%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET667+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 : n011.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 05:08:16 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 10 unt; 0 def)
% Number of atoms : 231 ( 8 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 285 ( 116 ~; 114 |; 18 &)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 121 ( 7 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(p31,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(p5,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',p5) ).
fof(p7,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',p7) ).
fof(prove_relset_1_30,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ( subset(identity_relation_of(X3),X4)
=> ( subset(X3,domain(X1,X2,X4))
& subset(X3,range(X1,X2,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_30) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
<=> member(ordered_pair(X2,X2),identity_relation_of(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),X3)
=> ( member(X1,domain_of(X3))
& member(X2,range_of(X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p29,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',p29) ).
fof(p27,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',p27) ).
fof(c_0_10,plain,
! [X133,X134,X135] :
( ~ ilf_type(X133,set_type)
| ~ ilf_type(X134,set_type)
| ~ ilf_type(X135,subset_type(cross_product(X133,X134)))
| relation_like(X135) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p24])])]) ).
fof(c_0_11,plain,
! [X152] : ilf_type(X152,set_type),
inference(variable_rename,[status(thm)],[p31]) ).
fof(c_0_12,plain,
! [X86,X87,X88,X89] :
( ( ~ ilf_type(X88,subset_type(cross_product(X86,X87)))
| ilf_type(X88,relation_type(X86,X87))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( ~ ilf_type(X89,relation_type(X86,X87))
| ilf_type(X89,subset_type(cross_product(X86,X87)))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])]) ).
fof(c_0_13,plain,
! [X93,X94,X95] :
( ( ~ subset(X93,X94)
| ~ ilf_type(X95,set_type)
| ~ member(X95,X93)
| member(X95,X94)
| ~ ilf_type(X94,set_type)
| ~ ilf_type(X93,set_type) )
& ( ilf_type(esk2_2(X93,X94),set_type)
| subset(X93,X94)
| ~ ilf_type(X94,set_type)
| ~ ilf_type(X93,set_type) )
& ( member(esk2_2(X93,X94),X93)
| subset(X93,X94)
| ~ ilf_type(X94,set_type)
| ~ ilf_type(X93,set_type) )
& ( ~ member(esk2_2(X93,X94),X94)
| subset(X93,X94)
| ~ ilf_type(X94,set_type)
| ~ ilf_type(X93,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)],[p7])])])])]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ( subset(identity_relation_of(X3),X4)
=> ( subset(X3,domain(X1,X2,X4))
& subset(X3,range(X1,X2,X4)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_30]) ).
fof(c_0_15,plain,
! [X109] :
( ( relation_like(X109)
| ~ ilf_type(X109,binary_relation_type)
| ~ ilf_type(X109,set_type) )
& ( ilf_type(X109,set_type)
| ~ ilf_type(X109,binary_relation_type)
| ~ ilf_type(X109,set_type) )
& ( ~ relation_like(X109)
| ~ ilf_type(X109,set_type)
| ilf_type(X109,binary_relation_type)
| ~ ilf_type(X109,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
cnf(c_0_16,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,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_13]) ).
fof(c_0_20,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,relation_type(esk13_0,esk14_0))
& subset(identity_relation_of(esk15_0),esk16_0)
& ( ~ subset(esk15_0,domain(esk13_0,esk14_0,esk16_0))
| ~ subset(esk15_0,range(esk13_0,esk14_0,esk16_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_21,plain,
! [X80,X81] :
( ( ~ member(X81,X80)
| member(ordered_pair(X81,X81),identity_relation_of(X80))
| ~ ilf_type(X81,set_type)
| ~ ilf_type(X80,set_type) )
& ( ~ member(ordered_pair(X81,X81),identity_relation_of(X80))
| member(X81,X80)
| ~ ilf_type(X81,set_type)
| ~ ilf_type(X80,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_22,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( relation_like(X1)
| ~ 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_24,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_18,c_0_17]),c_0_17])]) ).
fof(c_0_25,plain,
! [X77,X78,X79] :
( ( member(X77,domain_of(X79))
| ~ member(ordered_pair(X77,X78),X79)
| ~ ilf_type(X79,binary_relation_type)
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,set_type) )
& ( member(X78,range_of(X79))
| ~ member(ordered_pair(X77,X78),X79)
| ~ ilf_type(X79,binary_relation_type)
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,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_26,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_19,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_27,negated_conjecture,
subset(identity_relation_of(esk15_0),esk16_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( member(ordered_pair(X1,X1),identity_relation_of(X2))
| ~ member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
ilf_type(esk16_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_32,plain,
! [X146,X147,X148] :
( ~ ilf_type(X146,set_type)
| ~ ilf_type(X147,set_type)
| ~ ilf_type(X148,relation_type(X146,X147))
| range(X146,X147,X148) = range_of(X148) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p29])])]) ).
cnf(c_0_33,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( member(X1,esk16_0)
| ~ member(X1,identity_relation_of(esk15_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( member(ordered_pair(X1,X1),identity_relation_of(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_17])]) ).
cnf(c_0_36,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_17])]) ).
cnf(c_0_37,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X140,X141,X142] :
( ~ ilf_type(X140,set_type)
| ~ ilf_type(X141,set_type)
| ~ ilf_type(X142,relation_type(X140,X141))
| domain(X140,X141,X142) = domain_of(X142) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
cnf(c_0_40,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_17]),c_0_17])]) ).
cnf(c_0_42,negated_conjecture,
( member(ordered_pair(X1,X1),esk16_0)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,negated_conjecture,
ilf_type(esk16_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
( member(X1,range_of(X2))
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_45,negated_conjecture,
( ~ subset(esk15_0,domain(esk13_0,esk14_0,esk16_0))
| ~ subset(esk15_0,range(esk13_0,esk14_0,esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_46,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_17]),c_0_17])]) ).
cnf(c_0_47,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_17]),c_0_17])]) ).
cnf(c_0_49,negated_conjecture,
( member(X1,domain_of(esk16_0))
| ~ member(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_50,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_51,plain,
( member(X1,range_of(X2))
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_17]),c_0_17])]) ).
cnf(c_0_52,negated_conjecture,
( ~ subset(esk15_0,domain(esk13_0,esk14_0,esk16_0))
| ~ subset(esk15_0,range_of(esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_31])]) ).
cnf(c_0_53,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_17]),c_0_17])]) ).
cnf(c_0_54,negated_conjecture,
( subset(X1,domain_of(esk16_0))
| ~ member(esk2_2(X1,domain_of(esk16_0)),esk15_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_17]),c_0_17])]) ).
cnf(c_0_56,negated_conjecture,
( member(X1,range_of(esk16_0))
| ~ member(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_42]),c_0_43])]) ).
cnf(c_0_57,negated_conjecture,
( ~ subset(esk15_0,domain_of(esk16_0))
| ~ subset(esk15_0,range_of(esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_31])]) ).
cnf(c_0_58,negated_conjecture,
subset(esk15_0,domain_of(esk16_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( subset(X1,range_of(esk16_0))
| ~ member(esk2_2(X1,range_of(esk16_0)),esk15_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
~ subset(esk15_0,range_of(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_55]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET667+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
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:30:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.371s
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