%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET686+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 : n015.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 05:08:19 PM UTC 2026
% Result : Theorem 1.32s 1.74s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 109 ( 14 unt; 0 def)
% Number of atoms : 452 ( 4 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 590 ( 247 ~; 241 |; 45 &)
% ( 10 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 218 ( 12 sgn 79 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p7,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',p7) ).
fof(p21,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',p21) ).
fof(p27,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(p17,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',p17) ).
fof(p9,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',p9) ).
fof(p24,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',p24) ).
fof(p5,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',p5) ).
fof(p20,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',p20) ).
fof(p15,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',p15) ).
fof(prove_relset_1_53,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ( ~ empty(X3)
& ilf_type(X3,set_type) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,inverse4(X1,X3,X4,X2))
<=> ? [X6] :
( ilf_type(X6,member_type(X3))
& member(ordered_pair(X5,X6),X4)
& member(X6,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_53) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,inverse2(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X2,X4),X3)
& member(X4,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p2,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',p2) ).
fof(p25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> inverse4(X1,X2,X3,X4) = inverse2(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
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)],[p7]) ).
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)],[p21]) ).
fof(c_0_15,plain,
! [X105,X106] :
( ( ~ ilf_type(X105,member_type(X106))
| member(X105,X106)
| empty(X106)
| ~ ilf_type(X106,set_type)
| ~ ilf_type(X105,set_type) )
& ( ~ member(X105,X106)
| ilf_type(X105,member_type(X106))
| empty(X106)
| ~ ilf_type(X106,set_type)
| ~ ilf_type(X105,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,
! [X155] : ilf_type(X155,set_type),
inference(variable_rename,[status(thm)],[p27]) ).
fof(c_0_17,plain,
! [X123,X124] :
( ( ~ ilf_type(X124,subset_type(X123))
| ilf_type(X124,member_type(power_set(X123)))
| ~ ilf_type(X124,set_type)
| ~ ilf_type(X123,set_type) )
& ( ~ ilf_type(X124,member_type(power_set(X123)))
| ilf_type(X124,subset_type(X123))
| ~ ilf_type(X124,set_type)
| ~ ilf_type(X123,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])]) ).
fof(c_0_18,plain,
! [X135] :
( ( ~ empty(power_set(X135))
| ~ ilf_type(X135,set_type) )
& ( ilf_type(power_set(X135),set_type)
| ~ ilf_type(X135,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)],[p9]) ).
fof(c_0_20,plain,
! [X144,X145,X146] :
( ~ ilf_type(X144,set_type)
| ~ ilf_type(X145,set_type)
| ~ ilf_type(X146,subset_type(cross_product(X144,X145)))
| relation_like(X146) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p24])])]) ).
fof(c_0_21,plain,
! [X98,X99,X100,X101] :
( ( ~ ilf_type(X100,subset_type(cross_product(X98,X99)))
| ilf_type(X100,relation_type(X98,X99))
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type) )
& ( ~ ilf_type(X101,relation_type(X98,X99))
| ilf_type(X101,subset_type(cross_product(X98,X99)))
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])]) ).
fof(c_0_22,plain,
! [X131,X132,X133] :
( ( ~ member(X131,power_set(X132))
| ~ ilf_type(X133,set_type)
| ~ member(X133,X131)
| member(X133,X132)
| ~ ilf_type(X132,set_type)
| ~ ilf_type(X131,set_type) )
& ( ilf_type(esk8_2(X131,X132),set_type)
| member(X131,power_set(X132))
| ~ ilf_type(X132,set_type)
| ~ ilf_type(X131,set_type) )
& ( member(esk8_2(X131,X132),X131)
| member(X131,power_set(X132))
| ~ ilf_type(X132,set_type)
| ~ ilf_type(X131,set_type) )
& ( ~ member(esk8_2(X131,X132),X132)
| member(X131,power_set(X132))
| ~ ilf_type(X132,set_type)
| ~ ilf_type(X131,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)],[p20])])])])]) ).
cnf(c_0_23,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_24,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,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_26,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X109,X110] :
( ( ~ empty(X109)
| ~ ilf_type(X110,set_type)
| ~ member(X110,X109)
| ~ ilf_type(X109,set_type) )
& ( ilf_type(esk4_1(X109),set_type)
| empty(X109)
| ~ ilf_type(X109,set_type) )
& ( member(esk4_1(X109),X109)
| empty(X109)
| ~ ilf_type(X109,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_28,plain,
! [X121] :
( ( relation_like(X121)
| ~ ilf_type(X121,binary_relation_type)
| ~ ilf_type(X121,set_type) )
& ( ilf_type(X121,set_type)
| ~ ilf_type(X121,binary_relation_type)
| ~ ilf_type(X121,set_type) )
& ( ~ relation_like(X121)
| ~ ilf_type(X121,set_type)
| ilf_type(X121,binary_relation_type)
| ~ ilf_type(X121,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])]) ).
cnf(c_0_29,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_20]) ).
cnf(c_0_30,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_21]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ( ~ empty(X3)
& ilf_type(X3,set_type) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,inverse4(X1,X3,X4,X2))
<=> ? [X6] :
( ilf_type(X6,member_type(X3))
& member(ordered_pair(X5,X6),X4)
& member(X6,X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_53])]) ).
cnf(c_0_32,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_22]) ).
cnf(c_0_33,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_23,c_0_24]),c_0_24])]) ).
cnf(c_0_34,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_25,c_0_24]),c_0_24])]) ).
cnf(c_0_35,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_24])]) ).
cnf(c_0_36,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,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_28]) ).
cnf(c_0_38,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_29,c_0_24]),c_0_24])]) ).
cnf(c_0_39,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_30,c_0_24]),c_0_24])]) ).
fof(c_0_40,negated_conjecture,
! [X161] :
( ~ empty(esk12_0)
& ilf_type(esk12_0,set_type)
& ~ empty(esk13_0)
& ilf_type(esk13_0,set_type)
& ~ empty(esk14_0)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk12_0,esk14_0))
& ilf_type(esk16_0,member_type(esk12_0))
& ( ~ member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_0))
| ~ ilf_type(X161,member_type(esk14_0))
| ~ member(ordered_pair(esk16_0,X161),esk15_0)
| ~ member(X161,esk13_0) )
& ( ilf_type(esk17_0,member_type(esk14_0))
| member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_0)) )
& ( member(ordered_pair(esk16_0,esk17_0),esk15_0)
| member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_0)) )
& ( member(esk17_0,esk13_0)
| member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_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_31])])])])]) ).
cnf(c_0_41,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_32,c_0_24]),c_0_24]),c_0_24])]) ).
cnf(c_0_42,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_43,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_44,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_45,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_24]),c_0_24])]) ).
cnf(c_0_46,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_22]) ).
cnf(c_0_47,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_22]) ).
fof(c_0_48,plain,
! [X81,X82,X83,X85] :
( ( ilf_type(esk1_3(X81,X82,X83),set_type)
| ~ member(X82,inverse2(X83,X81))
| ~ ilf_type(X83,binary_relation_type)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( member(ordered_pair(X82,esk1_3(X81,X82,X83)),X83)
| ~ member(X82,inverse2(X83,X81))
| ~ ilf_type(X83,binary_relation_type)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( member(esk1_3(X81,X82,X83),X81)
| ~ member(X82,inverse2(X83,X81))
| ~ ilf_type(X83,binary_relation_type)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( ~ ilf_type(X85,set_type)
| ~ member(ordered_pair(X82,X85),X83)
| ~ member(X85,X81)
| member(X82,inverse2(X83,X81))
| ~ ilf_type(X83,binary_relation_type)
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,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_49,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_51,negated_conjecture,
ilf_type(esk15_0,relation_type(esk12_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_52,plain,
! [X86,X87,X88,X89,X90] :
( ( member(X88,X86)
| ~ member(ordered_pair(X88,X89),X90)
| ~ ilf_type(X90,relation_type(X86,X87))
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type)
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( member(X89,X87)
| ~ member(ordered_pair(X88,X89),X90)
| ~ ilf_type(X90,relation_type(X86,X87))
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X88,set_type)
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_53,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_54,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_43,c_0_24]),c_0_24])]) ).
cnf(c_0_55,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_44,c_0_24]),c_0_24])]),c_0_45]) ).
cnf(c_0_56,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_46,c_0_24]),c_0_24])]) ).
cnf(c_0_57,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_47,c_0_24]),c_0_24])]) ).
cnf(c_0_58,negated_conjecture,
( ~ member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_0))
| ~ ilf_type(X1,member_type(esk14_0))
| ~ member(ordered_pair(esk16_0,X1),esk15_0)
| ~ member(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_59,negated_conjecture,
( member(ordered_pair(esk16_0,esk17_0),esk15_0)
| member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_60,plain,
( member(ordered_pair(X1,esk1_3(X2,X1,X3)),X3)
| ~ member(X1,inverse2(X3,X2))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_24])]) ).
cnf(c_0_62,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_63,plain,
! [X147,X148,X149,X150] :
( ~ ilf_type(X147,set_type)
| ~ ilf_type(X148,set_type)
| ~ ilf_type(X149,relation_type(X147,X148))
| ~ ilf_type(X150,set_type)
| inverse4(X147,X148,X149,X150) = inverse2(X149,X150) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p25])])]) ).
cnf(c_0_64,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_52]) ).
cnf(c_0_65,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_53,c_0_39]) ).
cnf(c_0_66,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_21]) ).
cnf(c_0_67,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_68,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_69,negated_conjecture,
( member(ordered_pair(esk16_0,esk17_0),esk15_0)
| ~ member(ordered_pair(esk16_0,X1),esk15_0)
| ~ member(X1,esk13_0)
| ~ ilf_type(X1,member_type(esk14_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,plain,
( member(ordered_pair(X1,esk1_3(X2,X1,X3)),X3)
| ~ member(X1,inverse2(X3,X2))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_24]),c_0_24])]) ).
cnf(c_0_71,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,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_64,c_0_24]),c_0_24]),c_0_24]),c_0_24])]) ).
cnf(c_0_74,negated_conjecture,
( member(X1,cross_product(esk12_0,esk14_0))
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_51]) ).
cnf(c_0_75,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_66,c_0_24]),c_0_24])]) ).
cnf(c_0_76,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( member(esk17_0,esk13_0)
| member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_78,negated_conjecture,
( member(ordered_pair(esk16_0,esk17_0),esk15_0)
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk13_0)
| ~ member(esk16_0,inverse2(esk15_0,X1))
| ~ ilf_type(esk1_3(X1,esk16_0,esk15_0),member_type(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_79,plain,
( member(esk1_3(X1,X2,X3),X1)
| ~ member(X2,inverse2(X3,X1))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_80,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_24]),c_0_24]),c_0_24])]) ).
cnf(c_0_81,negated_conjecture,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),esk15_0)
| ~ ilf_type(cross_product(esk12_0,esk14_0),relation_type(X4,X2)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( member(esk17_0,esk13_0)
| ~ member(ordered_pair(esk16_0,X1),esk15_0)
| ~ member(X1,esk13_0)
| ~ ilf_type(X1,member_type(esk14_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| member(esk16_0,inverse4(esk12_0,esk14_0,esk15_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_85,negated_conjecture,
( member(ordered_pair(esk16_0,esk17_0),esk15_0)
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk13_0)
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk14_0)
| ~ member(esk16_0,inverse2(esk15_0,X1)) ),
inference(spm,[status(thm)],[c_0_78,c_0_55]) ).
cnf(c_0_86,plain,
( member(esk1_3(X1,X2,X3),X1)
| ~ member(X2,inverse2(X3,X1))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_24]),c_0_24])]) ).
cnf(c_0_87,negated_conjecture,
( member(ordered_pair(esk16_0,esk17_0),esk15_0)
| member(esk16_0,inverse2(esk15_0,esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_80]),c_0_51])]) ).
cnf(c_0_88,negated_conjecture,
( member(X1,esk14_0)
| ~ member(ordered_pair(X2,X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( member(esk17_0,esk13_0)
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk13_0)
| ~ member(esk16_0,inverse2(esk15_0,X1))
| ~ ilf_type(esk1_3(X1,esk16_0,esk15_0),member_type(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_70]),c_0_71])]) ).
cnf(c_0_90,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| ~ member(ordered_pair(esk16_0,X1),esk15_0)
| ~ member(X1,esk13_0)
| ~ ilf_type(X1,member_type(esk14_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_84]) ).
cnf(c_0_91,plain,
( member(X2,inverse2(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ member(X1,X4)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_92,negated_conjecture,
( member(ordered_pair(esk16_0,esk17_0),esk15_0)
| ~ member(esk1_3(esk13_0,esk16_0,esk15_0),esk14_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_71])]),c_0_87]) ).
cnf(c_0_93,negated_conjecture,
( member(esk1_3(X1,X2,esk15_0),esk14_0)
| ~ member(X2,inverse2(esk15_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_70]),c_0_71])]) ).
cnf(c_0_94,negated_conjecture,
( member(esk17_0,esk13_0)
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk13_0)
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk14_0)
| ~ member(esk16_0,inverse2(esk15_0,X1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_55]) ).
cnf(c_0_95,negated_conjecture,
( member(esk16_0,inverse2(esk15_0,esk13_0))
| member(esk17_0,esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_80]),c_0_51])]) ).
cnf(c_0_96,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk13_0)
| ~ member(esk16_0,inverse2(esk15_0,X1))
| ~ ilf_type(esk1_3(X1,esk16_0,esk15_0),member_type(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_70]),c_0_71])]) ).
cnf(c_0_97,plain,
( member(X1,inverse2(X2,X3))
| ~ member(ordered_pair(X1,X4),X2)
| ~ member(X4,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_24]),c_0_24]),c_0_24])]) ).
cnf(c_0_98,negated_conjecture,
member(ordered_pair(esk16_0,esk17_0),esk15_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_87]) ).
cnf(c_0_99,negated_conjecture,
( member(esk17_0,esk13_0)
| ~ member(esk1_3(esk13_0,esk16_0,esk15_0),esk14_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_86]),c_0_71])]),c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk13_0)
| ~ member(esk1_3(X1,esk16_0,esk15_0),esk14_0)
| ~ member(esk16_0,inverse2(esk15_0,X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_55]) ).
cnf(c_0_101,negated_conjecture,
( member(esk16_0,inverse2(esk15_0,esk13_0))
| ilf_type(esk17_0,member_type(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_80]),c_0_51])]) ).
cnf(c_0_102,negated_conjecture,
( ~ member(esk16_0,inverse2(esk15_0,esk13_0))
| ~ member(ordered_pair(esk16_0,X1),esk15_0)
| ~ member(X1,esk13_0)
| ~ ilf_type(X1,member_type(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_80]),c_0_51])]) ).
cnf(c_0_103,negated_conjecture,
( member(esk16_0,inverse2(esk15_0,X1))
| ~ member(esk17_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_71])]) ).
cnf(c_0_104,negated_conjecture,
member(esk17_0,esk13_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_93]),c_0_95]) ).
cnf(c_0_105,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| ~ member(esk1_3(esk13_0,esk16_0,esk15_0),esk14_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_86]),c_0_71])]),c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( ~ member(ordered_pair(esk16_0,X1),esk15_0)
| ~ member(X1,esk13_0)
| ~ ilf_type(X1,member_type(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104])]) ).
cnf(c_0_107,negated_conjecture,
ilf_type(esk17_0,member_type(esk14_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_93]),c_0_101]) ).
cnf(c_0_108,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_98]),c_0_104]),c_0_107])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET686+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
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:31:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.32/1.74 % Version : CSE_E---1.7
% 1.32/1.74 % Problem : theBenchmark.p
% 1.32/1.74 % SZS status Theorem for theBenchmark.p
% 1.32/1.74 % SZS output start CNFRefutation
% See solution above
% 1.32/1.74 % Total time : 1.370s
%------------------------------------------------------------------------------