%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET663+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 1.71s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 128 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 53 |; 12 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(p33,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(prove_relset_1_26,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( ilf_type(X3,relation_type(empty_set,X2))
=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_26) ).
fof(p28,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/sandbox2/benchmark/theBenchmark.p',p28) ).
fof(p6,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/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X1,empty_set)
=> X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
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/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( ( domain_of(X1) = empty_set
| range_of(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(c_0_8,plain,
! [X77,X78,X79] :
( ( subset(domain_of(X79),X77)
| ~ ilf_type(X79,relation_type(X77,X78))
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X77,set_type) )
& ( subset(range_of(X79),X78)
| ~ ilf_type(X79,relation_type(X77,X78))
| ~ 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)],[p3])])])]) ).
fof(c_0_9,plain,
! [X149] : ilf_type(X149,set_type),
inference(variable_rename,[status(thm)],[p33]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( ilf_type(X3,relation_type(empty_set,X2))
=> X3 = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_26]) ).
fof(c_0_11,plain,
! [X134,X135,X136] :
( ~ ilf_type(X134,set_type)
| ~ ilf_type(X135,set_type)
| ~ ilf_type(X136,subset_type(cross_product(X134,X135)))
| relation_like(X136) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p28])])]) ).
fof(c_0_12,plain,
! [X81,X82,X83,X84] :
( ( ~ ilf_type(X83,subset_type(cross_product(X81,X82)))
| ilf_type(X83,relation_type(X81,X82))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( ~ ilf_type(X84,relation_type(X81,X82))
| ilf_type(X84,subset_type(cross_product(X81,X82)))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
fof(c_0_13,plain,
! [X75] :
( ~ ilf_type(X75,set_type)
| ~ subset(X75,empty_set)
| X75 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_14,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk13_0,esk14_0))
& ilf_type(esk15_0,relation_type(empty_set,esk14_0))
& esk15_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X100] :
( ( relation_like(X100)
| ~ ilf_type(X100,binary_relation_type)
| ~ ilf_type(X100,set_type) )
& ( ilf_type(X100,set_type)
| ~ ilf_type(X100,binary_relation_type)
| ~ ilf_type(X100,set_type) )
& ( ~ relation_like(X100)
| ~ ilf_type(X100,set_type)
| ilf_type(X100,binary_relation_type)
| ~ ilf_type(X100,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
cnf(c_0_18,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_11]) ).
cnf(c_0_19,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_20,plain,
( X1 = empty_set
| ~ ilf_type(X1,set_type)
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
ilf_type(esk15_0,relation_type(empty_set,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,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_18,c_0_15]),c_0_15])]) ).
cnf(c_0_25,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_19,c_0_15]),c_0_15])]) ).
fof(c_0_26,plain,
! [X76] :
( ( domain_of(X76) != empty_set
| X76 = empty_set
| ~ ilf_type(X76,binary_relation_type) )
& ( range_of(X76) != empty_set
| X76 = empty_set
| ~ ilf_type(X76,binary_relation_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
cnf(c_0_27,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_15])]) ).
cnf(c_0_28,negated_conjecture,
subset(domain_of(esk15_0),empty_set),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
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_23]) ).
cnf(c_0_30,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,plain,
( X1 = empty_set
| domain_of(X1) != empty_set
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
domain_of(esk15_0) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
esk15_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15])]) ).
cnf(c_0_36,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
~ ilf_type(esk15_0,binary_relation_type),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET663+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n008.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
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:30:59 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.29/1.71 % Version : CSE_E---1.7
% 1.29/1.71 % Problem : theBenchmark.p
% 1.29/1.71 % SZS status Theorem for theBenchmark.p
% 1.29/1.71 % SZS output start CNFRefutation
% See solution above
% 1.29/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------