%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET641+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:13 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 234 ( 89 ~; 90 |; 18 &)
% ( 7 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 2 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p14,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',p14) ).
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/sandbox/benchmark/theBenchmark.p',p5) ).
fof(p18,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
fof(prove_relset_1_3,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( subset(X1,cross_product(X2,X3))
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_3) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
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/sandbox/benchmark/theBenchmark.p',p10) ).
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/sandbox/benchmark/theBenchmark.p',p7) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(c_0_8,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
fof(c_0_9,plain,
! [X68,X69,X70] :
( ( ~ subset(X68,X69)
| ~ ilf_type(X70,set_type)
| ~ member(X70,X68)
| member(X70,X69)
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) )
& ( ilf_type(esk4_2(X68,X69),set_type)
| subset(X68,X69)
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) )
& ( member(esk4_2(X68,X69),X68)
| subset(X68,X69)
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) )
& ( ~ member(esk4_2(X68,X69),X69)
| subset(X68,X69)
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])]) ).
fof(c_0_10,plain,
! [X102] : ilf_type(X102,set_type),
inference(variable_rename,[status(thm)],[p18]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( subset(X1,cross_product(X2,X3))
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_3]) ).
fof(c_0_12,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p12]) ).
fof(c_0_13,plain,
! [X88,X89] :
( ( ~ empty(X88)
| ~ ilf_type(X89,set_type)
| ~ member(X89,X88)
| ~ ilf_type(X88,set_type) )
& ( ilf_type(esk8_1(X88),set_type)
| empty(X88)
| ~ ilf_type(X88,set_type) )
& ( member(esk8_1(X88),X88)
| empty(X88)
| ~ ilf_type(X88,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_14,plain,
! [X79,X80,X81] :
( ( ~ member(X79,power_set(X80))
| ~ ilf_type(X81,set_type)
| ~ member(X81,X79)
| member(X81,X80)
| ~ ilf_type(X80,set_type)
| ~ ilf_type(X79,set_type) )
& ( ilf_type(esk6_2(X79,X80),set_type)
| member(X79,power_set(X80))
| ~ ilf_type(X80,set_type)
| ~ ilf_type(X79,set_type) )
& ( member(esk6_2(X79,X80),X79)
| member(X79,power_set(X80))
| ~ ilf_type(X80,set_type)
| ~ ilf_type(X79,set_type) )
& ( ~ member(esk6_2(X79,X80),X80)
| member(X79,power_set(X80))
| ~ ilf_type(X80,set_type)
| ~ ilf_type(X79,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])])]) ).
cnf(c_0_15,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& subset(esk12_0,cross_product(esk13_0,esk14_0))
& ~ ilf_type(esk12_0,relation_type(esk13_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_18,plain,
! [X74,X75] :
( ( ~ ilf_type(X75,subset_type(X74))
| ilf_type(X75,member_type(power_set(X74)))
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type) )
& ( ~ ilf_type(X75,member_type(power_set(X74)))
| ilf_type(X75,subset_type(X74))
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
fof(c_0_19,plain,
! [X84,X85] :
( ( ~ ilf_type(X84,member_type(X85))
| member(X84,X85)
| empty(X85)
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) )
& ( ~ member(X84,X85)
| ilf_type(X84,member_type(X85))
| empty(X85)
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_20,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| ~ subset(X3,X2)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_23,negated_conjecture,
subset(esk12_0,cross_product(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_16]),c_0_16])]) ).
cnf(c_0_27,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_16]),c_0_16])]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,cross_product(esk13_0,esk14_0))
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_30,plain,
! [X52,X53,X54,X55] :
( ( ~ ilf_type(X54,subset_type(cross_product(X52,X53)))
| ilf_type(X54,relation_type(X52,X53))
| ~ ilf_type(X53,set_type)
| ~ ilf_type(X52,set_type) )
& ( ~ ilf_type(X55,relation_type(X52,X53))
| ilf_type(X55,subset_type(cross_product(X52,X53)))
| ~ ilf_type(X53,set_type)
| ~ ilf_type(X52,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_31,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_16]),c_0_16])]) ).
cnf(c_0_32,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_16]),c_0_16])]),c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( member(X1,power_set(cross_product(esk13_0,esk14_0)))
| ~ member(esk6_2(X1,cross_product(esk13_0,esk14_0)),esk12_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_16]),c_0_16])]) ).
cnf(c_0_35,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
member(esk12_0,power_set(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,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_16]),c_0_16])]) ).
cnf(c_0_39,negated_conjecture,
ilf_type(esk12_0,subset_type(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ ilf_type(esk12_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET641+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:30:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------