%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU078+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 : n009.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 05:10:35 PM UTC 2026
% Result : Theorem 24.31s 16.06s
% Output : CNFRefutation 24.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 105 ( 27 unt; 0 def)
% Number of atoms : 343 ( 76 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 408 ( 170 ~; 171 |; 40 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 3 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 192 ( 15 sgn 99 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t56_zfmisc_1,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t159_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
fof(t173_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( relation_inverse_image(X2,X1) = empty_set
<=> disjoint(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t144_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] :
~ ( in(X2,relation_rng(X1))
& ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3) )
<=> one_to_one(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(t39_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
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(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
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(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(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(c_0_21,plain,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[t56_zfmisc_1]) ).
fof(c_0_22,plain,
! [X126,X127] :
( ~ disjoint(X126,X127)
| disjoint(X127,X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(c_0_23,plain,
! [X152,X153] :
( in(X152,X153)
| disjoint(singleton(X152),X153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
inference(assume_negation,[status(cth)],[t159_funct_1]) ).
fof(c_0_25,plain,
! [X138,X139] :
( ( relation_inverse_image(X139,X138) != empty_set
| disjoint(relation_rng(X139),X138)
| ~ relation(X139) )
& ( ~ disjoint(relation_rng(X139),X138)
| relation_inverse_image(X139,X138) = empty_set
| ~ relation(X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t173_relat_1])])]) ).
cnf(c_0_26,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,negated_conjecture,
! [X135,X136] :
( relation(esk19_0)
& function(esk19_0)
& ( ~ one_to_one(esk19_0)
| ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X135)) )
& ( one_to_one(esk19_0)
| subset(relation_inverse_image(esk19_0,singleton(X136)),singleton(esk21_1(X136))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_29,plain,
( relation_inverse_image(X1,X2) = empty_set
| ~ disjoint(relation_rng(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( disjoint(X1,singleton(X2))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_31,plain,
! [X144] : subset(empty_set,X144),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(c_0_32,plain,
! [X128,X130,X131] :
( ( in(esk17_1(X128),relation_rng(X128))
| one_to_one(X128)
| ~ relation(X128)
| ~ function(X128) )
& ( relation_inverse_image(X128,singleton(esk17_1(X128))) != singleton(X130)
| one_to_one(X128)
| ~ relation(X128)
| ~ function(X128) )
& ( ~ one_to_one(X128)
| ~ in(X131,relation_rng(X128))
| relation_inverse_image(X128,singleton(X131)) = singleton(esk18_2(X128,X131))
| ~ relation(X128)
| ~ function(X128) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t144_funct_1])])])])]) ).
cnf(c_0_33,negated_conjecture,
( ~ one_to_one(esk19_0)
| ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( relation_inverse_image(X1,singleton(X2)) = empty_set
| in(X2,relation_rng(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_37,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_38,plain,
! [X145,X146] :
( ( ~ subset(X145,singleton(X146))
| X145 = empty_set
| X145 = singleton(X146) )
& ( X145 != empty_set
| subset(X145,singleton(X146)) )
& ( X145 != singleton(X146)
| subset(X145,singleton(X146)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
cnf(c_0_39,plain,
( relation_inverse_image(X1,singleton(X2)) = singleton(esk18_2(X1,X2))
| ~ one_to_one(X1)
| ~ in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,negated_conjecture,
( in(esk20_0,relation_rng(esk19_0))
| ~ one_to_one(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).
fof(c_0_42,plain,
! [X125] : subset(X125,X125),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_43,plain,
! [X157] :
( ~ empty(X157)
| X157 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_44,plain,
! [X120] :
( element(esk13_1(X120),powerset(X120))
& empty(esk13_1(X120)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_45,plain,
! [X149,X150,X151] :
( ~ in(X149,X150)
| ~ element(X150,powerset(X151))
| element(X149,X151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_46,plain,
! [X115] :
( ( element(esk9_1(X115),powerset(X115))
| empty(X115) )
& ( ~ empty(esk9_1(X115))
| empty(X115) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
fof(c_0_47,plain,
! [X142,X143] :
( ~ element(X142,X143)
| empty(X143)
| in(X142,X143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_48,plain,
! [X105] : element(esk6_1(X105),X105),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_49,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_50,negated_conjecture,
( one_to_one(esk19_0)
| subset(relation_inverse_image(esk19_0,singleton(X1)),singleton(esk21_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_51,negated_conjecture,
( ~ subset(singleton(esk18_2(esk19_0,esk20_0)),singleton(X1))
| ~ one_to_one(esk19_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_39]),c_0_36]),c_0_40])]),c_0_41]) ).
cnf(c_0_52,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,plain,
empty(esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_55,plain,
( ~ epred1_0
<=> ! [X1] : ~ empty(X1) ),
introduced(definition) ).
cnf(c_0_56,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( element(esk9_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
element(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_60,plain,
! [X88,X89,X90,X91,X92,X93] :
( ( ~ in(X90,X89)
| X90 = X88
| X89 != singleton(X88) )
& ( X91 != X88
| in(X91,X89)
| X89 != singleton(X88) )
& ( ~ in(esk2_2(X92,X93),X93)
| esk2_2(X92,X93) != X92
| X93 = singleton(X92) )
& ( in(esk2_2(X92,X93),X93)
| esk2_2(X92,X93) = X92
| X93 = singleton(X92) ) ),
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])])])])])]) ).
fof(c_0_61,plain,
! [X80,X81,X82,X83,X84,X85,X86] :
( ( in(X83,relation_dom(X80))
| ~ in(X83,X82)
| X82 != relation_inverse_image(X80,X81)
| ~ relation(X80)
| ~ function(X80) )
& ( in(apply(X80,X83),X81)
| ~ in(X83,X82)
| X82 != relation_inverse_image(X80,X81)
| ~ relation(X80)
| ~ function(X80) )
& ( ~ in(X84,relation_dom(X80))
| ~ in(apply(X80,X84),X81)
| in(X84,X82)
| X82 != relation_inverse_image(X80,X81)
| ~ relation(X80)
| ~ function(X80) )
& ( ~ in(esk1_3(X80,X85,X86),X86)
| ~ in(esk1_3(X80,X85,X86),relation_dom(X80))
| ~ in(apply(X80,esk1_3(X80,X85,X86)),X85)
| X86 = relation_inverse_image(X80,X85)
| ~ relation(X80)
| ~ function(X80) )
& ( in(esk1_3(X80,X85,X86),relation_dom(X80))
| in(esk1_3(X80,X85,X86),X86)
| X86 = relation_inverse_image(X80,X85)
| ~ relation(X80)
| ~ function(X80) )
& ( in(apply(X80,esk1_3(X80,X85,X86)),X85)
| in(esk1_3(X80,X85,X86),X86)
| X86 = relation_inverse_image(X80,X85)
| ~ relation(X80)
| ~ function(X80) ) ),
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)],[d13_funct_1])])])])])]) ).
fof(c_0_62,plain,
! [X95,X96,X97,X99,X100,X101,X103] :
( ( in(esk3_3(X95,X96,X97),relation_dom(X95))
| ~ in(X97,X96)
| X96 != relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( X97 = apply(X95,esk3_3(X95,X96,X97))
| ~ in(X97,X96)
| X96 != relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( ~ in(X100,relation_dom(X95))
| X99 != apply(X95,X100)
| in(X99,X96)
| X96 != relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( ~ in(esk4_2(X95,X101),X101)
| ~ in(X103,relation_dom(X95))
| esk4_2(X95,X101) != apply(X95,X103)
| X101 = relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( in(esk5_2(X95,X101),relation_dom(X95))
| in(esk4_2(X95,X101),X101)
| X101 = relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( esk4_2(X95,X101) = apply(X95,esk5_2(X95,X101))
| in(esk4_2(X95,X101),X101)
| X101 = relation_rng(X95)
| ~ relation(X95)
| ~ function(X95) ) ),
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_funct_1])])])])])]) ).
cnf(c_0_63,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(X1)) = singleton(esk21_1(X1))
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set
| one_to_one(esk19_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_64,negated_conjecture,
~ one_to_one(esk19_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_65,plain,
! [X154,X155,X156] :
( ~ in(X154,X155)
| ~ element(X155,powerset(X156))
| ~ empty(X156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_66,plain,
element(esk13_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_67,plain,
esk13_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_68,plain,
( epred1_0
| ~ empty(X1) ),
inference(split_equiv,[status(thm)],[c_0_55]) ).
cnf(c_0_69,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_70,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk9_1(X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_71,plain,
( empty(X1)
| in(esk6_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_72,plain,
( empty(X1)
| ~ empty(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_73,plain,
! [X158,X159] :
( ~ in(X158,X159)
| ~ empty(X159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_74,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_75,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_76,plain,
( X1 = apply(X2,esk3_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_77,plain,
( in(esk3_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_78,plain,
( one_to_one(X1)
| relation_inverse_image(X1,singleton(esk17_1(X1))) != singleton(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_79,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(X1)) = singleton(esk21_1(X1))
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set ),
inference(sr,[status(thm)],[c_0_63,c_0_64]) ).
fof(c_0_80,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition) ).
cnf(c_0_81,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_82,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_83,plain,
epred1_0,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_84,plain,
( element(esk6_1(esk9_1(X1)),X1)
| empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_85,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_86,plain,
( in(X1,X2)
| X2 != singleton(X1) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_87,plain,
( in(esk3_3(X1,X2,X3),X4)
| X4 != relation_inverse_image(X1,X5)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,X5)
| ~ in(X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set
| singleton(esk21_1(esk17_1(esk19_0))) != singleton(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_36]),c_0_40])]),c_0_64]) ).
cnf(c_0_89,plain,
~ epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_55]),c_0_80]),c_0_83])]) ).
cnf(c_0_90,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_91,plain,
( empty(X1)
| in(esk6_1(esk9_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_84]) ).
cnf(c_0_92,plain,
( X1 != singleton(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_93,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
cnf(c_0_94,plain,
( in(esk3_3(X1,X2,X3),relation_inverse_image(X1,X4))
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,X4)
| ~ in(X3,X2) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_95,negated_conjecture,
relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set,
inference(er,[status(thm)],[c_0_88]) ).
cnf(c_0_96,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_80]),c_0_89]) ).
cnf(c_0_97,plain,
( esk6_1(esk9_1(X1)) = X2
| X1 != singleton(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
fof(c_0_98,plain,
! [X108] : ~ empty(singleton(X108)),
inference(variable_rename,[status(thm)],[c_0_93]) ).
cnf(c_0_99,negated_conjecture,
( X1 != relation_rng(esk19_0)
| ~ in(X2,singleton(esk17_1(esk19_0)))
| ~ in(X2,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_36]),c_0_40])]),c_0_96]) ).
cnf(c_0_100,plain,
esk6_1(esk9_1(singleton(X1))) = X1,
inference(er,[status(thm)],[c_0_97]) ).
cnf(c_0_101,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_102,negated_conjecture,
( X1 != relation_rng(esk19_0)
| ~ in(esk17_1(esk19_0),X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_91]),c_0_100]),c_0_101]) ).
cnf(c_0_103,plain,
( in(esk17_1(X1),relation_rng(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_104,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_102,c_0_103]),c_0_36]),c_0_40])]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU078+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n009.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 02:42:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 24.31/16.06 % Version : CSE_E---1.7
% 24.31/16.06 % Problem : theBenchmark.p
% 24.31/16.06 % SZS status Theorem for theBenchmark.p
% 24.31/16.06 % SZS output start CNFRefutation
% See solution above
% 24.41/16.15 % Total time : 12.396s
%------------------------------------------------------------------------------