%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU053+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 05:10:33 PM UTC 2026
% Result : Theorem 15.93s 10.34s
% Output : CNFRefutation 16.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 104 ( 31 unt; 0 def)
% Number of atoms : 268 ( 79 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 281 ( 117 ~; 120 |; 26 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 162 ( 14 sgn 70 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t122_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_intersection2(X2,X3)) = set_intersection2(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t117_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(t149_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_image(X1,empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t17_zfmisc_1,axiom,
! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_18,plain,
! [X146,X147,X148] :
( ~ in(X146,X147)
| ~ element(X147,powerset(X148))
| ~ empty(X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_19,plain,
! [X98] : element(esk4_1(X98),X98),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_20,plain,
! [X139,X140] :
( ~ element(X139,X140)
| empty(X140)
| in(X139,X140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_21,plain,
! [X152,X153] :
( ~ empty(X152)
| X152 = X153
| ~ empty(X153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_22,plain,
! [X105] :
( ( empty(relation_dom(X105))
| ~ empty(X105) )
& ( relation(relation_dom(X105))
| ~ empty(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
element(esk4_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ empty(X1)
| ~ in(X2,esk4_1(powerset(X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( empty(X1)
| in(esk4_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
( X1 = relation_dom(X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( empty(esk4_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_32,plain,
! [X141,X142] :
( ( ~ element(X141,powerset(X142))
| subset(X141,X142) )
& ( ~ subset(X141,X142)
| element(X141,powerset(X142)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_33,plain,
( esk4_1(powerset(X1)) = relation_dom(X2)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_34,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_intersection2(X2,X3)) = set_intersection2(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t122_funct_1]) ).
cnf(c_0_35,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( relation_dom(X1) = relation_dom(X2)
| ~ empty(X2)
| ~ empty(X3)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
fof(c_0_37,plain,
! [X82,X83] : set_intersection2(X82,X83) = set_intersection2(X83,X82),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_38,plain,
! [X91,X92] :
( ( ~ disjoint(X91,X92)
| set_intersection2(X91,X92) = empty_set )
& ( set_intersection2(X91,X92) != empty_set
| disjoint(X91,X92) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(c_0_39,negated_conjecture,
! [X131,X132] :
( relation(esk15_0)
& function(esk15_0)
& relation_image(esk15_0,set_intersection2(X131,X132)) = set_intersection2(relation_image(esk15_0,X131),relation_image(esk15_0,X132))
& ~ one_to_one(esk15_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
fof(c_0_40,plain,
! [X128,X129] :
( ~ relation(X129)
| ~ function(X129)
| ~ in(X128,relation_dom(X129))
| relation_image(X129,singleton(X128)) = singleton(apply(X129,X128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_funct_1])]) ).
fof(c_0_41,plain,
! [X93,X94,X95] :
( ( ~ one_to_one(X93)
| ~ in(X94,relation_dom(X93))
| ~ in(X95,relation_dom(X93))
| apply(X93,X94) != apply(X93,X95)
| X94 = X95
| ~ relation(X93)
| ~ function(X93) )
& ( in(esk2_1(X93),relation_dom(X93))
| one_to_one(X93)
| ~ relation(X93)
| ~ function(X93) )
& ( in(esk3_1(X93),relation_dom(X93))
| one_to_one(X93)
| ~ relation(X93)
| ~ function(X93) )
& ( apply(X93,esk2_1(X93)) = apply(X93,esk3_1(X93))
| one_to_one(X93)
| ~ relation(X93)
| ~ function(X93) )
& ( esk2_1(X93) != esk3_1(X93)
| one_to_one(X93)
| ~ relation(X93)
| ~ function(X93) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
cnf(c_0_42,plain,
subset(esk4_1(powerset(X1)),X1),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_43,plain,
( relation_dom(X1) = relation_dom(relation_dom(X2))
| ~ empty(X3)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_44,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_45,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
relation_image(esk15_0,set_intersection2(X1,X2)) = set_intersection2(relation_image(esk15_0,X1),relation_image(esk15_0,X2)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( relation_image(X1,singleton(X2)) = singleton(apply(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,plain,
( apply(X1,esk2_1(X1)) = apply(X1,esk3_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,negated_conjecture,
~ one_to_one(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_53,plain,
( in(esk3_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( subset(relation_dom(X1),X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_33]) ).
cnf(c_0_55,plain,
( relation_dom(X1) = relation_dom(relation_dom(X2))
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_56,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X2,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_58,plain,
! [X133] :
( ~ relation(X133)
| relation_image(X133,empty_set) = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t149_relat_1])]) ).
fof(c_0_59,plain,
! [X138] : set_intersection2(X138,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
cnf(c_0_60,negated_conjecture,
( set_intersection2(singleton(apply(esk15_0,X1)),relation_image(esk15_0,X2)) = relation_image(esk15_0,set_intersection2(singleton(X1),X2))
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50])]) ).
cnf(c_0_61,negated_conjecture,
apply(esk15_0,esk3_1(esk15_0)) = apply(esk15_0,esk2_1(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_50])]),c_0_52]) ).
cnf(c_0_62,negated_conjecture,
in(esk3_1(esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_49]),c_0_50])]),c_0_52]) ).
cnf(c_0_63,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_64,plain,
( subset(relation_dom(relation_dom(X1)),X2)
| ~ empty(X3)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( relation_image(esk15_0,set_intersection2(X1,X2)) = empty_set
| ~ disjoint(relation_image(esk15_0,X2),relation_image(esk15_0,X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( disjoint(relation_image(esk15_0,X1),relation_image(esk15_0,X2))
| relation_image(esk15_0,set_intersection2(X1,X2)) != empty_set ),
inference(spm,[status(thm)],[c_0_57,c_0_47]) ).
cnf(c_0_67,plain,
( relation_image(X1,empty_set) = empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,negated_conjecture,
set_intersection2(singleton(apply(esk15_0,esk2_1(esk15_0))),relation_image(esk15_0,X1)) = relation_image(esk15_0,set_intersection2(singleton(esk3_1(esk15_0)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_70,negated_conjecture,
in(esk2_1(esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_49]),c_0_50])]),c_0_52]) ).
fof(c_0_71,plain,
! [X106] : set_intersection2(X106,X106) = X106,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
cnf(c_0_72,plain,
( subset(relation_dom(relation_dom(X1)),X2)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_44]) ).
cnf(c_0_73,plain,
( relation_dom(X1) = relation_dom(empty_set)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_44]) ).
cnf(c_0_74,negated_conjecture,
( relation_image(esk15_0,set_intersection2(X1,X2)) = empty_set
| relation_image(esk15_0,set_intersection2(X2,X1)) != empty_set ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,negated_conjecture,
relation_image(esk15_0,empty_set) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_67]),c_0_68]),c_0_68]),c_0_49])]) ).
cnf(c_0_76,negated_conjecture,
relation_image(esk15_0,set_intersection2(singleton(esk3_1(esk15_0)),X1)) = relation_image(esk15_0,set_intersection2(singleton(esk2_1(esk15_0)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_69]),c_0_70])]) ).
cnf(c_0_77,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
( subset(relation_dom(relation_dom(relation_dom(X1))),X2)
| ~ empty(X2)
| ~ empty(X3)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_79,plain,
( relation_dom(X1) = relation_dom(empty_set)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_44]) ).
cnf(c_0_80,negated_conjecture,
( relation_image(esk15_0,set_intersection2(X1,X2)) = empty_set
| ~ disjoint(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_46]),c_0_75])]) ).
cnf(c_0_81,negated_conjecture,
relation_image(esk15_0,set_intersection2(singleton(esk2_1(esk15_0)),singleton(esk3_1(esk15_0)))) = relation_image(esk15_0,singleton(esk3_1(esk15_0))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
fof(c_0_82,plain,
! [X134,X135] :
( X134 = X135
| disjoint(singleton(X134),singleton(X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_zfmisc_1])]) ).
cnf(c_0_83,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_84,plain,
( subset(relation_dom(relation_dom(relation_dom(X1))),empty_set)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_44]) ).
fof(c_0_85,plain,
! [X149] :
( ~ empty(X149)
| X149 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_86,plain,
( empty(relation_dom(empty_set))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_79]) ).
fof(c_0_87,plain,
! [X84,X85,X86,X87,X88,X89] :
( ( ~ in(X86,X85)
| X86 = X84
| X85 != singleton(X84) )
& ( X87 != X84
| in(X87,X85)
| X85 != singleton(X84) )
& ( ~ in(esk1_2(X88,X89),X89)
| esk1_2(X88,X89) != X88
| X89 = singleton(X88) )
& ( in(esk1_2(X88,X89),X89)
| esk1_2(X88,X89) = X88
| X89 = singleton(X88) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_88,negated_conjecture,
( relation_image(esk15_0,singleton(esk3_1(esk15_0))) = empty_set
| ~ disjoint(singleton(esk3_1(esk15_0)),singleton(esk2_1(esk15_0))) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,plain,
( X1 = X2
| disjoint(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_90,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_83]) ).
cnf(c_0_91,plain,
( subset(relation_dom(relation_dom(relation_dom(X1))),empty_set)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_44]) ).
cnf(c_0_92,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,plain,
empty(relation_dom(empty_set)),
inference(spm,[status(thm)],[c_0_86,c_0_44]) ).
cnf(c_0_94,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( relation_image(esk15_0,singleton(esk3_1(esk15_0))) = empty_set
| esk3_1(esk15_0) = esk2_1(esk15_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
( ~ empty(X1)
| ~ in(X2,relation_dom(relation_dom(relation_dom(X1)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_44])]) ).
cnf(c_0_97,plain,
relation_dom(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_94])]) ).
cnf(c_0_99,negated_conjecture,
( singleton(apply(esk15_0,esk2_1(esk15_0))) = empty_set
| esk3_1(esk15_0) = esk2_1(esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_95]),c_0_61]),c_0_49]),c_0_50]),c_0_62])]) ).
cnf(c_0_100,plain,
~ in(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_44]),c_0_97]),c_0_97])]) ).
cnf(c_0_101,plain,
( one_to_one(X1)
| esk2_1(X1) != esk3_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_102,negated_conjecture,
esk3_1(esk15_0) = esk2_1(esk15_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_103,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_49]),c_0_50])]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU053+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.31 % Computer : n017.cluster.edu
% 0.15/0.31 % Model : x86_64 x86_64
% 0.15/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.31 % Memory : 8042.1875MB
% 0.15/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.31 % CPULimit : 300
% 0.15/0.31 % WCLimit : 300
% 0.15/0.31 % DateTime : Tue May 5 02:40:28 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 15.93/10.34 % Version : CSE_E---1.7
% 15.93/10.34 % Problem : theBenchmark.p
% 15.93/10.34 % SZS status Theorem for theBenchmark.p
% 15.93/10.34 % SZS output start CNFRefutation
% See solution above
% 16.04/10.41 % Total time : 7.383s
%------------------------------------------------------------------------------