain,
~ empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_99,plain,
function(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_100,plain,
relation_empty_yielding(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_101,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_102,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_103,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_104,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_105,plain,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_106,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_107,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_108,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_109,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_110,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_111,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_112,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_113,axiom,
X1 = X1 ).
cnf(i_0_114,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_115,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_116,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_117,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_118,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_119,axiom,
( X1 != X2
| esk12_2(X1,X3) = esk12_2(X2,X3) ) ).
cnf(i_0_120,axiom,
( X1 != X2
| esk12_2(X3,X1) = esk12_2(X3,X2) ) ).
cnf(i_0_121,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_122,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_123,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_124,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_125,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_126,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_127,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_128,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_129,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_130,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_131,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_113_001,axiom,
X1 = X1 ).
cnf(i_0_114_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_115_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_116_004,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_117_005,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_118_006,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_119_007,axiom,
( X1 != X2
| esk12_2(X1,X3) = esk12_2(X2,X3) ) ).
cnf(i_0_120_008,axiom,
( X1 != X2
| esk12_2(X3,X1) = esk12_2(X3,X2) ) ).
cnf(i_0_121_009,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_122_010,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_123_011,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_124_012,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_125_013,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_126_014,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_127_015,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_128_016,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_129_017,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_130_018,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_131_019,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_132,plain,
( ~ relation(X1)
| ~ function(X1)
| X1 = identity_relation(relation_dom(X1))
| in(esk12_2(relation_dom(X1),X1),relation_dom(X1)) ),
inference(equality_inference,[],[68]) ).
cnf(i_0_133,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X2,X1)
| apply(identity_relation(X1),X2) = X2 ),
inference(equality_inference,[],[70]) ).
cnf(i_0_134,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| relation_dom(identity_relation(X1)) = X1 ),
inference(equality_inference,[],[79]) ).
cnf(i_0_135,plain,
$false,
inference(scs_inference,[],[i_0_94,i_0_92,i_0_91,i_0_81,i_0_133]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU217+3 : 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 : n019.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 02:49:59 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.28/1.62 % Version : CSE_E---1.7
% 0.28/1.62 % Problem : theBenchmark.p
% 0.28/1.62 % SZS status Theorem for theBenchmark.p
% 0.28/1.62 % SZS output start CNFRefutation
% See solution above
% 0.28/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------