%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU177+1 : TPTP v9.2.1. Released v3.3.0.
% 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 05:10:57 PM UTC 2026
% Result : Theorem 0.28s 1.60s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_31)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_zfmisc_1,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(t20_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(fc3_subset_1,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
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_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
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(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_19,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_20,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t20_relat_1]) ).
fof(i_0_21,plain,
! [X79,X80,X81,X83,X84,X85,X87] :
( ( ~ in(X81,X80)
| in(ordered_pair(esk11_3(X79,X80,X81),X81),X79)
| X80 != relation_rng(X79)
| ~ relation(X79) )
& ( ~ in(ordered_pair(X84,X83),X79)
| in(X83,X80)
| X80 != relation_rng(X79)
| ~ relation(X79) )
& ( ~ in(esk12_2(X79,X85),X85)
| ~ in(ordered_pair(X87,esk12_2(X79,X85)),X79)
| X85 = relation_rng(X79)
| ~ relation(X79) )
& ( in(esk12_2(X79,X85),X85)
| in(ordered_pair(esk13_2(X79,X85),esk12_2(X79,X85)),X79)
| X85 = relation_rng(X79)
| ~ relation(X79) ) ),
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_relat_1])])])])])]) ).
fof(i_0_22,plain,
! [X64,X65] : ordered_pair(X64,X65) = unordered_pair(unordered_pair(X64,X65),singleton(X64)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_23,plain,
! [X69,X70,X71,X73,X74,X75,X77] :
( ( ~ in(X71,X70)
| in(ordered_pair(X71,esk8_3(X69,X70,X71)),X69)
| X70 != relation_dom(X69)
| ~ relation(X69) )
& ( ~ in(ordered_pair(X73,X74),X69)
| in(X73,X70)
| X70 != relation_dom(X69)
| ~ relation(X69) )
& ( ~ in(esk9_2(X69,X75),X75)
| ~ in(ordered_pair(esk9_2(X69,X75),X77),X69)
| X75 = relation_dom(X69)
| ~ relation(X69) )
& ( in(esk9_2(X69,X75),X75)
| in(ordered_pair(esk9_2(X69,X75),esk10_2(X69,X75)),X69)
| X75 = relation_dom(X69)
| ~ relation(X69) ) ),
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)],[d4_relat_1])])])])])]) ).
fof(i_0_24,plain,
! [X58,X59] : ~ empty(ordered_pair(X58,X59)),
inference(variable_rename,[status(thm)],[i_0_19]) ).
fof(i_0_25,negated_conjecture,
( relation(esk7_0)
& in(ordered_pair(esk5_0,esk6_0),esk7_0)
& ( ~ in(esk5_0,relation_dom(esk7_0))
| ~ in(esk6_0,relation_rng(esk7_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_20])])]) ).
fof(i_0_26,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc3_subset_1]) ).
fof(i_0_27,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_28,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(i_0_29,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_30,plain,
( in(ordered_pair(esk11_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_21]) ).
cnf(i_0_31,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_22]) ).
cnf(i_0_32,plain,
( in(ordered_pair(X1,esk8_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_23]) ).
cnf(i_0_33,plain,
( X2 = relation_dom(X1)
| ~ in(esk9_2(X1,X2),X2)
| ~ in(ordered_pair(esk9_2(X1,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]) ).
cnf(i_0_34,plain,
( in(esk12_2(X1,X2),X2)
| in(ordered_pair(esk13_2(X1,X2),esk12_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]) ).
cnf(i_0_35,plain,
( in(esk9_2(X1,X2),X2)
| in(ordered_pair(esk9_2(X1,X2),esk10_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]) ).
cnf(i_0_36,plain,
( X2 = relation_rng(X1)
| ~ in(esk12_2(X1,X2),X2)
| ~ in(ordered_pair(X3,esk12_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]) ).
cnf(i_0_37,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_23]) ).
cnf(i_0_38,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_21]) ).
cnf(i_0_39,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_24]) ).
cnf(i_0_40,negated_conjecture,
in(ordered_pair(esk5_0,esk6_0),esk7_0),
inference(split_conjunct,[status(thm)],[i_0_25]) ).
fof(i_0_41,plain,
! [X49,X50] : ~ empty(unordered_pair(X49,X50)),
inference(variable_rename,[status(thm)],[i_0_26]) ).
fof(i_0_42,plain,
! [X56,X57] :
( ~ in(X56,X57)
| ~ in(X57,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_27])]) ).
fof(i_0_43,plain,
! [X51,X52] :
( ~ element(X51,X52)
| empty(X52)
| in(X51,X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_44,plain,
! [X60,X61] :
( ~ in(X60,X61)
| element(X60,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_45,plain,
! [X62,X63] :
( ~ in(X62,X63)
| ~ empty(X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_46,plain,
! [X41,X42] : unordered_pair(X41,X42) = unordered_pair(X42,X41),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_47,plain,
! [X43] : element(esk1_1(X43),X43),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_48,plain,
! [X48] : ~ empty(singleton(X48)),
inference(variable_rename,[status(thm)],[i_0_28]) ).
fof(i_0_49,plain,
! [X54,X55] :
( ~ empty(X54)
| X54 = X55
| ~ empty(X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_50,plain,
! [X53] :
( ~ empty(X53)
| X53 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_51,plain,
~ empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_29])]) ).
fof(i_0_52,plain,
( empty(esk2_0)
& relation(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_53,plain,
empty(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_54,plain,
( in(unordered_pair(unordered_pair(esk11_3(X3,X2,X1),X1),singleton(esk11_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_30,c_0_31]),
[final] ).
cnf(i_0_55,plain,
( in(unordered_pair(unordered_pair(X1,esk8_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_32,c_0_31]),
[final] ).
cnf(i_0_56,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(esk9_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(esk9_2(X1,X2),X3),singleton(esk9_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_33,c_0_31]),
[final] ).
cnf(i_0_57,plain,
( X2 = relation_rng(X1)
| in(esk12_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk13_2(X1,X2),esk12_2(X1,X2)),singleton(esk13_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_34,c_0_31]),
[final] ).
cnf(i_0_58,plain,
( X2 = relation_dom(X1)
| in(esk9_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk9_2(X1,X2),esk10_2(X1,X2)),singleton(esk9_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_35,c_0_31]),
[final] ).
cnf(i_0_59,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(esk12_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk12_2(X1,X2)),singleton(X3)),X1) ),
inference(rw,[status(thm)],[i_0_36,c_0_31]),
[final] ).
cnf(i_0_60,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[i_0_37,c_0_31]),
[final] ).
cnf(i_0_61,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[i_0_38,c_0_31]),
[final] ).
cnf(i_0_62,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),singleton(X1))),
inference(rw,[status(thm)],[i_0_39,c_0_31]),
[final] ).
cnf(i_0_63,negated_conjecture,
in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk7_0),
inference(rw,[status(thm)],[i_0_40,c_0_31]),
[final] ).
cnf(i_0_64,negated_conjecture,
( ~ in(esk5_0,relation_dom(esk7_0))
| ~ in(esk6_0,relation_rng(esk7_0)) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_65,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_66,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_67,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_68,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_69,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_70,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_71,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_72,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_73,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_74,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_75,plain,
~ empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_76,negated_conjecture,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_77,plain,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_78,plain,
empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_79,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_80,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_81,axiom,
X1 = X1 ).
cnf(i_0_82,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_83,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_84,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_85,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_86,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_87,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_88,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_89,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_90,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_91,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_92,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_93,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_81_001,axiom,
X1 = X1 ).
cnf(i_0_82_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_83_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_84_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_85_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_86_006,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_87_007,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_88_008,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_89_009,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_90_010,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_91_011,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_92_012,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_93_013,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_94,plain,
( ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| in(unordered_pair(unordered_pair(esk11_3(X1,relation_rng(X1),X2),X2),singleton(esk11_3(X1,relation_rng(X1),X2))),X1) ),
inference(equality_inference,[],[54]) ).
cnf(i_0_95,plain,
( ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| in(unordered_pair(unordered_pair(X2,esk8_3(X1,relation_dom(X1),X2)),singleton(X2)),X1) ),
inference(equality_inference,[],[55]) ).
cnf(i_0_96,plain,
( ~ relation(X1)
| in(X2,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(equality_inference,[],[60]) ).
cnf(i_0_97,plain,
( ~ relation(X1)
| in(X2,relation_rng(X1))
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X1) ),
inference(equality_inference,[],[61]) ).
cnf(i_0_98,plain,
~ in(esk7_0,unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_63,i_0_66]) ).
cnf(i_0_99,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_100,plain,
element(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk7_0),
inference(scs_inference,[],[i_0_63,i_0_66,i_0_68]) ).
cnf(i_0_101,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_102,plain,
~ in(X1,esk3_0),
inference(scs_inference,[],[i_0_63,i_0_78,i_0_66,i_0_68,i_0_69]) ).
cnf(i_0_103,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_104,plain,
in(esk1_1(esk4_0),esk4_0),
inference(scs_inference,[],[i_0_63,i_0_71,i_0_75,i_0_78,i_0_66,i_0_68,i_0_69,i_0_67]) ).
cnf(i_0_105,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_106,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_67]) ).
cnf(i_0_107,plain,
in(esk5_0,relation_dom(esk7_0)),
inference(scs_inference,[],[i_0_63,i_0_76,i_0_71,i_0_75,i_0_78,i_0_66,i_0_68,i_0_69,i_0_67,i_0_96]) ).
cnf(i_0_108,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| in(X1,relation_dom(X3)) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_109,plain,
in(esk6_0,relation_rng(esk7_0)),
inference(scs_inference,[],[i_0_63,i_0_76,i_0_71,i_0_75,i_0_78,i_0_66,i_0_68,i_0_69,i_0_67,i_0_96,i_0_97]) ).
cnf(i_0_110,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| in(X2,relation_rng(X3)) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_111,plain,
~ in(esk7_0,unordered_pair(singleton(esk5_0),unordered_pair(esk5_0,esk6_0))),
inference(scs_inference,[],[i_0_63,i_0_76,i_0_70,i_0_71,i_0_75,i_0_78,i_0_66,i_0_68,i_0_69,i_0_67,i_0_96,i_0_97,i_0_89]) ).
cnf(i_0_112,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_113,plain,
esk3_0 != esk4_0,
inference(scs_inference,[],[i_0_63,i_0_76,i_0_70,i_0_71,i_0_75,i_0_78,i_0_66,i_0_68,i_0_69,i_0_67,i_0_96,i_0_97,i_0_89,i_0_91]) ).
cnf(i_0_114,plain,
esk3_0 != relation_dom(esk7_0),
inference(scs_inference,[],[i_0_63,i_0_76,i_0_70,i_0_71,i_0_75,i_0_78,i_0_66,i_0_68,i_0_69,i_0_67,i_0_96,i_0_97,i_0_89,i_0_91,i_0_60]) ).
cnf(i_0_115,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X4 != relation_dom(X3)
| ~ relation(X3)
| in(X1,X4) ),
inference(rename_variables,[],[i_0_60]) ).
cnf(i_0_116,plain,
$false,
inference(scs_inference,[],[i_0_63,i_0_76,i_0_70,i_0_71,i_0_75,i_0_78,i_0_66,i_0_68,i_0_69,i_0_67,i_0_96,i_0_97,i_0_89,i_0_91,i_0_60,i_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU177+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n019.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 02:47:44 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.28/1.60 % Version : CSE_E---1.7
% 0.28/1.60 % Problem : theBenchmark.p
% 0.28/1.60 % SZS status Theorem for theBenchmark.p
% 0.28/1.60 % SZS output start CNFRefutation
% See solution above
% 0.28/1.67 % Total time : 1.269s
%------------------------------------------------------------------------------