%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET659+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 02:14:55 PM UTC 2026
% Result : Theorem 0.82s 0.58s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 90 ( 17 unt; 0 def)
% Number of atoms : 361 ( 30 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 448 ( 177 ~; 184 |; 33 &)
% ( 10 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 158 ( 9 sgn 74 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p30,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/sandbox2/benchmark/theBenchmark.p',p30) ).
fof(p34,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(prove_relset_1_22,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( member(ordered_pair(X4,X5),X3)
& ilf_type(X5,set_type) ) ) )
<=> domain(X2,X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_22) ).
fof(p31,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(p24,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/sandbox2/benchmark/theBenchmark.p',p24) ).
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/sandbox2/benchmark/theBenchmark.p',p17) ).
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(p7,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/sandbox2/benchmark/theBenchmark.p',p7) ).
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/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(p27,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/sandbox2/benchmark/theBenchmark.p',p27) ).
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/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(p20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,domain_of(X1))
<=> ? [X3] :
( member(ordered_pair(X2,X3),X1)
& ilf_type(X3,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p9,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(c_0_14,plain,
! [X79,X80,X81] :
( domain(X79,X80,X81) = domain_of(X81)
| ~ ilf_type(X81,relation_type(X79,X80))
| ~ ilf_type(X80,set_type)
| ~ ilf_type(X79,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p30])])])]) ).
fof(c_0_15,plain,
! [X91] : ilf_type(X91,set_type),
inference(variable_rename,[status(thm)],[p34]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ! [X4] :
( ilf_type(X4,set_type)
=> ( member(X4,X2)
=> ? [X5] :
( member(ordered_pair(X4,X5),X3)
& ilf_type(X5,set_type) ) ) )
<=> domain(X2,X1,X3) = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_22]) ).
fof(c_0_17,plain,
! [X82,X83,X84] :
( ilf_type(domain(X82,X83,X84),subset_type(X82))
| ~ ilf_type(X84,relation_type(X82,X83))
| ~ ilf_type(X83,set_type)
| ~ ilf_type(X82,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p31])])])]) ).
cnf(c_0_18,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| domain(X1,X2,X3) = domain_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,negated_conjecture,
! [X96,X97] :
( ( domain(esk15_0,esk14_0,esk16_0) = esk15_0
| ~ ilf_type(X97,set_type)
| ~ member(X97,esk15_0)
| member(ordered_pair(X97,esk18_1(X97)),esk16_0) )
& ( domain(esk15_0,esk14_0,esk16_0) = esk15_0
| ~ ilf_type(X97,set_type)
| ~ member(X97,esk15_0)
| ilf_type(esk18_1(X97),set_type) )
& ( domain(esk15_0,esk14_0,esk16_0) != esk15_0
| ~ member(ordered_pair(esk17_0,X96),esk16_0)
| ~ ilf_type(X96,set_type) )
& ( domain(esk15_0,esk14_0,esk16_0) != esk15_0
| member(esk17_0,esk15_0) )
& ( domain(esk15_0,esk14_0,esk16_0) != esk15_0
| ilf_type(esk17_0,set_type) )
& ilf_type(esk16_0,relation_type(esk15_0,esk14_0))
& ilf_type(esk15_0,set_type)
& ilf_type(esk14_0,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)],[c_0_16])])])])])]) ).
fof(c_0_21,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)],[p24]) ).
fof(c_0_22,plain,
! [X43,X44] :
( ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| ilf_type(X44,subset_type(X43))
| ~ ilf_type(X44,member_type(power_set(X43))) )
& ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| ilf_type(X44,member_type(power_set(X43)))
| ~ ilf_type(X44,subset_type(X43)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])])]) ).
cnf(c_0_23,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| domain(X1,X2,X3) = domain_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19])]) ).
cnf(c_0_25,negated_conjecture,
ilf_type(esk16_0,relation_type(esk15_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_27,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)],[p7])])])])]) ).
fof(c_0_28,plain,
! [X61,X62] :
( ( ~ ilf_type(X61,set_type)
| ~ ilf_type(X62,set_type)
| empty(X62)
| ilf_type(X61,member_type(X62))
| ~ member(X61,X62) )
& ( ~ ilf_type(X61,set_type)
| ~ ilf_type(X62,set_type)
| empty(X62)
| member(X61,X62)
| ~ ilf_type(X61,member_type(X62)) ) ),
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_21])])])])]) ).
cnf(c_0_29,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X2))
| ilf_type(X1,member_type(power_set(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_19]),c_0_19])]) ).
cnf(c_0_31,negated_conjecture,
domain(esk15_0,esk14_0,esk16_0) = domain_of(esk16_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_32,plain,
! [X60] :
( ( ~ ilf_type(X60,set_type)
| ilf_type(power_set(X60),set_type) )
& ( ~ ilf_type(X60,set_type)
| ~ empty(power_set(X60)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
fof(c_0_33,plain,
! [X41] :
( ( ~ ilf_type(X41,set_type)
| ilf_type(X41,binary_relation_type)
| ~ ilf_type(X41,set_type)
| ~ relation_like(X41) )
& ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X41,binary_relation_type)
| ilf_type(X41,set_type) )
& ( ~ ilf_type(X41,set_type)
| ~ ilf_type(X41,binary_relation_type)
| relation_like(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).
fof(c_0_34,plain,
! [X72,X73,X74] :
( relation_like(X74)
| ~ ilf_type(X74,subset_type(cross_product(X72,X73)))
| ~ ilf_type(X73,set_type)
| ~ ilf_type(X72,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])])]) ).
cnf(c_0_35,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_27]) ).
fof(c_0_36,plain,
! [X56,X57,X58] :
( ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X56,power_set(X57))
| ~ member(esk8_2(X56,X57),X57) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X56,power_set(X57))
| member(esk8_2(X56,X57),X56) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X56,power_set(X57))
| ilf_type(esk8_2(X56,X57),set_type) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| member(X58,X57)
| ~ member(X58,X56)
| ~ ilf_type(X58,set_type)
| ~ member(X56,power_set(X57)) ) ),
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)],[p22])])])])])]) ).
cnf(c_0_37,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,member_type(X2))
| empty(X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,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_29,c_0_19]),c_0_19])]) ).
cnf(c_0_39,negated_conjecture,
ilf_type(domain_of(esk16_0),subset_type(esk15_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_31]) ).
cnf(c_0_40,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,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_33]) ).
cnf(c_0_42,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_34]) ).
cnf(c_0_43,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_35,c_0_19]),c_0_19])]) ).
cnf(c_0_44,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X1,power_set(X2))
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( ~ ilf_type(X2,member_type(X1))
| member(X2,X1)
| empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_19]),c_0_19])]) ).
cnf(c_0_46,negated_conjecture,
ilf_type(domain_of(esk16_0),member_type(power_set(esk15_0))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_19])]) ).
fof(c_0_48,plain,
! [X51,X52,X53] :
( ( ~ ilf_type(X51,set_type)
| ~ ilf_type(X52,set_type)
| subset(X51,X52)
| ~ member(esk7_2(X51,X52),X52) )
& ( ~ ilf_type(X51,set_type)
| ~ ilf_type(X52,set_type)
| subset(X51,X52)
| member(esk7_2(X51,X52),X51) )
& ( ~ ilf_type(X51,set_type)
| ~ ilf_type(X52,set_type)
| subset(X51,X52)
| ilf_type(esk7_2(X51,X52),set_type) )
& ( ~ ilf_type(X51,set_type)
| ~ ilf_type(X52,set_type)
| member(X53,X52)
| ~ member(X53,X51)
| ~ ilf_type(X53,set_type)
| ~ subset(X51,X52) ) ),
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)],[p20])])])])])]) ).
fof(c_0_49,plain,
! [X6,X7,X9] :
( ( ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X7,set_type)
| member(X7,domain_of(X6))
| ~ member(ordered_pair(X7,X9),X6)
| ~ ilf_type(X9,set_type) )
& ( ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ member(X7,domain_of(X6))
| member(ordered_pair(X7,esk1_2(X6,X7)),X6) )
& ( ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ member(X7,domain_of(X6))
| ilf_type(esk1_2(X6,X7),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_50,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_41]) ).
cnf(c_0_51,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_42,c_0_19]),c_0_19])]) ).
cnf(c_0_52,negated_conjecture,
ilf_type(esk16_0,subset_type(cross_product(esk15_0,esk14_0))),
inference(spm,[status(thm)],[c_0_43,c_0_25]) ).
cnf(c_0_53,negated_conjecture,
( ~ ilf_type(X1,set_type)
| ~ member(X1,esk15_0)
| domain(esk15_0,esk14_0,esk16_0) = esk15_0
| member(ordered_pair(X1,esk18_1(X1)),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_54,plain,
( ~ member(X1,X3)
| ~ member(X3,power_set(X2))
| member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_19]),c_0_19]),c_0_19])]) ).
cnf(c_0_55,negated_conjecture,
member(domain_of(esk16_0),power_set(esk15_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_56,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(X1,X2)
| member(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ ilf_type(X1,set_type)
| member(X2,domain_of(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_19])]) ).
cnf(c_0_59,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(X1,esk15_0)
| member(ordered_pair(X1,esk18_1(X1)),esk16_0)
| domain(esk15_0,esk14_0,esk16_0) = esk15_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_19])]) ).
fof(c_0_61,plain,
! [X31,X32] :
( ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| X31 = X32
| ~ subset(X32,X31)
| ~ subset(X31,X32) )
& ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| X31 != X32
| subset(X32,X31) )
& ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| X31 != X32
| subset(X31,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)],[p9])])])])]) ).
cnf(c_0_62,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk7_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(X1,domain_of(esk16_0))
| member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_64,plain,
( member(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_19]),c_0_19])]) ).
cnf(c_0_65,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X1,X3),X2)
| member(X1,domain_of(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_19]),c_0_19])]) ).
cnf(c_0_66,negated_conjecture,
ilf_type(esk16_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( ~ member(X1,esk15_0)
| member(ordered_pair(X1,esk18_1(X1)),esk16_0)
| domain_of(esk16_0) = esk15_0 ),
inference(rw,[status(thm)],[c_0_60,c_0_31]) ).
cnf(c_0_68,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
( ~ member(esk7_2(X1,X2),X2)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_19]),c_0_19])]) ).
cnf(c_0_70,negated_conjecture,
( member(esk7_2(domain_of(esk16_0),X1),esk15_0)
| subset(domain_of(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,domain_of(X2))
| member(ordered_pair(X1,esk1_2(X2,X1)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_72,negated_conjecture,
( ~ member(ordered_pair(X1,X2),esk16_0)
| member(X1,domain_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( member(ordered_pair(esk7_2(esk15_0,X1),esk18_1(esk7_2(esk15_0,X1))),esk16_0)
| subset(esk15_0,X1)
| domain_of(esk16_0) = esk15_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_64]) ).
cnf(c_0_74,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_19]),c_0_19])]) ).
cnf(c_0_75,negated_conjecture,
subset(domain_of(esk16_0),esk15_0),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( domain(esk15_0,esk14_0,esk16_0) != esk15_0
| ~ member(ordered_pair(esk17_0,X1),esk16_0)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_77,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,domain_of(X2))
| member(ordered_pair(X1,esk1_2(X2,X1)),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_19])]) ).
cnf(c_0_78,negated_conjecture,
( member(esk7_2(esk15_0,X1),domain_of(esk16_0))
| subset(esk15_0,X1)
| domain_of(esk16_0) = esk15_0 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_79,negated_conjecture,
( ~ subset(esk15_0,domain_of(esk16_0))
| domain_of(esk16_0) = esk15_0 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,negated_conjecture,
( domain(esk15_0,esk14_0,esk16_0) != esk15_0
| member(esk17_0,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_81,negated_conjecture,
( ~ member(ordered_pair(esk17_0,X1),esk16_0)
| domain(esk15_0,esk14_0,esk16_0) != esk15_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_19])]) ).
cnf(c_0_82,negated_conjecture,
( ~ member(X1,domain_of(esk16_0))
| member(ordered_pair(X1,esk1_2(esk16_0,X1)),esk16_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_83,negated_conjecture,
domain_of(esk16_0) = esk15_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_78]),c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( domain_of(esk16_0) != esk15_0
| member(esk17_0,esk15_0) ),
inference(rw,[status(thm)],[c_0_80,c_0_31]) ).
cnf(c_0_85,negated_conjecture,
( ~ member(ordered_pair(esk17_0,X1),esk16_0)
| domain_of(esk16_0) != esk15_0 ),
inference(rw,[status(thm)],[c_0_81,c_0_31]) ).
cnf(c_0_86,negated_conjecture,
( ~ member(X1,esk15_0)
| member(ordered_pair(X1,esk1_2(esk16_0,X1)),esk16_0) ),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
member(esk17_0,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_83])]) ).
cnf(c_0_88,negated_conjecture,
~ member(ordered_pair(esk17_0,X1),esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_83])]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET659+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:33:44 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.47 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.82/0.58 % Version: 3.5.1
% 0.82/0.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.82/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.82/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.82/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.82/0.58 % Starting sh5l with 300s (1) cores
% 0.82/0.58 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1064541 completed with status 0
% 0.82/0.58 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.82/0.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.82/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.82/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.58 % No SInE strategy applied
% 0.82/0.58 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.82/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.82/0.58 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with 209s (1) cores
% 0.82/0.58 % Starting new_bool_3 with 189s (1) cores
% 0.82/0.58 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.82/0.58 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1064554 completed with status 0
% 0.82/0.58 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.82/0.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.82/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.82/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.58 % No SInE strategy applied
% 0.82/0.58 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.82/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.82/0.58 % Preprocessing time : 0.002 s
% 0.82/0.58 % Presaturation interreduction done
% 0.82/0.58
% 0.82/0.58 % Proof found!
% 0.82/0.58 % SZS status Theorem
% 0.82/0.58 % SZS output start CNFRefutation
% See solution above
% 0.82/0.58 % Parsed axioms : 35
% 0.82/0.58 % Removed by relevancy pruning/SinE : 0
% 0.82/0.58 % Initial clauses : 73
% 0.82/0.58 % Removed in clause preprocessing : 3
% 0.82/0.58 % Initial clauses in saturation : 70
% 0.82/0.58 % Processed clauses : 1125
% 0.82/0.58 % ...of these trivial : 25
% 0.82/0.58 % ...subsumed : 579
% 0.82/0.58 % ...remaining for further processing : 521
% 0.82/0.58 % Other redundant clauses eliminated : 17
% 0.82/0.58 % Clauses deleted for lack of memory : 0
% 0.82/0.58 % Backward-subsumed : 12
% 0.82/0.58 % Backward-rewritten : 133
% 0.82/0.58 % Generated clauses : 4547
% 0.82/0.58 % ...of the previous two non-redundant : 4381
% 0.82/0.58 % ...aggressively subsumed : 0
% 0.82/0.58 % Contextual simplify-reflections : 4
% 0.82/0.58 % Paramodulations : 4518
% 0.82/0.58 % Factorizations : 12
% 0.82/0.58 % NegExts : 0
% 0.82/0.58 % Equation resolutions : 17
% 0.82/0.58 % Disequality decompositions : 0
% 0.82/0.58 % Total rewrite steps : 424
% 0.82/0.58 % ...of those cached : 328
% 0.82/0.58 % Propositional unsat checks : 0
% 0.82/0.58 % Propositional check models : 0
% 0.82/0.58 % Propositional check unsatisfiable : 0
% 0.82/0.58 % Propositional clauses : 0
% 0.82/0.58 % Propositional clauses after purity: 0
% 0.82/0.58 % Propositional unsat core size : 0
% 0.82/0.58 % Propositional preprocessing time : 0.000
% 0.82/0.58 % Propositional encoding time : 0.000
% 0.82/0.58 % Propositional solver time : 0.000
% 0.82/0.58 % Success case prop preproc time : 0.000
% 0.82/0.58 % Success case prop encoding time : 0.000
% 0.82/0.58 % Success case prop solver time : 0.000
% 0.82/0.58 % Current number of processed clauses : 326
% 0.82/0.58 % Positive orientable unit clauses : 69
% 0.82/0.58 % Positive unorientable unit clauses: 1
% 0.82/0.58 % Negative unit clauses : 3
% 0.82/0.58 % Non-unit-clauses : 253
% 0.82/0.58 % Current number of unprocessed clauses: 3354
% 0.82/0.58 % ...number of literals in the above : 13717
% 0.82/0.58 % Current number of archived formulas : 0
% 0.82/0.58 % Current number of archived clauses : 191
% 0.82/0.58 % Clause-clause subsumption calls (NU) : 22943
% 0.82/0.58 % Rec. Clause-clause subsumption calls : 12326
% 0.82/0.58 % Non-unit clause-clause subsumptions : 490
% 0.82/0.58 % Unit Clause-clause subsumption calls : 901
% 0.82/0.58 % Rewrite failures with RHS unbound : 0
% 0.82/0.58 % BW rewrite match attempts : 23
% 0.82/0.58 % BW rewrite match successes : 5
% 0.82/0.58 % Condensation attempts : 0
% 0.82/0.58 % Condensation successes : 0
% 0.82/0.58 % Termbank termtop insertions : 62857
% 0.82/0.58 % Search garbage collected termcells : 1643
% 0.82/0.58
% 0.82/0.58 % -------------------------------------------------
% 0.82/0.58 % User time : 0.081 s
% 0.82/0.58 % System time : 0.006 s
% 0.82/0.58 % Total time : 0.087 s
% 0.82/0.58 % Maximum resident set size: 3936 pages
% 0.82/0.58
% 0.82/0.58 % -------------------------------------------------
% 0.82/0.58 % User time : 0.373 s
% 0.82/0.58 % System time : 0.038 s
% 0.82/0.58 % Total time : 0.411 s
% 0.82/0.58 % Maximum resident set size: 4864 pages
% 0.82/0.58 % E exiting
%------------------------------------------------------------------------------