%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET675+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 : n003.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 05:08:17 PM UTC 2026
% Result : Theorem 1.29s 1.71s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 9 unt; 0 def)
% Number of atoms : 194 ( 50 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 232 ( 98 ~; 88 |; 12 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 123 ( 5 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(p35,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p35) ).
fof(prove_relset_1_39,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( image4(X2,X1,X3,inverse4(X2,X1,X3,X1)) = range(X2,X1,X3)
& inverse4(X2,X1,X3,image4(X2,X1,X3,X2)) = domain(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_39) ).
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/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( image4(X1,X2,X3,X1) = range(X1,X2,X3)
& inverse4(X1,X2,X3,X2) = domain(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(p33,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> inverse4(X1,X2,X3,X4) = inverse2(X3,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(p31,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> image4(X1,X2,X3,X4) = image(X3,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(p12,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',p12) ).
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/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(p4,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',p4) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> inverse2(X1,range_of(X1)) = domain_of(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> image(X1,domain_of(X1)) = range_of(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(c_0_12,plain,
! [X153,X154,X155] :
( ~ ilf_type(X153,set_type)
| ~ ilf_type(X154,set_type)
| ~ ilf_type(X155,relation_type(X153,X154))
| range(X153,X154,X155) = range_of(X155) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p29])])]) ).
fof(c_0_13,plain,
! [X175] : ilf_type(X175,set_type),
inference(variable_rename,[status(thm)],[p35]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( image4(X2,X1,X3,inverse4(X2,X1,X3,X1)) = range(X2,X1,X3)
& inverse4(X2,X1,X3,image4(X2,X1,X3,X2)) = domain(X2,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_39]) ).
fof(c_0_15,plain,
! [X147,X148,X149] :
( ~ ilf_type(X147,set_type)
| ~ ilf_type(X148,set_type)
| ~ ilf_type(X149,relation_type(X147,X148))
| domain(X147,X148,X149) = domain_of(X149) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
cnf(c_0_16,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_12]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,negated_conjecture,
( ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,relation_type(esk12_0,esk11_0))
& ( image4(esk12_0,esk11_0,esk13_0,inverse4(esk12_0,esk11_0,esk13_0,esk11_0)) != range(esk12_0,esk11_0,esk13_0)
| inverse4(esk12_0,esk11_0,esk13_0,image4(esk12_0,esk11_0,esk13_0,esk12_0)) != domain(esk12_0,esk11_0,esk13_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_19,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_15]) ).
cnf(c_0_20,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_16,c_0_17]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
ilf_type(esk13_0,relation_type(esk12_0,esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,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_19,c_0_17]),c_0_17])]) ).
fof(c_0_23,plain,
! [X91,X92,X93] :
( ( image4(X91,X92,X93,X91) = range(X91,X92,X93)
| ~ ilf_type(X93,relation_type(X91,X92))
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( inverse4(X91,X92,X93,X92) = domain(X91,X92,X93)
| ~ ilf_type(X93,relation_type(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)],[p3])])])]) ).
cnf(c_0_24,negated_conjecture,
( image4(esk12_0,esk11_0,esk13_0,inverse4(esk12_0,esk11_0,esk13_0,esk11_0)) != range(esk12_0,esk11_0,esk13_0)
| inverse4(esk12_0,esk11_0,esk13_0,image4(esk12_0,esk11_0,esk13_0,esk12_0)) != domain(esk12_0,esk11_0,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
range(esk12_0,esk11_0,esk13_0) = range_of(esk13_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
domain(esk12_0,esk11_0,esk13_0) = domain_of(esk13_0),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,plain,
( image4(X1,X2,X3,X1) = range(X1,X2,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( image4(esk12_0,esk11_0,esk13_0,inverse4(esk12_0,esk11_0,esk13_0,esk11_0)) != range_of(esk13_0)
| inverse4(esk12_0,esk11_0,esk13_0,image4(esk12_0,esk11_0,esk13_0,esk12_0)) != domain_of(esk13_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( image4(X1,X2,X3,X1) = range(X1,X2,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_17]),c_0_17])]) ).
cnf(c_0_30,plain,
( inverse4(X1,X2,X3,X2) = domain(X1,X2,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X167,X168,X169,X170] :
( ~ ilf_type(X167,set_type)
| ~ ilf_type(X168,set_type)
| ~ ilf_type(X169,relation_type(X167,X168))
| ~ ilf_type(X170,set_type)
| inverse4(X167,X168,X169,X170) = inverse2(X169,X170) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])]) ).
cnf(c_0_32,negated_conjecture,
( image4(esk12_0,esk11_0,esk13_0,inverse4(esk12_0,esk11_0,esk13_0,esk11_0)) != range_of(esk13_0)
| inverse4(esk12_0,esk11_0,esk13_0,range_of(esk13_0)) != domain_of(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]),c_0_21])]) ).
cnf(c_0_33,plain,
( inverse4(X1,X2,X3,X2) = domain(X1,X2,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_17]),c_0_17])]) ).
cnf(c_0_34,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_35,plain,
! [X159,X160,X161,X162] :
( ~ ilf_type(X159,set_type)
| ~ ilf_type(X160,set_type)
| ~ ilf_type(X161,relation_type(X159,X160))
| ~ ilf_type(X162,set_type)
| image4(X159,X160,X161,X162) = image(X161,X162) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p31])])]) ).
cnf(c_0_36,negated_conjecture,
( image4(esk12_0,esk11_0,esk13_0,domain_of(esk13_0)) != range_of(esk13_0)
| inverse4(esk12_0,esk11_0,esk13_0,range_of(esk13_0)) != domain_of(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26]),c_0_21])]) ).
cnf(c_0_37,plain,
( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_38,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_39,plain,
! [X111] :
( ( relation_like(X111)
| ~ ilf_type(X111,binary_relation_type)
| ~ ilf_type(X111,set_type) )
& ( ilf_type(X111,set_type)
| ~ ilf_type(X111,binary_relation_type)
| ~ ilf_type(X111,set_type) )
& ( ~ relation_like(X111)
| ~ ilf_type(X111,set_type)
| ilf_type(X111,binary_relation_type)
| ~ ilf_type(X111,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])]) ).
fof(c_0_40,plain,
! [X138,X139,X140] :
( ~ ilf_type(X138,set_type)
| ~ ilf_type(X139,set_type)
| ~ ilf_type(X140,subset_type(cross_product(X138,X139)))
| relation_like(X140) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).
fof(c_0_41,plain,
! [X94,X95,X96,X97] :
( ( ~ ilf_type(X96,subset_type(cross_product(X94,X95)))
| ilf_type(X96,relation_type(X94,X95))
| ~ ilf_type(X95,set_type)
| ~ ilf_type(X94,set_type) )
& ( ~ ilf_type(X97,relation_type(X94,X95))
| ilf_type(X97,subset_type(cross_product(X94,X95)))
| ~ ilf_type(X95,set_type)
| ~ ilf_type(X94,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).
cnf(c_0_42,negated_conjecture,
( image4(esk12_0,esk11_0,esk13_0,domain_of(esk13_0)) != range_of(esk13_0)
| inverse2(esk13_0,range_of(esk13_0)) != domain_of(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_21])]) ).
cnf(c_0_43,plain,
( image4(X1,X2,X3,X4) = image(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_17]),c_0_17]),c_0_17])]) ).
fof(c_0_44,plain,
! [X90] :
( ~ ilf_type(X90,binary_relation_type)
| inverse2(X90,range_of(X90)) = domain_of(X90) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])]) ).
fof(c_0_45,plain,
! [X89] :
( ~ ilf_type(X89,binary_relation_type)
| image(X89,domain_of(X89)) = range_of(X89) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_46,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_39]) ).
cnf(c_0_47,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_40]) ).
cnf(c_0_48,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_41]) ).
cnf(c_0_49,negated_conjecture,
( image(esk13_0,domain_of(esk13_0)) != range_of(esk13_0)
| inverse2(esk13_0,range_of(esk13_0)) != domain_of(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_21])]) ).
cnf(c_0_50,plain,
( inverse2(X1,range_of(X1)) = domain_of(X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( image(X1,domain_of(X1)) = range_of(X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_46]) ).
cnf(c_0_53,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_47,c_0_17]),c_0_17])]) ).
cnf(c_0_54,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_48,c_0_17]),c_0_17])]) ).
cnf(c_0_55,negated_conjecture,
~ ilf_type(esk13_0,binary_relation_type),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_56,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_17])]) ).
cnf(c_0_57,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
~ relation_like(esk13_0),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_21]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET675+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
% 0.14/0.31 % Computer : n003.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 02:31:41 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.32 % 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 : 1.371s
%------------------------------------------------------------------------------