%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET655+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 : n011.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 02:14:54 PM UTC 2026
% Result : Theorem 18.05s 3.07s
% Output : CNFRefutation 18.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 18 unt; 0 def)
% Number of atoms : 312 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 382 ( 149 ~; 153 |; 28 &)
% ( 7 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 153 ( 3 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,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',p3) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(prove_relset_1_17,conjecture,
! [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,X3))
=> ( ( subset(X3,X4)
& subset(X1,X2) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_17) ).
fof(p12,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',p12) ).
fof(p7,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',p7) ).
fof(p11,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',p11) ).
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)
=> ( ( subset(X3,X4)
& subset(X1,X2) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(p10,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',p10) ).
fof(p5,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',p5) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(c_0_11,plain,
! [X13,X14,X15,X16] :
( ( ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ilf_type(X16,subset_type(cross_product(X13,X14)))
| ~ ilf_type(X16,relation_type(X13,X14)) )
& ( ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ilf_type(X15,relation_type(X13,X14))
| ~ ilf_type(X15,subset_type(cross_product(X13,X14))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])]) ).
fof(c_0_12,plain,
! [X56] : ilf_type(X56,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_13,negated_conjecture,
~ ! [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,X3))
=> ( ( subset(X3,X4)
& subset(X1,X2) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_17]) ).
fof(c_0_14,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)],[p12]) ).
fof(c_0_15,plain,
! [X26,X27] :
( ( ~ ilf_type(X26,set_type)
| ~ ilf_type(X27,set_type)
| ilf_type(X27,subset_type(X26))
| ~ ilf_type(X27,member_type(power_set(X26))) )
& ( ~ ilf_type(X26,set_type)
| ~ ilf_type(X27,set_type)
| ilf_type(X27,member_type(power_set(X26)))
| ~ ilf_type(X27,subset_type(X26)) ) ),
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])])])])]) ).
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,
( ~ ilf_type(esk14_0,relation_type(esk11_0,esk13_0))
& subset(esk12_0,esk13_0)
& subset(esk10_0,esk11_0)
& ilf_type(esk14_0,relation_type(esk10_0,esk12_0))
& ilf_type(esk13_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk11_0,set_type)
& ilf_type(esk10_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_19,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
inference(fof_simplification,[status(thm)],[p11]) ).
fof(c_0_20,plain,
! [X9,X10,X11,X12] :
( subset(cross_product(X9,X11),cross_product(X10,X12))
| ~ subset(X11,X12)
| ~ subset(X9,X10)
| ~ ilf_type(X12,set_type)
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X9,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
fof(c_0_21,plain,
! [X31,X32,X33] :
( ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| member(X31,power_set(X32))
| ~ member(esk4_2(X31,X32),X32) )
& ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| member(X31,power_set(X32))
| member(esk4_2(X31,X32),X31) )
& ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| member(X31,power_set(X32))
| ilf_type(esk4_2(X31,X32),set_type) )
& ( ~ ilf_type(X31,set_type)
| ~ ilf_type(X32,set_type)
| member(X33,X32)
| ~ member(X33,X31)
| ~ ilf_type(X33,set_type)
| ~ member(X31,power_set(X32)) ) ),
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)],[p10])])])])])]) ).
fof(c_0_22,plain,
! [X20,X21,X22] :
( ( ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,set_type)
| subset(X20,X21)
| ~ member(esk2_2(X20,X21),X21) )
& ( ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,set_type)
| subset(X20,X21)
| member(esk2_2(X20,X21),X20) )
& ( ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,set_type)
| subset(X20,X21)
| ilf_type(esk2_2(X20,X21),set_type) )
& ( ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,set_type)
| member(X22,X21)
| ~ member(X22,X20)
| ~ ilf_type(X22,set_type)
| ~ subset(X20,X21) ) ),
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)],[p5])])])])])]) ).
fof(c_0_23,plain,
! [X36,X37] :
( ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X37,set_type)
| empty(X37)
| ilf_type(X36,member_type(X37))
| ~ member(X36,X37) )
& ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X37,set_type)
| empty(X37)
| member(X36,X37)
| ~ ilf_type(X36,member_type(X37)) ) ),
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_14])])])])]) ).
cnf(c_0_24,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_15]) ).
cnf(c_0_25,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_26,negated_conjecture,
ilf_type(esk14_0,relation_type(esk10_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X35] :
( ( ~ ilf_type(X35,set_type)
| ilf_type(power_set(X35),set_type) )
& ( ~ ilf_type(X35,set_type)
| ~ empty(power_set(X35)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_28,plain,
( ~ subset(X3,X4)
| ~ subset(X1,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| subset(cross_product(X1,X3),cross_product(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,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_21]) ).
cnf(c_0_30,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,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_32,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_24,c_0_17]),c_0_17])]) ).
cnf(c_0_33,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk10_0,esk12_0))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X6,X7,X8] :
( subset(X6,X8)
| ~ subset(X7,X8)
| ~ subset(X6,X7)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_36,plain,
( ~ subset(X1,X3)
| ~ subset(X2,X4)
| subset(cross_product(X1,X2),cross_product(X3,X4)) ),
inference(cn,[status(thm)],[inference(rw,[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]),c_0_17])]) ).
cnf(c_0_37,negated_conjecture,
subset(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_38,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_29,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_39,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_17]),c_0_17])]) ).
cnf(c_0_40,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_31,c_0_17]),c_0_17])]) ).
cnf(c_0_41,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk10_0,esk12_0)))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17])]) ).
cnf(c_0_43,plain,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( ~ subset(X1,X2)
| subset(cross_product(X1,esk12_0),cross_product(X2,esk13_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
subset(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_47,plain,
( ~ member(X1,power_set(X3))
| subset(X1,X2)
| member(esk2_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
member(esk14_0,power_set(cross_product(esk10_0,esk12_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
fof(c_0_49,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
cnf(c_0_50,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_51,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_52,plain,
( ~ subset(X1,X3)
| ~ subset(X3,X2)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_53,negated_conjecture,
subset(cross_product(esk10_0,esk12_0),cross_product(esk11_0,esk13_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,plain,
( ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_17]),c_0_17])]) ).
cnf(c_0_55,negated_conjecture,
( subset(esk14_0,X1)
| member(esk2_2(esk14_0,X1),cross_product(esk10_0,esk12_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_56,plain,
! [X40,X41] :
( ( ~ ilf_type(X40,set_type)
| empty(X40)
| member(esk6_1(X40),X40) )
& ( ~ ilf_type(X40,set_type)
| empty(X40)
| ilf_type(esk6_1(X40),set_type) )
& ( ~ ilf_type(X40,set_type)
| ~ member(X41,X40)
| ~ ilf_type(X41,set_type)
| ~ empty(X40) ) ),
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_49])])])])])]) ).
cnf(c_0_57,plain,
( ~ subset(X3,X2)
| ~ member(X1,X3)
| member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_58,plain,
( member(X1,power_set(X2))
| member(esk4_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_17]),c_0_17])]) ).
cnf(c_0_59,negated_conjecture,
( ~ subset(X1,cross_product(esk10_0,esk12_0))
| subset(X1,cross_product(esk11_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
subset(esk14_0,cross_product(esk10_0,esk12_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk4_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_63,plain,
( ~ subset(X1,X3)
| member(X1,power_set(X2))
| member(esk4_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
subset(esk14_0,cross_product(esk11_0,esk13_0)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,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_66,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_17]),c_0_17])]) ).
cnf(c_0_67,plain,
( ~ member(esk4_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_17]),c_0_17])]) ).
cnf(c_0_68,negated_conjecture,
( member(esk14_0,power_set(X1))
| member(esk4_2(esk14_0,X1),cross_product(esk11_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X2)))
| ilf_type(X1,subset_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_70,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_65,c_0_17]),c_0_17])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
member(esk14_0,power_set(cross_product(esk11_0,esk13_0))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ilf_type(X1,relation_type(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_73,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_69,c_0_17]),c_0_17])]) ).
cnf(c_0_74,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk11_0,esk13_0)))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,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_72,c_0_17]),c_0_17])]) ).
cnf(c_0_76,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk11_0,esk13_0))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
~ ilf_type(esk14_0,relation_type(esk11_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET655+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:31:11 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 18.05/3.07 % Version: 3.5.1
% 18.05/3.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 18.05/3.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.05/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.05/3.07 % Starting new_bool_3 with 300s (1) cores
% 18.05/3.07 % Starting new_bool_1 with 300s (1) cores
% 18.05/3.07 % Starting sh5l with 300s (1) cores
% 18.05/3.07 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1065952 completed with status 0
% 18.05/3.07 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 18.05/3.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 18.05/3.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.05/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.05/3.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.05/3.07 % No SInE strategy applied
% 18.05/3.07 % Search class: FGHSF-FFMM21-SFFFFFNN
% 18.05/3.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 18.05/3.07 % Starting SubtermCWHack with 136s (1) cores
% 18.05/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 18.05/3.07 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 18.05/3.07 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 18.05/3.07 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 18.05/3.07 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 1065962 completed with status 0
% 18.05/3.07 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 18.05/3.07 % Preprocessing class: FSMSSMSSSSSNFFN.
% 18.05/3.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.05/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.05/3.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.05/3.07 % No SInE strategy applied
% 18.05/3.07 % Search class: FGHSF-FFMM21-SFFFFFNN
% 18.05/3.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 18.05/3.07 % Starting SubtermCWHack with 136s (1) cores
% 18.05/3.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 18.05/3.07 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 18.05/3.07 % Preprocessing time : 0.002 s
% 18.05/3.07 % Presaturation interreduction done
% 18.05/3.07
% 18.05/3.07 % Proof found!
% 18.05/3.07 % SZS status Theorem
% 18.05/3.07 % SZS output start CNFRefutation
% See solution above
% 18.05/3.07 % Parsed axioms : 20
% 18.05/3.07 % Removed by relevancy pruning/SinE : 0
% 18.05/3.07 % Initial clauses : 44
% 18.05/3.07 % Removed in clause preprocessing : 0
% 18.05/3.07 % Initial clauses in saturation : 44
% 18.05/3.07 % Processed clauses : 10672
% 18.05/3.07 % ...of these trivial : 428
% 18.05/3.07 % ...subsumed : 5935
% 18.05/3.07 % ...remaining for further processing : 4309
% 18.05/3.07 % Other redundant clauses eliminated : 0
% 18.05/3.07 % Clauses deleted for lack of memory : 0
% 18.05/3.07 % Backward-subsumed : 263
% 18.05/3.07 % Backward-rewritten : 36
% 18.05/3.07 % Generated clauses : 130371
% 18.05/3.07 % ...of the previous two non-redundant : 126635
% 18.05/3.07 % ...aggressively subsumed : 0
% 18.05/3.07 % Contextual simplify-reflections : 6
% 18.05/3.07 % Paramodulations : 130371
% 18.05/3.07 % Factorizations : 0
% 18.05/3.07 % NegExts : 0
% 18.05/3.07 % Equation resolutions : 0
% 18.05/3.07 % Disequality decompositions : 0
% 18.05/3.07 % Total rewrite steps : 4495
% 18.05/3.07 % ...of those cached : 2190
% 18.05/3.07 % Propositional unsat checks : 0
% 18.05/3.07 % Propositional check models : 0
% 18.05/3.07 % Propositional check unsatisfiable : 0
% 18.05/3.07 % Propositional clauses : 0
% 18.05/3.07 % Propositional clauses after purity: 0
% 18.05/3.07 % Propositional unsat core size : 0
% 18.05/3.07 % Propositional preprocessing time : 0.000
% 18.05/3.07 % Propositional encoding time : 0.000
% 18.05/3.07 % Propositional solver time : 0.000
% 18.05/3.07 % Success case prop preproc time : 0.000
% 18.05/3.07 % Success case prop encoding time : 0.000
% 18.05/3.07 % Success case prop solver time : 0.000
% 18.05/3.07 % Current number of processed clauses : 3979
% 18.05/3.07 % Positive orientable unit clauses : 745
% 18.05/3.07 % Positive unorientable unit clauses: 0
% 18.05/3.07 % Negative unit clauses : 7
% 18.05/3.07 % Non-unit-clauses : 3227
% 18.05/3.07 % Current number of unprocessed clauses: 115925
% 18.05/3.07 % ...number of literals in the above : 225009
% 18.05/3.07 % Current number of archived formulas : 0
% 18.05/3.07 % Current number of archived clauses : 330
% 18.05/3.07 % Clause-clause subsumption calls (NU) : 950539
% 18.05/3.07 % Rec. Clause-clause subsumption calls : 870567
% 18.05/3.07 % Non-unit clause-clause subsumptions : 5560
% 18.05/3.07 % Unit Clause-clause subsumption calls : 33575
% 18.05/3.07 % Rewrite failures with RHS unbound : 0
% 18.05/3.07 % BW rewrite match attempts : 14891
% 18.05/3.07 % BW rewrite match successes : 36
% 18.05/3.07 % Condensation attempts : 0
% 18.05/3.07 % Condensation successes : 0
% 18.05/3.07 % Termbank termtop insertions : 2473301
% 18.05/3.07 % Search garbage collected termcells : 948
% 18.05/3.07
% 18.05/3.07 % -------------------------------------------------
% 18.05/3.07 % User time : 2.421 s
% 18.05/3.07 % System time : 0.126 s
% 18.05/3.07 % Total time : 2.548 s
% 18.05/3.07 % Maximum resident set size: 3656 pages
% 18.05/3.07
% 18.05/3.07 % -------------------------------------------------
% 18.05/3.07 % User time : 12.212 s
% 18.05/3.07 % System time : 0.573 s
% 18.05/3.07 % Total time : 12.785 s
% 18.05/3.07 % Maximum resident set size: 4864 pages
% 18.05/3.07 % E exiting
%------------------------------------------------------------------------------