%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET680+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n025.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 05:08:18 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 98 ( 14 unt; 0 def)
% Number of atoms : 378 ( 4 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 477 ( 197 ~; 191 |; 36 &)
% ( 10 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 191 ( 13 sgn 73 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
fof(p31,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(p26,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(p17,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(prove_relset_1_47,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_47) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> domain(X1,X2,X3) = domain_of(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(c_0_13,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p8]) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_15,plain,
! [X111,X112] :
( ( ~ ilf_type(X111,member_type(X112))
| member(X111,X112)
| empty(X112)
| ~ ilf_type(X112,set_type)
| ~ ilf_type(X111,set_type) )
& ( ~ member(X111,X112)
| ilf_type(X111,member_type(X112))
| empty(X112)
| ~ ilf_type(X112,set_type)
| ~ ilf_type(X111,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_16,plain,
! [X165] : ilf_type(X165,set_type),
inference(variable_rename,[status(thm)],[p31]) ).
fof(c_0_17,plain,
! [X129,X130] :
( ( ~ ilf_type(X130,subset_type(X129))
| ilf_type(X130,member_type(power_set(X129)))
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) )
& ( ~ ilf_type(X130,member_type(power_set(X129)))
| ilf_type(X130,subset_type(X129))
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])]) ).
fof(c_0_18,plain,
! [X141] :
( ( ~ empty(power_set(X141))
| ~ ilf_type(X141,set_type) )
& ( ilf_type(power_set(X141),set_type)
| ~ ilf_type(X141,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p10]) ).
fof(c_0_20,plain,
! [X137,X138,X139] :
( ( ~ member(X137,power_set(X138))
| ~ ilf_type(X139,set_type)
| ~ member(X139,X137)
| member(X139,X138)
| ~ ilf_type(X138,set_type)
| ~ ilf_type(X137,set_type) )
& ( ilf_type(esk8_2(X137,X138),set_type)
| member(X137,power_set(X138))
| ~ ilf_type(X138,set_type)
| ~ ilf_type(X137,set_type) )
& ( member(esk8_2(X137,X138),X137)
| member(X137,power_set(X138))
| ~ ilf_type(X138,set_type)
| ~ ilf_type(X137,set_type) )
& ( ~ member(esk8_2(X137,X138),X138)
| member(X137,power_set(X138))
| ~ ilf_type(X138,set_type)
| ~ ilf_type(X137,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])])])]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X115,X116] :
( ( ~ empty(X115)
| ~ ilf_type(X116,set_type)
| ~ member(X116,X115)
| ~ ilf_type(X115,set_type) )
& ( ilf_type(esk4_1(X115),set_type)
| empty(X115)
| ~ ilf_type(X115,set_type) )
& ( member(esk4_1(X115),X115)
| empty(X115)
| ~ ilf_type(X115,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])]) ).
fof(c_0_26,plain,
! [X150,X151,X152] :
( ~ ilf_type(X150,set_type)
| ~ ilf_type(X151,set_type)
| ~ ilf_type(X152,subset_type(cross_product(X150,X151)))
| relation_like(X152) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])]) ).
fof(c_0_27,plain,
! [X104,X105,X106,X107] :
( ( ~ ilf_type(X106,subset_type(cross_product(X104,X105)))
| ilf_type(X106,relation_type(X104,X105))
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X104,set_type) )
& ( ~ ilf_type(X107,relation_type(X104,X105))
| ilf_type(X107,subset_type(cross_product(X104,X105)))
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X104,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
cnf(c_0_28,plain,
( member(X3,X2)
| ~ member(X1,power_set(X2))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22])]) ).
cnf(c_0_30,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_22]),c_0_22])]) ).
cnf(c_0_31,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22])]) ).
cnf(c_0_32,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X127] :
( ( relation_like(X127)
| ~ ilf_type(X127,binary_relation_type)
| ~ ilf_type(X127,set_type) )
& ( ilf_type(X127,set_type)
| ~ ilf_type(X127,binary_relation_type)
| ~ ilf_type(X127,set_type) )
& ( ~ relation_like(X127)
| ~ ilf_type(X127,set_type)
| ilf_type(X127,binary_relation_type)
| ~ ilf_type(X127,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])]) ).
cnf(c_0_34,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_36,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_47])]) ).
cnf(c_0_37,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_38,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_39,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_22]),c_0_22])]) ).
cnf(c_0_42,plain,
( member(X1,power_set(X2))
| ~ member(esk8_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_43,plain,
( member(esk8_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_44,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_22]),c_0_22])]) ).
cnf(c_0_46,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_22]),c_0_22])]) ).
fof(c_0_47,negated_conjecture,
! [X170] :
( ~ empty(esk12_0)
& ilf_type(esk12_0,set_type)
& ~ empty(esk13_0)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,relation_type(esk12_0,esk13_0))
& ilf_type(esk15_0,member_type(esk12_0))
& ( ~ member(esk15_0,domain(esk12_0,esk13_0,esk14_0))
| ~ ilf_type(X170,member_type(esk13_0))
| ~ member(ordered_pair(esk15_0,X170),esk14_0) )
& ( ilf_type(esk16_0,member_type(esk13_0))
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) )
& ( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])])]) ).
fof(c_0_48,plain,
! [X153,X154,X155] :
( ~ ilf_type(X153,set_type)
| ~ ilf_type(X154,set_type)
| ~ ilf_type(X155,relation_type(X153,X154))
| domain(X153,X154,X155) = domain_of(X155) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
fof(c_0_49,plain,
! [X92,X93,X94,X95,X96] :
( ( member(X94,X92)
| ~ member(ordered_pair(X94,X95),X96)
| ~ ilf_type(X96,relation_type(X92,X93))
| ~ ilf_type(X95,set_type)
| ~ ilf_type(X94,set_type)
| ~ ilf_type(X93,set_type)
| ~ ilf_type(X92,set_type) )
& ( member(X95,X93)
| ~ member(ordered_pair(X94,X95),X96)
| ~ ilf_type(X96,relation_type(X92,X93))
| ~ ilf_type(X95,set_type)
| ~ ilf_type(X94,set_type)
| ~ ilf_type(X93,set_type)
| ~ ilf_type(X92,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
cnf(c_0_50,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_51,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_22]),c_0_22])]) ).
cnf(c_0_52,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_22]),c_0_22])]),c_0_41]) ).
cnf(c_0_53,plain,
( member(X1,power_set(X2))
| ~ member(esk8_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_22]),c_0_22])]) ).
cnf(c_0_54,plain,
( member(esk8_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_22]),c_0_22])]) ).
fof(c_0_55,plain,
! [X85,X86,X88] :
( ( ilf_type(esk1_2(X85,X86),set_type)
| ~ member(X85,domain_of(X86))
| ~ ilf_type(X86,binary_relation_type)
| ~ ilf_type(X85,set_type) )
& ( member(ordered_pair(X85,esk1_2(X85,X86)),X86)
| ~ member(X85,domain_of(X86))
| ~ ilf_type(X86,binary_relation_type)
| ~ ilf_type(X85,set_type) )
& ( ~ ilf_type(X88,set_type)
| ~ member(ordered_pair(X85,X88),X86)
| member(X85,domain_of(X86))
| ~ ilf_type(X86,binary_relation_type)
| ~ ilf_type(X85,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])]) ).
cnf(c_0_56,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,negated_conjecture,
ilf_type(esk14_0,relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ ilf_type(X4,relation_type(X5,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
cnf(c_0_62,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_63,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_64,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(esk15_0,domain(esk12_0,esk13_0,esk14_0))
| ~ ilf_type(X1,member_type(esk13_0))
| ~ member(ordered_pair(esk15_0,X1),esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_66,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_67,plain,
( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_22])]) ).
cnf(c_0_69,negated_conjecture,
relation_like(esk14_0),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_70,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_22]),c_0_22])]) ).
cnf(c_0_71,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ ilf_type(X4,relation_type(X5,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_72,negated_conjecture,
( member(X1,cross_product(esk12_0,esk13_0))
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_58]) ).
cnf(c_0_73,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_22]),c_0_22])]) ).
cnf(c_0_74,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_75,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,plain,
( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_22])]) ).
cnf(c_0_77,negated_conjecture,
ilf_type(esk14_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| member(esk15_0,domain_of(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_70]),c_0_58])]) ).
cnf(c_0_79,negated_conjecture,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),esk14_0)
| ~ ilf_type(cross_product(esk12_0,esk13_0),relation_type(X4,X2)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| ~ ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( member(X1,esk13_0)
| ~ member(ordered_pair(X2,X1),esk14_0) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_84,plain,
( member(X2,domain_of(X3))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_85,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| ~ member(esk1_2(esk15_0,esk14_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_81,c_0_52]) ).
cnf(c_0_86,negated_conjecture,
( member(esk1_2(X1,esk14_0),esk13_0)
| ~ member(X1,domain_of(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_76]),c_0_77])]) ).
cnf(c_0_87,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
( member(esk15_0,domain_of(esk14_0))
| ilf_type(esk16_0,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_70]),c_0_58])]) ).
cnf(c_0_89,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_22]),c_0_22])]) ).
cnf(c_0_90,negated_conjecture,
member(ordered_pair(esk15_0,esk16_0),esk14_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_78]) ).
cnf(c_0_91,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| ~ ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_76]),c_0_77])]),c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ member(esk15_0,domain_of(esk14_0))
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_70]),c_0_58])]) ).
cnf(c_0_93,negated_conjecture,
member(esk15_0,domain_of(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_77])]) ).
cnf(c_0_94,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| ~ member(esk1_2(esk15_0,esk14_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_91,c_0_52]) ).
cnf(c_0_95,negated_conjecture,
( ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_96,negated_conjecture,
ilf_type(esk16_0,member_type(esk13_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_86]),c_0_88]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_90]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET680+3 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:31:58 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------