%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:14:59 PM UTC 2026
% Result : Theorem 0.14s 0.56s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 16 unt; 0 def)
% Number of atoms : 341 ( 5 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 417 ( 161 ~; 160 |; 43 &)
% ( 9 <=>; 44 =>; 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 : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 151 ( 7 sgn 71 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_52,conjecture,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ( ilf_type(X3,set_type)
& ~ empty(X3) )
=> ! [X4] :
( ilf_type(X4,relation_type(X3,X1))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,image4(X3,X1,X4,X2))
<=> ? [X6] :
( member(X6,X2)
& member(ordered_pair(X6,X5),X4)
& ilf_type(X6,member_type(X3)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_52) ).
fof(p5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(p27,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(p15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( ilf_type(X1,set_type)
& relation_like(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
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(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)
=> image4(X1,X2,X3,X4) = image(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,image(X3,X1))
<=> ? [X4] :
( member(X4,X1)
& member(ordered_pair(X4,X2),X3)
& ilf_type(X4,set_type) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
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(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(X4,X2)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ( ilf_type(X3,set_type)
& ~ empty(X3) )
=> ! [X4] :
( ilf_type(X4,relation_type(X3,X1))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,image4(X3,X1,X4,X2))
<=> ? [X6] :
( member(X6,X2)
& member(ordered_pair(X6,X5),X4)
& ilf_type(X6,member_type(X3)) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_52]) ).
fof(c_0_11,plain,
! [X24,X25,X26,X27] :
( ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| ilf_type(X27,subset_type(cross_product(X24,X25)))
| ~ ilf_type(X27,relation_type(X24,X25)) )
& ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| ilf_type(X26,relation_type(X24,X25))
| ~ ilf_type(X26,subset_type(cross_product(X24,X25))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])]) ).
fof(c_0_12,plain,
! [X81] : ilf_type(X81,set_type),
inference(variable_rename,[status(thm)],[p27]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ( ilf_type(X3,set_type)
& ~ empty(X3) )
=> ! [X4] :
( ilf_type(X4,relation_type(X3,X1))
=> ! [X5] :
( ilf_type(X5,member_type(X1))
=> ( member(X5,image4(X3,X1,X4,X2))
<=> ? [X6] :
( member(X6,X2)
& member(ordered_pair(X6,X5),X4)
& ilf_type(X6,member_type(X3)) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X47] :
( ( ~ ilf_type(X47,set_type)
| ilf_type(X47,binary_relation_type)
| ~ ilf_type(X47,set_type)
| ~ relation_like(X47) )
& ( ~ ilf_type(X47,set_type)
| ~ ilf_type(X47,binary_relation_type)
| ilf_type(X47,set_type) )
& ( ~ ilf_type(X47,set_type)
| ~ ilf_type(X47,binary_relation_type)
| relation_like(X47) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).
fof(c_0_15,plain,
! [X70,X71,X72] :
( relation_like(X72)
| ~ ilf_type(X72,subset_type(cross_product(X70,X71)))
| ~ ilf_type(X71,set_type)
| ~ ilf_type(X70,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p24])])])]) ).
cnf(c_0_16,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,negated_conjecture,
! [X87] :
( ( member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0))
| member(esk17_0,esk13_0) )
& ( member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0))
| member(ordered_pair(esk17_0,esk16_0),esk15_0) )
& ( member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0))
| ilf_type(esk17_0,member_type(esk14_0)) )
& ( ~ member(X87,esk13_0)
| ~ member(ordered_pair(X87,esk16_0),esk15_0)
| ~ ilf_type(X87,member_type(esk14_0))
| ~ member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0)) )
& ilf_type(esk16_0,member_type(esk12_0))
& ilf_type(esk15_0,relation_type(esk14_0,esk12_0))
& ilf_type(esk14_0,set_type)
& ~ empty(esk14_0)
& ilf_type(esk13_0,set_type)
& ~ empty(esk13_0)
& ilf_type(esk12_0,set_type)
& ~ empty(esk12_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])]) ).
cnf(c_0_19,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,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_16,c_0_17]),c_0_17])]) ).
cnf(c_0_22,negated_conjecture,
ilf_type(esk15_0,relation_type(esk14_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X73,X74,X75,X76] :
( image4(X73,X74,X75,X76) = image(X75,X76)
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,relation_type(X73,X74))
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X73,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p25])])])]) ).
fof(c_0_24,plain,
! [X7,X8,X9,X11] :
( ( ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,binary_relation_type)
| member(X8,image(X9,X7))
| ~ member(X11,X7)
| ~ member(ordered_pair(X11,X8),X9)
| ~ ilf_type(X11,set_type) )
& ( ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,binary_relation_type)
| ~ member(X8,image(X9,X7))
| member(esk1_3(X7,X8,X9),X7) )
& ( ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,binary_relation_type)
| ~ member(X8,image(X9,X7))
| member(ordered_pair(esk1_3(X7,X8,X9),X8),X9) )
& ( ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,binary_relation_type)
| ~ member(X8,image(X9,X7))
| ilf_type(esk1_3(X7,X8,X9),set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_25,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_17])]) ).
cnf(c_0_27,negated_conjecture,
ilf_type(esk15_0,subset_type(cross_product(esk14_0,esk12_0))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| image4(X1,X2,X3,X4) = image(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,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_30,plain,
! [X12,X13,X14,X15,X16] :
( ( ~ ilf_type(X12,set_type)
| ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X16,relation_type(X12,X13))
| ~ member(ordered_pair(X14,X15),X16)
| member(X15,X13) )
& ( ~ ilf_type(X12,set_type)
| ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X16,relation_type(X12,X13))
| ~ member(ordered_pair(X14,X15),X16)
| member(X14,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])]) ).
cnf(c_0_31,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1))
| member(ordered_pair(esk1_3(X1,X2,X3),X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_17])]) ).
cnf(c_0_33,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| image4(X1,X2,X3,X4) = image(X3,X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_17]),c_0_17])]) ).
fof(c_0_35,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p7]) ).
fof(c_0_36,plain,
! [X35,X36] :
( ( ~ ilf_type(X35,set_type)
| empty(X35)
| member(esk4_1(X35),X35) )
& ( ~ ilf_type(X35,set_type)
| empty(X35)
| ilf_type(esk4_1(X35),set_type) )
& ( ~ ilf_type(X35,set_type)
| ~ member(X36,X35)
| ~ ilf_type(X36,set_type)
| ~ empty(X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])])]) ).
cnf(c_0_37,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X2,X5))
| ~ member(ordered_pair(X1,X3),X4)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1))
| member(ordered_pair(esk1_3(X1,X2,X3),X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_17]),c_0_17])]) ).
cnf(c_0_39,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0))
| member(esk17_0,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,negated_conjecture,
image4(esk14_0,esk12_0,esk15_0,X1) = image(esk15_0,X1),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_42,negated_conjecture,
( member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0))
| ilf_type(esk17_0,member_type(esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_43,plain,
! [X31,X32] :
( ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| empty(X32)
| ilf_type(X31,member_type(X32))
| ~ member(X31,X32) )
& ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| empty(X32)
| member(X31,X32)
| ~ ilf_type(X31,member_type(X32)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])]) ).
cnf(c_0_44,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( ~ ilf_type(X4,relation_type(X2,X5))
| ~ member(ordered_pair(X1,X3),X4)
| member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(X2,image(esk15_0,X1))
| member(ordered_pair(esk1_3(X1,X2,esk15_0),X2),esk15_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( member(esk17_0,esk13_0)
| member(esk16_0,image(esk15_0,esk13_0)) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1))
| member(esk1_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_49,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| member(esk16_0,image(esk15_0,esk13_0)) ),
inference(rw,[status(thm)],[c_0_42,c_0_41]) ).
cnf(c_0_50,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2)
| empty(X2)
| ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_17]),c_0_17])]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(ordered_pair(X1,X2),esk15_0)
| member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_53,negated_conjecture,
( member(esk17_0,esk13_0)
| member(ordered_pair(esk1_3(esk13_0,esk16_0,esk15_0),esk16_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
( ~ ilf_type(X3,binary_relation_type)
| ~ member(X2,image(X3,X1))
| member(esk1_3(X1,X2,X3),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_17]),c_0_17])]) ).
cnf(c_0_55,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| member(ordered_pair(esk1_3(esk13_0,esk16_0,esk15_0),esk16_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
cnf(c_0_56,plain,
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(X1,X4)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X1,set_type)
| member(X2,image(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(X1,esk13_0)
| ~ member(ordered_pair(X1,esk16_0),esk15_0)
| ~ ilf_type(X1,member_type(esk14_0))
| ~ member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_58,plain,
( ~ member(X1,X2)
| ilf_type(X1,member_type(X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_17]),c_0_17])]),c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( member(esk17_0,esk13_0)
| member(esk1_3(esk13_0,esk16_0,esk15_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(X2,image(esk15_0,X1))
| member(esk1_3(X1,X2,esk15_0),X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_39]) ).
cnf(c_0_61,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| member(esk1_3(esk13_0,esk16_0,esk15_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
cnf(c_0_62,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X4,X3)
| ~ member(ordered_pair(X4,X1),X2)
| member(X1,image(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_63,negated_conjecture,
( ~ ilf_type(X1,member_type(esk14_0))
| ~ member(X1,esk13_0)
| ~ member(ordered_pair(X1,esk16_0),esk15_0)
| ~ member(esk16_0,image(esk15_0,esk13_0)) ),
inference(rw,[status(thm)],[c_0_57,c_0_41]) ).
cnf(c_0_64,negated_conjecture,
( ilf_type(esk1_3(esk13_0,esk16_0,esk15_0),member_type(esk14_0))
| member(esk17_0,esk13_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( member(esk17_0,esk13_0)
| member(esk1_3(esk13_0,esk16_0,esk15_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_47]) ).
cnf(c_0_66,negated_conjecture,
( member(esk16_0,image4(esk14_0,esk12_0,esk15_0,esk13_0))
| member(ordered_pair(esk17_0,esk16_0),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_67,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| ilf_type(esk1_3(esk13_0,esk16_0,esk15_0),member_type(esk14_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( ilf_type(esk17_0,member_type(esk14_0))
| member(esk1_3(esk13_0,esk16_0,esk15_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
cnf(c_0_69,negated_conjecture,
( ~ member(X3,X2)
| ~ member(ordered_pair(X3,X1),esk15_0)
| member(X1,image(esk15_0,X2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_39]) ).
cnf(c_0_70,negated_conjecture,
member(esk17_0,esk13_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_47]),c_0_65]),c_0_53]) ).
cnf(c_0_71,negated_conjecture,
( member(esk16_0,image(esk15_0,esk13_0))
| member(ordered_pair(esk17_0,esk16_0),esk15_0) ),
inference(rw,[status(thm)],[c_0_66,c_0_41]) ).
cnf(c_0_72,negated_conjecture,
ilf_type(esk17_0,member_type(esk14_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_67]),c_0_49]),c_0_68]),c_0_55]) ).
cnf(c_0_73,negated_conjecture,
( ~ member(ordered_pair(esk17_0,X1),esk15_0)
| member(X1,image(esk15_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( member(ordered_pair(esk17_0,esk16_0),esk15_0)
| member(ordered_pair(esk1_3(esk13_0,esk16_0,esk15_0),esk16_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
~ member(ordered_pair(esk17_0,esk16_0),esk15_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_72]),c_0_70])]),c_0_73]) ).
cnf(c_0_76,negated_conjecture,
( member(ordered_pair(esk17_0,esk16_0),esk15_0)
| member(esk1_3(esk13_0,esk16_0,esk15_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
member(esk16_0,image(esk15_0,esk13_0)),
inference(sr,[status(thm)],[c_0_71,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( ilf_type(esk1_3(esk13_0,esk16_0,esk15_0),member_type(esk14_0))
| member(ordered_pair(esk17_0,esk16_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( member(ordered_pair(esk17_0,esk16_0),esk15_0)
| member(esk1_3(esk13_0,esk16_0,esk15_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( ~ ilf_type(X1,member_type(esk14_0))
| ~ member(X1,esk13_0)
| ~ member(ordered_pair(X1,esk16_0),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_77])]) ).
cnf(c_0_81,negated_conjecture,
ilf_type(esk1_3(esk13_0,esk16_0,esk15_0),member_type(esk14_0)),
inference(sr,[status(thm)],[c_0_78,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
member(esk1_3(esk13_0,esk16_0,esk15_0),esk13_0),
inference(sr,[status(thm)],[c_0_79,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
~ member(ordered_pair(esk1_3(esk13_0,esk16_0,esk15_0),esk16_0),esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_74,c_0_75]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 % Computer : n001.cluster.edu
% 0.10/0.44 % Model : x86_64 x86_64
% 0.10/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.44 % Memory : 8046.5625MB
% 0.10/0.44 % OS : Linux 6.8.0-71-generic
% 0.10/0.44 % CPULimit : 300
% 0.10/0.44 % WCLimit : 300
% 0.10/0.44 % DateTime : Mon Sep 21 05:38:14 UTC 2026
% 0.10/0.44 % CPUTime :
% 0.10/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.49 Running first-order theorem proving
% 0.14/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.56 % Version: 3.5.1
% 0.14/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.56 % Starting sh5l with 300s (1) cores
% 0.14/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2297540 completed with status 0
% 0.14/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.56 % No SInE strategy applied
% 0.14/0.56 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.14/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.14/0.56 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.56 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.56 % G-E--_208_C18_F1_SE_CS_SP_PS_S2g with pid 2297549 completed with status 0
% 0.14/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2g
% 0.14/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.56 % No SInE strategy applied
% 0.14/0.56 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.14/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.14/0.56 % Preprocessing time : 0.002 s
% 0.14/0.56 % Presaturation interreduction done
% 0.14/0.56
% 0.14/0.56 % Proof found!
% 0.14/0.56 % SZS status Theorem
% 0.14/0.56 % SZS output start CNFRefutation
% See solution above
% 0.14/0.56 % Parsed axioms : 28
% 0.14/0.56 % Removed by relevancy pruning/SinE : 0
% 0.14/0.56 % Initial clauses : 64
% 0.14/0.56 % Removed in clause preprocessing : 3
% 0.14/0.56 % Initial clauses in saturation : 61
% 0.14/0.56 % Processed clauses : 500
% 0.14/0.56 % ...of these trivial : 24
% 0.14/0.56 % ...subsumed : 118
% 0.14/0.56 % ...remaining for further processing : 357
% 0.14/0.56 % Other redundant clauses eliminated : 1
% 0.14/0.56 % Clauses deleted for lack of memory : 0
% 0.14/0.56 % Backward-subsumed : 8
% 0.14/0.56 % Backward-rewritten : 62
% 0.14/0.56 % Generated clauses : 1354
% 0.14/0.56 % ...of the previous two non-redundant : 1311
% 0.14/0.56 % ...aggressively subsumed : 0
% 0.14/0.56 % Contextual simplify-reflections : 12
% 0.14/0.56 % Paramodulations : 1338
% 0.14/0.56 % Factorizations : 2
% 0.14/0.56 % NegExts : 0
% 0.14/0.56 % Equation resolutions : 1
% 0.14/0.56 % Disequality decompositions : 0
% 0.14/0.56 % Total rewrite steps : 256
% 0.14/0.56 % ...of those cached : 180
% 0.14/0.56 % Propositional unsat checks : 0
% 0.14/0.56 % Propositional check models : 0
% 0.14/0.56 % Propositional check unsatisfiable : 0
% 0.14/0.56 % Propositional clauses : 0
% 0.14/0.56 % Propositional clauses after purity: 0
% 0.14/0.56 % Propositional unsat core size : 0
% 0.14/0.56 % Propositional preprocessing time : 0.000
% 0.14/0.56 % Propositional encoding time : 0.000
% 0.14/0.56 % Propositional solver time : 0.000
% 0.14/0.56 % Success case prop preproc time : 0.000
% 0.14/0.56 % Success case prop encoding time : 0.000
% 0.14/0.56 % Success case prop solver time : 0.000
% 0.14/0.56 % Current number of processed clauses : 229
% 0.14/0.56 % Positive orientable unit clauses : 60
% 0.14/0.56 % Positive unorientable unit clauses: 1
% 0.14/0.56 % Negative unit clauses : 9
% 0.14/0.56 % Non-unit-clauses : 159
% 0.14/0.56 % Current number of unprocessed clauses: 915
% 0.14/0.56 % ...number of literals in the above : 2890
% 0.14/0.56 % Current number of archived formulas : 0
% 0.14/0.56 % Current number of archived clauses : 127
% 0.14/0.56 % Clause-clause subsumption calls (NU) : 6425
% 0.14/0.56 % Rec. Clause-clause subsumption calls : 4446
% 0.14/0.56 % Non-unit clause-clause subsumptions : 110
% 0.14/0.56 % Unit Clause-clause subsumption calls : 654
% 0.14/0.56 % Rewrite failures with RHS unbound : 0
% 0.14/0.56 % BW rewrite match attempts : 34
% 0.14/0.56 % BW rewrite match successes : 12
% 0.14/0.56 % Condensation attempts : 0
% 0.14/0.56 % Condensation successes : 0
% 0.14/0.56 % Termbank termtop insertions : 30786
% 0.14/0.56 % Search garbage collected termcells : 1446
% 0.14/0.56
% 0.14/0.56 % -------------------------------------------------
% 0.14/0.56 % User time : 0.048 s
% 0.14/0.56 % System time : 0.009 s
% 0.14/0.56 % Total time : 0.057 s
% 0.14/0.56 % Maximum resident set size: 3672 pages
% 0.14/0.56
% 0.14/0.56 % -------------------------------------------------
% 0.14/0.56 % User time : 0.220 s
% 0.14/0.56 % System time : 0.036 s
% 0.14/0.56 % Total time : 0.255 s
% 0.14/0.56 % Maximum resident set size: 4864 pages
% 0.14/0.56 % E exiting
%------------------------------------------------------------------------------