%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET683+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 : n008.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 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 87 ( 13 unt; 0 def)
% Number of atoms : 330 ( 8 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 405 ( 162 ~; 146 |; 37 &)
% ( 7 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 6 con; 0-3 aty)
% Number of variables : 167 ( 9 sgn 81 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p4,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',p4) ).
fof(p5,axiom,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ? [X2] : ilf_type(X2,member_type(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(p15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(p6,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',p6) ).
fof(prove_relset_1_50,conjecture,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
=> ? [X5] :
( member(X5,domain(X2,X1,X3))
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_50) ).
fof(p18,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',p18) ).
fof(p24,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(p2,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',p2) ).
fof(p12,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',p12) ).
fof(p21,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/sandbox/benchmark/theBenchmark.p',p21) ).
fof(p20,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',p20) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,range_of(X2))
=> ? [X3] :
( member(X3,domain_of(X2))
& ilf_type(X3,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(p10,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',p10) ).
fof(p14,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',p14) ).
fof(c_0_15,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)],[p4]) ).
fof(c_0_16,plain,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ? [X2] : ilf_type(X2,member_type(X1)) ),
inference(fof_simplification,[status(thm)],[p5]) ).
fof(c_0_17,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
inference(fof_simplification,[status(thm)],[p15]) ).
fof(c_0_18,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p6]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
=> ? [X5] :
( member(X5,domain(X2,X1,X3))
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_50]) ).
fof(c_0_20,plain,
! [X50,X51,X52] :
( relation_like(X52)
| ~ ilf_type(X52,subset_type(cross_product(X50,X51)))
| ~ ilf_type(X51,set_type)
| ~ ilf_type(X50,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])]) ).
fof(c_0_21,plain,
! [X22] : ilf_type(X22,set_type),
inference(variable_rename,[status(thm)],[p24]) ).
fof(c_0_22,plain,
! [X54,X55,X56,X57] :
( ( ~ ilf_type(X54,set_type)
| ~ ilf_type(X55,set_type)
| ilf_type(X57,subset_type(cross_product(X54,X55)))
| ~ ilf_type(X57,relation_type(X54,X55)) )
& ( ~ ilf_type(X54,set_type)
| ~ ilf_type(X55,set_type)
| ilf_type(X56,relation_type(X54,X55))
| ~ ilf_type(X56,subset_type(cross_product(X54,X55))) ) ),
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])])])])]) ).
fof(c_0_23,plain,
! [X11,X12] :
( ( ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| empty(X12)
| ilf_type(X11,member_type(X12))
| ~ member(X11,X12) )
& ( ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| empty(X12)
| member(X11,X12)
| ~ ilf_type(X11,member_type(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)],[c_0_15])])])])]) ).
fof(c_0_24,plain,
! [X23] :
( ilf_type(esk6_1(X23),member_type(X23))
| ~ ilf_type(X23,set_type)
| empty(X23) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_25,plain,
! [X25,X26] :
( ( ~ ilf_type(X25,set_type)
| ~ ilf_type(X26,set_type)
| ilf_type(X26,subset_type(X25))
| ~ ilf_type(X26,member_type(power_set(X25))) )
& ( ~ ilf_type(X25,set_type)
| ~ ilf_type(X26,set_type)
| ilf_type(X26,member_type(power_set(X25)))
| ~ ilf_type(X26,subset_type(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)],[p12])])])])]) ).
fof(c_0_26,plain,
! [X47] :
( ( ~ ilf_type(X47,set_type)
| ilf_type(power_set(X47),set_type) )
& ( ~ ilf_type(X47,set_type)
| ~ empty(power_set(X47)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_27,plain,
! [X19,X20,X21] :
( ilf_type(domain(X19,X20,X21),subset_type(X19))
| ~ ilf_type(X21,relation_type(X19,X20))
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X19,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p21])])])]) ).
fof(c_0_28,plain,
! [X16,X17,X18] :
( domain(X16,X17,X18) = domain_of(X18)
| ~ ilf_type(X18,relation_type(X16,X17))
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p20])])])]) ).
fof(c_0_29,plain,
! [X13,X14] :
( ( ~ ilf_type(X13,set_type)
| empty(X13)
| member(esk5_1(X13),X13) )
& ( ~ ilf_type(X13,set_type)
| empty(X13)
| ilf_type(esk5_1(X13),set_type) )
& ( ~ ilf_type(X13,set_type)
| ~ member(X14,X13)
| ~ ilf_type(X14,set_type)
| ~ empty(X13) ) ),
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_18])])])])])]) ).
fof(c_0_30,plain,
! [X37,X38] :
( ( ~ ilf_type(X37,set_type)
| ~ ilf_type(X38,binary_relation_type)
| ~ member(X37,range_of(X38))
| member(esk8_2(X37,X38),domain_of(X38)) )
& ( ~ ilf_type(X37,set_type)
| ~ ilf_type(X38,binary_relation_type)
| ~ member(X37,range_of(X38))
| ilf_type(esk8_2(X37,X38),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])])])])])]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
=> ? [X5] :
( member(X5,domain(X2,X1,X3))
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_32,plain,
! [X27,X28,X29] :
( range(X27,X28,X29) = range_of(X29)
| ~ ilf_type(X29,relation_type(X27,X28))
| ~ ilf_type(X28,set_type)
| ~ ilf_type(X27,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])])]) ).
fof(c_0_33,plain,
! [X49] :
( ( ~ ilf_type(X49,set_type)
| ilf_type(X49,binary_relation_type)
| ~ ilf_type(X49,set_type)
| ~ relation_like(X49) )
& ( ~ ilf_type(X49,set_type)
| ~ ilf_type(X49,binary_relation_type)
| ilf_type(X49,set_type) )
& ( ~ ilf_type(X49,set_type)
| ~ ilf_type(X49,binary_relation_type)
| relation_like(X49) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])]) ).
cnf(c_0_34,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_20]) ).
cnf(c_0_35,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_36,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_22]) ).
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_23]) ).
cnf(c_0_38,plain,
( ~ ilf_type(X1,set_type)
| ilf_type(esk6_1(X1),member_type(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_39,plain,
! [X43,X44,X45] :
( ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| member(X43,power_set(X44))
| ~ member(esk10_2(X43,X44),X44) )
& ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| member(X43,power_set(X44))
| member(esk10_2(X43,X44),X43) )
& ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| member(X43,power_set(X44))
| ilf_type(esk10_2(X43,X44),set_type) )
& ( ~ ilf_type(X43,set_type)
| ~ ilf_type(X44,set_type)
| member(X45,X44)
| ~ member(X45,X43)
| ~ ilf_type(X45,set_type)
| ~ member(X43,power_set(X44)) ) ),
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)],[p14])])])])])]) ).
cnf(c_0_40,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_25]) ).
cnf(c_0_41,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_42,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_27]) ).
cnf(c_0_43,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_28]) ).
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_29]) ).
cnf(c_0_45,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2))
| member(esk8_2(X1,X2),domain_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_46,negated_conjecture,
! [X10] :
( ( ~ member(X10,domain(esk2_0,esk1_0,esk3_0))
| ~ ilf_type(X10,member_type(esk2_0)) )
& member(esk4_0,range(esk2_0,esk1_0,esk3_0))
& ilf_type(esk4_0,member_type(esk1_0))
& ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
& ilf_type(esk2_0,set_type)
& ~ empty(esk2_0)
& ilf_type(esk1_0,set_type)
& ~ empty(esk1_0) ),
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_31])])])])]) ).
cnf(c_0_47,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| range(X1,X2,X3) = range_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_48,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_49,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_34,c_0_35]),c_0_35])]) ).
cnf(c_0_50,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_36,c_0_35]),c_0_35])]) ).
cnf(c_0_51,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_35]),c_0_35])]) ).
cnf(c_0_52,plain,
( ilf_type(esk6_1(X1),member_type(X1))
| empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_35])]) ).
cnf(c_0_53,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_39]) ).
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_40,c_0_35]),c_0_35])]) ).
cnf(c_0_55,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_35])]) ).
cnf(c_0_56,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_42,c_0_35]),c_0_35])]) ).
cnf(c_0_57,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_43,c_0_35]),c_0_35])]) ).
cnf(c_0_58,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_35]),c_0_35])]) ).
cnf(c_0_59,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2))
| member(esk8_2(X1,X2),domain_of(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_35])]) ).
cnf(c_0_60,negated_conjecture,
member(esk4_0,range(esk2_0,esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_61,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| range(X1,X2,X3) = range_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_35]),c_0_35])]) ).
cnf(c_0_62,negated_conjecture,
ilf_type(esk3_0,relation_type(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_63,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_48]) ).
cnf(c_0_64,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| relation_like(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(X1,domain(esk2_0,esk1_0,esk3_0))
| ~ ilf_type(X1,member_type(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_66,plain,
( member(esk6_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_67,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_23]) ).
cnf(c_0_68,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_53,c_0_35]),c_0_35]),c_0_35])]) ).
cnf(c_0_69,plain,
( ~ ilf_type(X1,subset_type(X2))
| member(X1,power_set(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_54]),c_0_55]) ).
cnf(c_0_70,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(domain_of(X1),subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_71,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X2,range_of(X1))
| ~ empty(domain_of(X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_72,negated_conjecture,
member(esk4_0,range_of(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_73,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_35])]) ).
cnf(c_0_74,negated_conjecture,
relation_like(esk3_0),
inference(spm,[status(thm)],[c_0_64,c_0_62]) ).
cnf(c_0_75,negated_conjecture,
( ~ ilf_type(esk6_1(domain(esk2_0,esk1_0,esk3_0)),member_type(esk2_0))
| empty(domain(esk2_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,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_67,c_0_35]),c_0_35])]),c_0_58]) ).
cnf(c_0_77,plain,
( ~ ilf_type(X3,subset_type(X2))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,negated_conjecture,
ilf_type(domain_of(esk3_0),subset_type(esk2_0)),
inference(spm,[status(thm)],[c_0_70,c_0_62]) ).
cnf(c_0_79,negated_conjecture,
( ~ ilf_type(esk3_0,binary_relation_type)
| ~ empty(domain_of(esk3_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
ilf_type(esk3_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( ~ member(esk6_1(domain(esk2_0,esk1_0,esk3_0)),esk2_0)
| empty(domain(esk2_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( ~ member(X1,domain_of(esk3_0))
| member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
~ empty(domain_of(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_84,negated_conjecture,
( ~ member(esk6_1(domain_of(esk3_0)),esk2_0)
| empty(domain_of(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_57]),c_0_62])]) ).
cnf(c_0_85,negated_conjecture,
member(esk6_1(domain_of(esk3_0)),esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_66]),c_0_83]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET683+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:32:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % new_bool_1 with pid 240118 completed with status 0
% 0.11/0.44 % Result found by new_bool_1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % SubtermCWHack with pid 240120 completed with status 0
% 0.11/0.44 % Result found by SubtermCWHack
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % Preprocessing time : 0.002 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 25
% 0.11/0.44 % Removed by relevancy pruning/SinE : 2
% 0.11/0.44 % Initial clauses : 42
% 0.11/0.44 % Removed in clause preprocessing : 1
% 0.11/0.44 % Initial clauses in saturation : 41
% 0.11/0.44 % Processed clauses : 147
% 0.11/0.44 % ...of these trivial : 7
% 0.11/0.44 % ...subsumed : 23
% 0.11/0.44 % ...remaining for further processing : 117
% 0.11/0.44 % Other redundant clauses eliminated : 0
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 4
% 0.11/0.44 % Generated clauses : 226
% 0.11/0.44 % ...of the previous two non-redundant : 211
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 1
% 0.11/0.44 % Paramodulations : 226
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 0
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 73
% 0.11/0.44 % ...of those cached : 52
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 113
% 0.11/0.44 % Positive orientable unit clauses : 33
% 0.11/0.44 % Positive unorientable unit clauses: 0
% 0.11/0.44 % Negative unit clauses : 6
% 0.11/0.44 % Non-unit-clauses : 74
% 0.11/0.44 % Current number of unprocessed clauses: 105
% 0.11/0.44 % ...number of literals in the above : 229
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 4
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 470
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 449
% 0.11/0.44 % Non-unit clause-clause subsumptions : 18
% 0.11/0.44 % Unit Clause-clause subsumption calls : 211
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 12
% 0.11/0.44 % BW rewrite match successes : 4
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 6715
% 0.11/0.44 % Search garbage collected termcells : 818
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.011 s
% 0.11/0.44 % System time : 0.004 s
% 0.11/0.44 % Total time : 0.015 s
% 0.11/0.44 % Maximum resident set size: 3664 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.013 s
% 0.11/0.44 % System time : 0.009 s
% 0.11/0.44 % Total time : 0.022 s
% 0.11/0.44 % Maximum resident set size: 4864 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------