%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET650+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 : n013.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 05:08:14 PM UTC 2026
% Result : Theorem 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 8 unt; 0 def)
% Number of atoms : 230 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 300 ( 123 ~; 124 |; 21 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 9 sgn 50 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,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)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(prove_relset_1_12,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_12) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,range_of(X1))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(p10,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',p10) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,domain_of(X1))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(p8,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',p8) ).
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(p23,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',p23) ).
fof(c_0_9,plain,
! [X76,X77,X78,X79,X80] :
( ( member(X78,X76)
| ~ member(ordered_pair(X78,X79),X80)
| ~ ilf_type(X80,relation_type(X76,X77))
| ~ ilf_type(X79,set_type)
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,set_type)
| ~ ilf_type(X76,set_type) )
& ( member(X79,X77)
| ~ member(ordered_pair(X78,X79),X80)
| ~ ilf_type(X80,relation_type(X76,X77))
| ~ ilf_type(X79,set_type)
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,set_type)
| ~ ilf_type(X76,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
fof(c_0_10,plain,
! [X136] : ilf_type(X136,set_type),
inference(variable_rename,[status(thm)],[p26]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_12]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ ilf_type(X4,relation_type(X5,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,negated_conjecture,
( ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,set_type)
& ilf_type(esk17_0,relation_type(esk15_0,esk16_0))
& ( ~ subset(domain_of(esk17_0),esk15_0)
| ~ subset(range_of(esk17_0),esk16_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_15,plain,
! [X86,X87,X89] :
( ( ilf_type(esk4_2(X86,X87),set_type)
| ~ member(X87,range_of(X86))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,binary_relation_type) )
& ( member(ordered_pair(esk4_2(X86,X87),X87),X86)
| ~ member(X87,range_of(X86))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,binary_relation_type) )
& ( ~ ilf_type(X89,set_type)
| ~ member(ordered_pair(X89,X87),X86)
| member(X87,range_of(X86))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,binary_relation_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])]) ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ ilf_type(X4,relation_type(X5,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]),c_0_13]),c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
ilf_type(esk17_0,relation_type(esk15_0,esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( member(ordered_pair(esk4_2(X1,X2),X2),X1)
| ~ member(X2,range_of(X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X98,X99,X100] :
( ( ~ subset(X98,X99)
| ~ ilf_type(X100,set_type)
| ~ member(X100,X98)
| member(X100,X99)
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type) )
& ( ilf_type(esk6_2(X98,X99),set_type)
| subset(X98,X99)
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type) )
& ( member(esk6_2(X98,X99),X98)
| subset(X98,X99)
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type) )
& ( ~ member(esk6_2(X98,X99),X99)
| subset(X98,X99)
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,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_20,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X4,relation_type(X2,X5))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_21,plain,
! [X81,X82,X84] :
( ( ilf_type(esk3_2(X81,X82),set_type)
| ~ member(X82,domain_of(X81))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,binary_relation_type) )
& ( member(ordered_pair(X82,esk3_2(X81,X82)),X81)
| ~ member(X82,domain_of(X81))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,binary_relation_type) )
& ( ~ ilf_type(X84,set_type)
| ~ member(ordered_pair(X82,X84),X81)
| member(X82,domain_of(X81))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,binary_relation_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])])]) ).
cnf(c_0_22,negated_conjecture,
( member(X1,esk16_0)
| ~ member(ordered_pair(X2,X1),esk17_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( member(ordered_pair(esk4_2(X1,X2),X2),X1)
| ~ member(X2,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_13])]) ).
cnf(c_0_24,plain,
( member(esk6_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X4,relation_type(X2,X5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_13]),c_0_13]),c_0_13]),c_0_13])]) ).
cnf(c_0_26,plain,
( member(ordered_pair(X1,esk3_2(X2,X1)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,esk16_0)
| ~ member(X1,range_of(esk17_0))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_13]),c_0_13])]) ).
fof(c_0_30,plain,
! [X91,X92,X93,X94] :
( ( ~ ilf_type(X93,subset_type(cross_product(X91,X92)))
| ilf_type(X93,relation_type(X91,X92))
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ~ ilf_type(X94,relation_type(X91,X92))
| ilf_type(X94,subset_type(cross_product(X91,X92)))
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p8])])])]) ).
cnf(c_0_31,negated_conjecture,
( member(X1,esk15_0)
| ~ member(ordered_pair(X1,X2),esk17_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_32,plain,
( member(ordered_pair(X1,esk3_2(X2,X1)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_13])]) ).
cnf(c_0_33,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_13]),c_0_13])]) ).
cnf(c_0_34,negated_conjecture,
( subset(range_of(esk17_0),X1)
| member(esk6_2(range_of(esk17_0),X1),esk16_0)
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_35,plain,
! [X106] :
( ( relation_like(X106)
| ~ ilf_type(X106,binary_relation_type)
| ~ ilf_type(X106,set_type) )
& ( ilf_type(X106,set_type)
| ~ ilf_type(X106,binary_relation_type)
| ~ ilf_type(X106,set_type) )
& ( ~ relation_like(X106)
| ~ ilf_type(X106,set_type)
| ilf_type(X106,binary_relation_type)
| ~ ilf_type(X106,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
fof(c_0_36,plain,
! [X129,X130,X131] :
( ~ ilf_type(X129,set_type)
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X131,subset_type(cross_product(X129,X130)))
| relation_like(X131) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).
cnf(c_0_37,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_30]) ).
cnf(c_0_38,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,domain_of(esk17_0))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( ~ subset(domain_of(esk17_0),esk15_0)
| ~ subset(range_of(esk17_0),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,negated_conjecture,
( subset(range_of(esk17_0),esk16_0)
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,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_35]) ).
cnf(c_0_42,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_36]) ).
cnf(c_0_43,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_37,c_0_13]),c_0_13])]) ).
cnf(c_0_44,negated_conjecture,
( subset(domain_of(esk17_0),X1)
| member(esk6_2(domain_of(esk17_0),X1),esk15_0)
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_45,negated_conjecture,
( ~ subset(domain_of(esk17_0),esk15_0)
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_41]) ).
cnf(c_0_47,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_42,c_0_13]),c_0_13])]) ).
cnf(c_0_48,negated_conjecture,
ilf_type(esk17_0,subset_type(cross_product(esk15_0,esk16_0))),
inference(spm,[status(thm)],[c_0_43,c_0_17]) ).
cnf(c_0_49,negated_conjecture,
~ ilf_type(esk17_0,binary_relation_type),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_45]) ).
cnf(c_0_50,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_13])]) ).
cnf(c_0_51,negated_conjecture,
relation_like(esk17_0),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET650+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
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % 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 02:31:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------