%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET674+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 : n015.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 43.80s 26.26s
% Output : CNFRefutation 44.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 107 ( 9 unt; 0 def)
% Number of atoms : 475 ( 42 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 648 ( 280 ~; 277 |; 34 &)
% ( 7 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-4 aty)
% Number of variables : 259 ( 17 sgn 96 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p7,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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p40,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p40) ).
fof(prove_relset_1_38,conjecture,
! [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',prove_relset_1_38) ).
fof(p5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,inverse2(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X2,X4),X3)
& member(X4,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p38,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',p38) ).
fof(p32,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',p32) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,image(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X2),X3)
& member(X4,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,range_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(p22,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/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(p36,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',p36) ).
fof(p34,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',p34) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(p29,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',p29) ).
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/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(p17,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',p17) ).
fof(c_0_16,plain,
! [X137,X138,X139,X140,X141] :
( ( member(X139,X137)
| ~ member(ordered_pair(X139,X140),X141)
| ~ ilf_type(X141,relation_type(X137,X138))
| ~ ilf_type(X140,set_type)
| ~ ilf_type(X139,set_type)
| ~ ilf_type(X138,set_type)
| ~ ilf_type(X137,set_type) )
& ( member(X140,X138)
| ~ member(ordered_pair(X139,X140),X141)
| ~ ilf_type(X141,relation_type(X137,X138))
| ~ ilf_type(X140,set_type)
| ~ ilf_type(X139,set_type)
| ~ ilf_type(X138,set_type)
| ~ ilf_type(X137,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_17,plain,
! [X227] : ilf_type(X227,set_type),
inference(variable_rename,[status(thm)],[p40]) ).
fof(c_0_18,negated_conjecture,
~ ! [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) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_38]) ).
fof(c_0_19,plain,
! [X129,X130,X131,X133] :
( ( ilf_type(esk4_3(X129,X130,X131),set_type)
| ~ member(X130,inverse2(X131,X129))
| ~ ilf_type(X131,binary_relation_type)
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) )
& ( member(ordered_pair(X130,esk4_3(X129,X130,X131)),X131)
| ~ member(X130,inverse2(X131,X129))
| ~ ilf_type(X131,binary_relation_type)
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) )
& ( member(esk4_3(X129,X130,X131),X129)
| ~ member(X130,inverse2(X131,X129))
| ~ ilf_type(X131,binary_relation_type)
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) )
& ( ~ ilf_type(X133,set_type)
| ~ member(ordered_pair(X130,X133),X131)
| ~ member(X133,X129)
| member(X130,inverse2(X131,X129))
| ~ ilf_type(X131,binary_relation_type)
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,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_20,plain,
! [X113,X114,X116] :
( ( ilf_type(esk1_2(X113,X114),set_type)
| ~ member(X113,domain_of(X114))
| ~ ilf_type(X114,binary_relation_type)
| ~ ilf_type(X113,set_type) )
& ( member(ordered_pair(X113,esk1_2(X113,X114)),X114)
| ~ member(X113,domain_of(X114))
| ~ ilf_type(X114,binary_relation_type)
| ~ ilf_type(X113,set_type) )
& ( ~ ilf_type(X116,set_type)
| ~ member(ordered_pair(X113,X116),X114)
| member(X113,domain_of(X114))
| ~ ilf_type(X114,binary_relation_type)
| ~ ilf_type(X113,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)],[p1])])])])]) ).
cnf(c_0_21,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_16]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,negated_conjecture,
( ilf_type(esk17_0,set_type)
& ilf_type(esk18_0,set_type)
& ilf_type(esk19_0,relation_type(esk17_0,esk18_0))
& ( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| inverse4(esk17_0,esk18_0,esk19_0,esk18_0) != domain(esk17_0,esk18_0,esk19_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_24,plain,
! [X219,X220,X221,X222] :
( ~ ilf_type(X219,set_type)
| ~ ilf_type(X220,set_type)
| ~ ilf_type(X221,relation_type(X219,X220))
| ~ ilf_type(X222,set_type)
| inverse4(X219,X220,X221,X222) = inverse2(X221,X222) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p38])])]) ).
fof(c_0_25,plain,
! [X199,X200,X201] :
( ~ ilf_type(X199,set_type)
| ~ ilf_type(X200,set_type)
| ~ ilf_type(X201,relation_type(X199,X200))
| domain(X199,X200,X201) = domain_of(X201) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])]) ).
cnf(c_0_26,plain,
( member(X2,inverse2(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ member(X1,X4)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,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_21,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
ilf_type(esk19_0,relation_type(esk17_0,esk18_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X124,X125,X126,X128] :
( ( ilf_type(esk3_3(X124,X125,X126),set_type)
| ~ member(X125,image(X126,X124))
| ~ ilf_type(X126,binary_relation_type)
| ~ ilf_type(X125,set_type)
| ~ ilf_type(X124,set_type) )
& ( member(ordered_pair(esk3_3(X124,X125,X126),X125),X126)
| ~ member(X125,image(X126,X124))
| ~ ilf_type(X126,binary_relation_type)
| ~ ilf_type(X125,set_type)
| ~ ilf_type(X124,set_type) )
& ( member(esk3_3(X124,X125,X126),X124)
| ~ member(X125,image(X126,X124))
| ~ ilf_type(X126,binary_relation_type)
| ~ ilf_type(X125,set_type)
| ~ ilf_type(X124,set_type) )
& ( ~ ilf_type(X128,set_type)
| ~ member(ordered_pair(X128,X125),X126)
| ~ member(X128,X124)
| member(X125,image(X126,X124))
| ~ ilf_type(X126,binary_relation_type)
| ~ ilf_type(X125,set_type)
| ~ ilf_type(X124,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)],[p4])])])])]) ).
fof(c_0_31,plain,
! [X117,X118,X120] :
( ( ilf_type(esk2_2(X117,X118),set_type)
| ~ member(X117,range_of(X118))
| ~ ilf_type(X118,binary_relation_type)
| ~ ilf_type(X117,set_type) )
& ( member(ordered_pair(esk2_2(X117,X118),X117),X118)
| ~ member(X117,range_of(X118))
| ~ ilf_type(X118,binary_relation_type)
| ~ ilf_type(X117,set_type) )
& ( ~ ilf_type(X120,set_type)
| ~ member(ordered_pair(X120,X117),X118)
| member(X117,range_of(X118))
| ~ ilf_type(X118,binary_relation_type)
| ~ ilf_type(X117,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)],[p2])])])])]) ).
cnf(c_0_32,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_16]) ).
cnf(c_0_33,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_24]) ).
cnf(c_0_34,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_25]) ).
fof(c_0_35,plain,
! [X171,X172,X173] :
( ( ~ subset(X171,X172)
| ~ ilf_type(X173,set_type)
| ~ member(X173,X171)
| member(X173,X172)
| ~ ilf_type(X172,set_type)
| ~ ilf_type(X171,set_type) )
& ( ilf_type(esk10_2(X171,X172),set_type)
| subset(X171,X172)
| ~ ilf_type(X172,set_type)
| ~ ilf_type(X171,set_type) )
& ( member(esk10_2(X171,X172),X171)
| subset(X171,X172)
| ~ ilf_type(X172,set_type)
| ~ ilf_type(X171,set_type) )
& ( ~ member(esk10_2(X171,X172),X172)
| subset(X171,X172)
| ~ ilf_type(X172,set_type)
| ~ ilf_type(X171,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)],[p22])])])])]) ).
cnf(c_0_36,plain,
( member(X1,inverse2(X2,X3))
| ~ member(ordered_pair(X1,X4),X2)
| ~ member(X4,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_37,plain,
( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_22])]) ).
cnf(c_0_38,negated_conjecture,
( member(X1,esk18_0)
| ~ member(ordered_pair(X2,X1),esk19_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
( member(X2,domain_of(X3))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_40,plain,
( member(ordered_pair(X1,esk4_3(X2,X1,X3)),X3)
| ~ member(X1,inverse2(X3,X2))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_41,plain,
( member(X2,image(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ member(X1,X4)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
( member(ordered_pair(esk2_2(X1,X2),X1),X2)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,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_32,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_44,negated_conjecture,
( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| inverse4(esk17_0,esk18_0,esk19_0,esk18_0) != domain(esk17_0,esk18_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_45,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_33,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_46,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_34,c_0_22]),c_0_22])]) ).
fof(c_0_47,plain,
! [X211,X212,X213,X214] :
( ~ ilf_type(X211,set_type)
| ~ ilf_type(X212,set_type)
| ~ ilf_type(X213,relation_type(X211,X212))
| ~ ilf_type(X214,set_type)
| image4(X211,X212,X213,X214) = image(X213,X214) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p36])])]) ).
fof(c_0_48,plain,
! [X205,X206,X207] :
( ~ ilf_type(X205,set_type)
| ~ ilf_type(X206,set_type)
| ~ ilf_type(X207,relation_type(X205,X206))
| range(X205,X206,X207) = range_of(X207) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p34])])]) ).
cnf(c_0_49,plain,
( subset(X1,X2)
| ~ member(esk10_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_50,plain,
( member(X1,inverse2(X2,X3))
| ~ member(esk1_2(X1,X2),X3)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_51,negated_conjecture,
( member(esk1_2(X1,esk19_0),esk18_0)
| ~ member(X1,domain_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_52,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_39,c_0_22]),c_0_22])]) ).
cnf(c_0_53,plain,
( member(ordered_pair(X1,esk4_3(X2,X1,X3)),X3)
| ~ member(X1,inverse2(X3,X2))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_22]),c_0_22])]) ).
cnf(c_0_54,plain,
( member(esk10_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_55,plain,
( member(X1,image(X2,X3))
| ~ member(ordered_pair(X4,X1),X2)
| ~ member(X4,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_56,plain,
( member(ordered_pair(esk2_2(X1,X2),X1),X2)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_22])]) ).
cnf(c_0_57,negated_conjecture,
( member(X1,esk17_0)
| ~ member(ordered_pair(X1,X2),esk19_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_58,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_59,plain,
( member(ordered_pair(esk3_3(X1,X2,X3),X2),X3)
| ~ member(X2,image(X3,X1))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_60,negated_conjecture,
( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| domain(esk17_0,esk18_0,esk19_0) != inverse2(esk19_0,esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_29])]) ).
cnf(c_0_61,negated_conjecture,
domain(esk17_0,esk18_0,esk19_0) = domain_of(esk19_0),
inference(spm,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_62,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_47]) ).
cnf(c_0_63,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_48]) ).
fof(c_0_64,plain,
! [X149,X150] :
( ( subset(X149,X150)
| X149 != X150
| ~ ilf_type(X150,set_type)
| ~ ilf_type(X149,set_type) )
& ( subset(X150,X149)
| X149 != X150
| ~ ilf_type(X150,set_type)
| ~ ilf_type(X149,set_type) )
& ( ~ subset(X149,X150)
| ~ subset(X150,X149)
| X149 = X150
| ~ ilf_type(X150,set_type)
| ~ ilf_type(X149,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])]) ).
cnf(c_0_65,plain,
( subset(X1,X2)
| ~ member(esk10_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_22]),c_0_22])]) ).
cnf(c_0_66,negated_conjecture,
( member(X1,inverse2(esk19_0,esk18_0))
| ~ member(X1,domain_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_67,plain,
( member(X1,domain_of(X2))
| ~ member(X1,inverse2(X2,X3))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_68,plain,
( subset(X1,X2)
| member(esk10_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_22]),c_0_22])]) ).
cnf(c_0_69,plain,
( member(X1,image(X2,X3))
| ~ member(esk2_2(X1,X2),X3)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_70,negated_conjecture,
( member(esk2_2(X1,esk19_0),esk17_0)
| ~ member(X1,range_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_71,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_58,c_0_22]),c_0_22])]) ).
cnf(c_0_72,plain,
( member(ordered_pair(esk3_3(X1,X2,X3),X2),X3)
| ~ member(X2,image(X3,X1))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_22]),c_0_22])]) ).
cnf(c_0_73,negated_conjecture,
( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| inverse2(esk19_0,esk18_0) != domain_of(esk19_0) ),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_74,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_62,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_75,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_63,c_0_22]),c_0_22])]) ).
cnf(c_0_76,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_77,negated_conjecture,
( subset(X1,inverse2(esk19_0,esk18_0))
| ~ member(esk10_2(X1,inverse2(esk19_0,esk18_0)),domain_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_78,plain,
( subset(inverse2(X1,X2),X3)
| member(esk10_2(inverse2(X1,X2),X3),domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
fof(c_0_79,plain,
! [X192,X193,X194] :
( ~ ilf_type(X192,set_type)
| ~ ilf_type(X193,set_type)
| ~ ilf_type(X194,subset_type(cross_product(X192,X193)))
| relation_like(X194) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p29])])]) ).
fof(c_0_80,plain,
! [X142,X143,X144,X145] :
( ( ~ ilf_type(X144,subset_type(cross_product(X142,X143)))
| ilf_type(X144,relation_type(X142,X143))
| ~ ilf_type(X143,set_type)
| ~ ilf_type(X142,set_type) )
& ( ~ ilf_type(X145,relation_type(X142,X143))
| ilf_type(X145,subset_type(cross_product(X142,X143)))
| ~ ilf_type(X143,set_type)
| ~ ilf_type(X142,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_81,negated_conjecture,
( member(X1,image(esk19_0,esk17_0))
| ~ member(X1,range_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_82,plain,
( member(X1,range_of(X2))
| ~ member(X1,image(X2,X3))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_83,negated_conjecture,
( range(esk17_0,esk18_0,esk19_0) != image(esk19_0,esk17_0)
| inverse2(esk19_0,esk18_0) != domain_of(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_29])]) ).
cnf(c_0_84,negated_conjecture,
range(esk17_0,esk18_0,esk19_0) = range_of(esk19_0),
inference(spm,[status(thm)],[c_0_75,c_0_29]) ).
cnf(c_0_85,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_22]),c_0_22])]) ).
cnf(c_0_86,negated_conjecture,
( subset(domain_of(esk19_0),inverse2(esk19_0,esk18_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_77,c_0_68]) ).
cnf(c_0_87,plain,
( subset(inverse2(X1,X2),domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_65,c_0_78]) ).
fof(c_0_88,plain,
! [X161] :
( ( relation_like(X161)
| ~ ilf_type(X161,binary_relation_type)
| ~ ilf_type(X161,set_type) )
& ( ilf_type(X161,set_type)
| ~ ilf_type(X161,binary_relation_type)
| ~ ilf_type(X161,set_type) )
& ( ~ relation_like(X161)
| ~ ilf_type(X161,set_type)
| ilf_type(X161,binary_relation_type)
| ~ ilf_type(X161,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])]) ).
cnf(c_0_89,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_79]) ).
cnf(c_0_90,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_80]) ).
cnf(c_0_91,negated_conjecture,
( subset(X1,image(esk19_0,esk17_0))
| ~ member(esk10_2(X1,image(esk19_0,esk17_0)),range_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_65,c_0_81]) ).
cnf(c_0_92,plain,
( subset(image(X1,X2),X3)
| member(esk10_2(image(X1,X2),X3),range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_82,c_0_68]) ).
cnf(c_0_93,negated_conjecture,
( image(esk19_0,esk17_0) != range_of(esk19_0)
| inverse2(esk19_0,esk18_0) != domain_of(esk19_0) ),
inference(rw,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_94,negated_conjecture,
( inverse2(esk19_0,esk18_0) = domain_of(esk19_0)
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_95,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_88]) ).
cnf(c_0_96,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_89,c_0_22]),c_0_22])]) ).
cnf(c_0_97,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_90,c_0_22]),c_0_22])]) ).
cnf(c_0_98,negated_conjecture,
( subset(range_of(esk19_0),image(esk19_0,esk17_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_91,c_0_68]) ).
cnf(c_0_99,plain,
( subset(image(X1,X2),range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_65,c_0_92]) ).
cnf(c_0_100,negated_conjecture,
( image(esk19_0,esk17_0) != range_of(esk19_0)
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_95]) ).
cnf(c_0_102,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
~ ilf_type(esk19_0,binary_relation_type),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_98]),c_0_99]),c_0_100]) ).
cnf(c_0_104,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_22])]) ).
cnf(c_0_105,negated_conjecture,
relation_like(esk19_0),
inference(spm,[status(thm)],[c_0_102,c_0_29]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET674+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n015.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 02:32:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 43.80/26.26 % Version : CSE_E---1.7
% 43.80/26.26 % Problem : theBenchmark.p
% 43.80/26.26 % SZS status Theorem for theBenchmark.p
% 43.80/26.26 % SZS output start CNFRefutation
% See solution above
% 44.00/26.44 % Total time : 19.406s
%------------------------------------------------------------------------------