%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM387+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 : n020.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 04:57:13 PM UTC 2026
% Result : Theorem 0.29s 1.62s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_45)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_ordinal1,axiom,
! [X1] : ~ empty(succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(t14_ordinal1,conjecture,
! [X1] : X1 != succ(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
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(fc2_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_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(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(cc2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc5_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_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(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_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_33,plain,
! [X1] : ~ empty(succ(X1)),
inference(fof_simplification,[status(thm)],[fc1_ordinal1]) ).
fof(i_0_34,negated_conjecture,
~ ! [X1] : X1 != succ(X1),
inference(assume_negation,[status(cth)],[t14_ordinal1]) ).
fof(i_0_35,plain,
! [X54] : ~ empty(succ(X54)),
inference(variable_rename,[status(thm)],[i_0_33]) ).
fof(i_0_36,plain,
! [X51] : succ(X51) = set_union2(X51,singleton(X51)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(i_0_37,plain,
! [X72] : in(X72,succ(X72)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(i_0_38,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_39,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_40,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_41,negated_conjecture,
esk12_0 = succ(esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_34])])]) ).
fof(i_0_42,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_43,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
cnf(i_0_44,plain,
~ empty(succ(X1)),
inference(split_conjunct,[status(thm)],[i_0_35]) ).
cnf(i_0_45,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_36]) ).
cnf(i_0_46,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[i_0_37]) ).
fof(i_0_47,plain,
! [X57,X58] :
( empty(X57)
| ~ empty(set_union2(X57,X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_38])]) ).
fof(i_0_48,plain,
! [X59,X60] :
( empty(X59)
| ~ empty(set_union2(X60,X59)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_39])]) ).
fof(i_0_49,plain,
! [X44,X45] :
( ~ in(X44,X45)
| ~ in(X45,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_40])]) ).
fof(i_0_50,plain,
! [X55,X56] :
( ~ relation(X55)
| ~ relation(X56)
| relation(set_union2(X55,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_relat_1])]) ).
fof(i_0_51,plain,
! [X77,X78] :
( ~ element(X77,X78)
| empty(X78)
| in(X77,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_52,plain,
! [X75,X76] :
( ~ in(X75,X76)
| element(X75,X76) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_53,plain,
! [X80,X81] :
( ~ in(X80,X81)
| ~ empty(X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_54,plain,
! [X49,X50] : set_union2(X49,X50) = set_union2(X50,X49),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_55,plain,
! [X48] :
( ( relation(X48)
| ~ relation(X48)
| ~ empty(X48)
| ~ function(X48) )
& ( function(X48)
| ~ relation(X48)
| ~ empty(X48)
| ~ function(X48) )
& ( one_to_one(X48)
| ~ relation(X48)
| ~ empty(X48)
| ~ function(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_56,plain,
! [X52] : element(esk1_1(X52),X52),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_57,plain,
! [X82,X83] :
( ~ empty(X82)
| X82 = X83
| ~ empty(X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
cnf(i_0_58,negated_conjecture,
esk12_0 = succ(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_41]) ).
fof(i_0_59,plain,
! [X61] : set_union2(X61,X61) = X61,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_60,plain,
! [X74] : set_union2(X74,empty_set) = X74,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_61,plain,
! [X47] :
( ~ empty(X47)
| relation(X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_62,plain,
! [X46] :
( ~ empty(X46)
| function(X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_63,plain,
! [X79] :
( ~ empty(X79)
| X79 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_64,plain,
~ empty(esk7_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_42])]) ).
fof(i_0_65,plain,
( ~ empty(esk6_0)
& relation(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_43])]) ).
fof(i_0_66,plain,
( relation(esk11_0)
& relation_non_empty(esk11_0)
& function(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc5_funct_1])]) ).
fof(i_0_67,plain,
( relation(esk10_0)
& relation_empty_yielding(esk10_0)
& function(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_68,plain,
( relation(esk9_0)
& relation_empty_yielding(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_69,plain,
( relation(esk8_0)
& function(esk8_0)
& one_to_one(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_70,plain,
( relation(esk5_0)
& empty(esk5_0)
& function(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_71,plain,
( empty(esk3_0)
& relation(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_72,plain,
( relation(esk2_0)
& function(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_73,plain,
empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_74,plain,
~ empty(set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[i_0_44,c_0_45]),
[final] ).
cnf(i_0_75,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[i_0_46,c_0_45]),
[final] ).
cnf(i_0_76,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_77,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_78,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_79,plain,
( relation(set_union2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_80,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_81,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_82,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_83,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_84,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_85,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_86,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_87,negated_conjecture,
esk12_0 = set_union2(esk12_0,singleton(esk12_0)),
inference(rw,[status(thm)],[i_0_58,c_0_45]),
[final] ).
cnf(i_0_88,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_89,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_90,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_91,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_92,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_93,plain,
~ empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_94,plain,
~ empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_95,plain,
relation_non_empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_96,plain,
relation_empty_yielding(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_97,plain,
relation_empty_yielding(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_98,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_99,plain,
one_to_one(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_100,plain,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_101,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_102,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_103,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_104,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_105,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_106,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_107,plain,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_108,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_109,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_110,plain,
function(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_111,plain,
function(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_112,plain,
function(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_113,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_114,plain,
function(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_115,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_116,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_117,plain,
empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_118,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_119,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_120,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_121,axiom,
X1 = X1 ).
cnf(i_0_122,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_123,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_124,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_125,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_126,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_127,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_128,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_129,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_130,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_131,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_132,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_133,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_134,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_135,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_121_001,axiom,
X1 = X1 ).
cnf(i_0_122_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_123_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_124_004,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_125_005,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_126_006,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_127_007,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_128_008,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_129_009,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_130_010,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_131_011,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_132_012,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_133_013,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_134_014,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_135_015,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_136,plain,
set_union2(esk12_0,singleton(esk12_0)) = esk12_0,
inference(scs_inference,[],[i_0_87,i_0_122]) ).
cnf(i_0_137,plain,
~ in(set_union2(X1,singleton(X1)),X1),
inference(scs_inference,[],[i_0_87,i_0_75,i_0_122,i_0_78]) ).
cnf(i_0_138,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_139,plain,
element(X1,set_union2(X1,singleton(X1))),
inference(scs_inference,[],[i_0_87,i_0_75,i_0_122,i_0_78,i_0_81]) ).
cnf(i_0_140,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_141,plain,
~ in(X1,esk5_0),
inference(scs_inference,[],[i_0_87,i_0_115,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82]) ).
cnf(i_0_142,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_143,plain,
relation(esk4_0),
inference(scs_inference,[],[i_0_87,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90]) ).
cnf(i_0_144,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_145,plain,
function(esk4_0),
inference(scs_inference,[],[i_0_87,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91]) ).
cnf(i_0_146,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_147,plain,
set_union2(esk12_0,esk12_0) = set_union2(esk12_0,singleton(esk12_0)),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123]) ).
cnf(i_0_148,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_149,plain,
esk5_0 != esk7_0,
inference(scs_inference,[],[i_0_87,i_0_88,i_0_93,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126]) ).
cnf(i_0_150,plain,
~ in(esk12_0,esk12_0),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_93,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127]) ).
cnf(i_0_151,plain,
~ in(set_union2(esk12_0,singleton(esk12_0)),set_union2(esk12_0,esk12_0)),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_93,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128]) ).
cnf(i_0_152,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_153,plain,
in(esk1_1(esk7_0),esk7_0),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_85,i_0_93,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128,i_0_80]) ).
cnf(i_0_154,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_85]) ).
cnf(i_0_155,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_156,plain,
one_to_one(esk5_0),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_85,i_0_93,i_0_105,i_0_113,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128,i_0_80,i_0_84]) ).
cnf(i_0_157,plain,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_158,plain,
( relation(X1)
| esk11_0 != X1 ),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_85,i_0_93,i_0_100,i_0_105,i_0_113,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128,i_0_80,i_0_84,i_0_129]) ).
cnf(i_0_159,plain,
( one_to_one(X1)
| esk8_0 != X1 ),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_85,i_0_93,i_0_99,i_0_100,i_0_105,i_0_113,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128,i_0_80,i_0_84,i_0_129,i_0_132]) ).
cnf(i_0_160,plain,
( function(X1)
| esk11_0 != X1 ),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_85,i_0_93,i_0_99,i_0_100,i_0_105,i_0_110,i_0_113,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128,i_0_80,i_0_84,i_0_129,i_0_132,i_0_133]) ).
cnf(i_0_161,plain,
( relation_non_empty(X1)
| esk11_0 != X1 ),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_85,i_0_93,i_0_95,i_0_99,i_0_100,i_0_105,i_0_110,i_0_113,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128,i_0_80,i_0_84,i_0_129,i_0_132,i_0_133,i_0_134]) ).
cnf(i_0_162,plain,
( relation_empty_yielding(X1)
| esk10_0 != X1 ),
inference(scs_inference,[],[i_0_87,i_0_88,i_0_148,i_0_85,i_0_93,i_0_95,i_0_96,i_0_99,i_0_100,i_0_105,i_0_110,i_0_113,i_0_115,i_0_116,i_0_75,i_0_122,i_0_78,i_0_81,i_0_82,i_0_90,i_0_91,i_0_123,i_0_126,i_0_127,i_0_128,i_0_80,i_0_84,i_0_129,i_0_132,i_0_133,i_0_134,i_0_135]) ).
cnf(i_0_163,plain,
relation(esk11_0),
inference(equality_inference,[],[158]) ).
cnf(i_0_164,plain,
one_to_one(esk8_0),
inference(equality_inference,[],[159]) ).
cnf(i_0_165,plain,
function(esk11_0),
inference(equality_inference,[],[160]) ).
cnf(i_0_166,plain,
relation_non_empty(esk11_0),
inference(equality_inference,[],[161]) ).
cnf(i_0_167,plain,
relation_empty_yielding(esk10_0),
inference(equality_inference,[],[162]) ).
cnf(i_0_168,plain,
~ in(esk7_0,esk1_1(esk7_0)),
inference(scs_inference,[],[i_0_153,i_0_78]) ).
cnf(i_0_169,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_170,plain,
~ in(X1,esk3_0),
inference(scs_inference,[],[i_0_153,i_0_117,i_0_78,i_0_82]) ).
cnf(i_0_171,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_172,plain,
function(esk3_0),
inference(scs_inference,[],[i_0_153,i_0_117,i_0_78,i_0_82,i_0_91]) ).
cnf(i_0_173,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_174,plain,
set_union2(esk12_0,singleton(esk12_0)) = set_union2(esk12_0,esk12_0),
inference(scs_inference,[],[i_0_147,i_0_153,i_0_117,i_0_78,i_0_82,i_0_91,i_0_122]) ).
cnf(i_0_175,plain,
in(esk1_1(esk6_0),esk6_0),
inference(scs_inference,[],[i_0_147,i_0_153,i_0_94,i_0_117,i_0_85,i_0_78,i_0_82,i_0_91,i_0_122,i_0_80]) ).
cnf(i_0_176,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_85]) ).
cnf(i_0_177,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_178,plain,
esk5_0 != set_union2(esk7_0,empty_set),
inference(scs_inference,[],[i_0_147,i_0_149,i_0_89,i_0_153,i_0_94,i_0_117,i_0_85,i_0_78,i_0_82,i_0_91,i_0_122,i_0_80,i_0_123]) ).
cnf(i_0_179,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_180,plain,
esk3_0 != esk6_0,
inference(scs_inference,[],[i_0_147,i_0_149,i_0_89,i_0_153,i_0_94,i_0_117,i_0_85,i_0_78,i_0_82,i_0_91,i_0_122,i_0_80,i_0_123,i_0_126]) ).
cnf(i_0_181,plain,
~ in(esk12_0,set_union2(esk12_0,esk12_0)),
inference(scs_inference,[],[i_0_87,i_0_151,i_0_147,i_0_149,i_0_89,i_0_153,i_0_94,i_0_117,i_0_85,i_0_78,i_0_82,i_0_91,i_0_122,i_0_80,i_0_123,i_0_126,i_0_127]) ).
cnf(i_0_182,plain,
$false,
inference(scs_inference,[],[i_0_87,i_0_136,i_0_151,i_0_147,i_0_149,i_0_150,i_0_89,i_0_153,i_0_94,i_0_117,i_0_85,i_0_75,i_0_78,i_0_82,i_0_91,i_0_122,i_0_80,i_0_123,i_0_126,i_0_127,i_0_128]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM387+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 : n020.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 00:31:20 EDT 2026
% 0.16/0.34 % 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
% 0.47/1.80 % Total time : 1.272s
%------------------------------------------------------------------------------