%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET657+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 : n016.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 05:08:15 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 15 unt; 0 def)
% Number of atoms : 316 ( 13 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 385 ( 154 ~; 155 |; 22 &)
% ( 6 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 171 ( 6 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(p37,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p37) ).
fof(p16,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
fof(p35,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',p35) ).
fof(prove_relset_1_19,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> subset(field_of(X3),union(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_19) ).
fof(p33,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',p33) ).
fof(p21,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(p36,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
file('/export/starexec/sandbox/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))
=> ilf_type(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
fof(p9,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',p9) ).
fof(p1,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)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(union(X1,X3),union(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p27,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',p27) ).
fof(p7,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',p7) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> field_of(X1) = union(domain_of(X1),range_of(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p14,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',p14) ).
fof(c_0_16,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_17,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p22]) ).
fof(c_0_18,plain,
! [X134,X135] :
( ( ~ ilf_type(X134,member_type(X135))
| member(X134,X135)
| empty(X135)
| ~ ilf_type(X135,set_type)
| ~ ilf_type(X134,set_type) )
& ( ~ member(X134,X135)
| ilf_type(X134,member_type(X135))
| empty(X135)
| ~ ilf_type(X135,set_type)
| ~ ilf_type(X134,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_19,plain,
! [X178] : ilf_type(X178,set_type),
inference(variable_rename,[status(thm)],[p37]) ).
fof(c_0_20,plain,
! [X121,X122] :
( ( ~ ilf_type(X122,subset_type(X121))
| ilf_type(X122,member_type(power_set(X121)))
| ~ ilf_type(X122,set_type)
| ~ ilf_type(X121,set_type) )
& ( ~ ilf_type(X122,member_type(power_set(X121)))
| ilf_type(X122,subset_type(X121))
| ~ ilf_type(X122,set_type)
| ~ ilf_type(X121,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p16])])])]) ).
fof(c_0_21,plain,
! [X133] :
( ( ~ empty(power_set(X133))
| ~ ilf_type(X133,set_type) )
& ( ilf_type(power_set(X133),set_type)
| ~ ilf_type(X133,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_22,plain,
! [X172,X173,X174] :
( ~ ilf_type(X172,set_type)
| ~ ilf_type(X173,set_type)
| ~ ilf_type(X174,relation_type(X172,X173))
| range(X172,X173,X174) = range_of(X174) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p35])])]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> subset(field_of(X3),union(X1,X2)) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_19]) ).
fof(c_0_24,plain,
! [X166,X167,X168] :
( ~ ilf_type(X166,set_type)
| ~ ilf_type(X167,set_type)
| ~ ilf_type(X168,relation_type(X166,X167))
| domain(X166,X167,X168) = domain_of(X168) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])]) ).
fof(c_0_25,plain,
! [X129,X130,X131] :
( ( ~ member(X129,power_set(X130))
| ~ ilf_type(X131,set_type)
| ~ member(X131,X129)
| member(X131,X130)
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) )
& ( ilf_type(esk5_2(X129,X130),set_type)
| member(X129,power_set(X130))
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) )
& ( member(esk5_2(X129,X130),X129)
| member(X129,power_set(X130))
| ~ ilf_type(X130,set_type)
| ~ ilf_type(X129,set_type) )
& ( ~ member(esk5_2(X129,X130),X130)
| member(X129,power_set(X130))
| ~ 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)],[p21])])])])]) ).
cnf(c_0_26,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_30,plain,
! [X175,X176,X177] :
( ~ ilf_type(X175,set_type)
| ~ ilf_type(X176,set_type)
| ~ ilf_type(X177,relation_type(X175,X176))
| ilf_type(range(X175,X176,X177),subset_type(X176)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p36])])]) ).
cnf(c_0_31,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_22]) ).
fof(c_0_32,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,relation_type(esk12_0,esk13_0))
& ~ subset(field_of(esk14_0),union(esk12_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_33,plain,
! [X169,X170,X171] :
( ~ ilf_type(X169,set_type)
| ~ ilf_type(X170,set_type)
| ~ ilf_type(X171,relation_type(X169,X170))
| ilf_type(domain(X169,X170,X171),subset_type(X169)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p34])])]) ).
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_24]) ).
cnf(c_0_35,plain,
( member(X3,X2)
| ~ member(X1,power_set(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_25]) ).
cnf(c_0_36,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27])]) ).
cnf(c_0_37,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_27]),c_0_27])]) ).
cnf(c_0_38,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_27])]) ).
cnf(c_0_39,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,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_31,c_0_27]),c_0_27])]) ).
cnf(c_0_41,negated_conjecture,
ilf_type(esk14_0,relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,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_27]),c_0_27])]) ).
cnf(c_0_44,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_27]),c_0_27]),c_0_27])]) ).
cnf(c_0_45,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_46,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_27]),c_0_27])]) ).
cnf(c_0_47,negated_conjecture,
range(esk12_0,esk13_0,esk14_0) = range_of(esk14_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_48,plain,
! [X109,X110,X111] :
( ( ~ subset(X109,X110)
| ~ ilf_type(X111,set_type)
| ~ member(X111,X109)
| member(X111,X110)
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,set_type) )
& ( ilf_type(esk2_2(X109,X110),set_type)
| subset(X109,X110)
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,set_type) )
& ( member(esk2_2(X109,X110),X109)
| subset(X109,X110)
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,set_type) )
& ( ~ member(esk2_2(X109,X110),X110)
| subset(X109,X110)
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,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)],[p9])])])])]) ).
cnf(c_0_49,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_27]),c_0_27])]) ).
cnf(c_0_50,negated_conjecture,
domain(esk12_0,esk13_0,esk14_0) = domain_of(esk14_0),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
fof(c_0_51,plain,
! [X90,X91,X92,X93] :
( ~ ilf_type(X90,set_type)
| ~ ilf_type(X91,set_type)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X93,set_type)
| ~ subset(X90,X91)
| ~ subset(X92,X93)
| subset(union(X90,X92),union(X91,X93)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_52,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
ilf_type(range_of(esk14_0),subset_type(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_41])]) ).
cnf(c_0_54,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_48]) ).
cnf(c_0_55,negated_conjecture,
ilf_type(domain_of(esk14_0),subset_type(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_41])]) ).
fof(c_0_56,plain,
! [X149,X150,X151] :
( ~ ilf_type(X149,set_type)
| ~ ilf_type(X150,set_type)
| ~ ilf_type(X151,subset_type(cross_product(X149,X150)))
| relation_like(X151) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
fof(c_0_57,plain,
! [X102,X103,X104,X105] :
( ( ~ ilf_type(X104,subset_type(cross_product(X102,X103)))
| ilf_type(X104,relation_type(X102,X103))
| ~ ilf_type(X103,set_type)
| ~ ilf_type(X102,set_type) )
& ( ~ ilf_type(X105,relation_type(X102,X103))
| ilf_type(X105,subset_type(cross_product(X102,X103)))
| ~ ilf_type(X103,set_type)
| ~ ilf_type(X102,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
cnf(c_0_58,plain,
( subset(union(X1,X3),union(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_59,plain,
! [X94] :
( ~ ilf_type(X94,binary_relation_type)
| field_of(X94) = union(domain_of(X94),range_of(X94)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])]) ).
cnf(c_0_60,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_48]) ).
cnf(c_0_61,negated_conjecture,
( member(X1,esk13_0)
| ~ member(X1,range_of(esk14_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_27]),c_0_27])]) ).
cnf(c_0_63,negated_conjecture,
( member(X1,esk12_0)
| ~ member(X1,domain_of(esk14_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
fof(c_0_64,plain,
! [X119] :
( ( relation_like(X119)
| ~ ilf_type(X119,binary_relation_type)
| ~ ilf_type(X119,set_type) )
& ( ilf_type(X119,set_type)
| ~ ilf_type(X119,binary_relation_type)
| ~ ilf_type(X119,set_type) )
& ( ~ relation_like(X119)
| ~ ilf_type(X119,set_type)
| ilf_type(X119,binary_relation_type)
| ~ ilf_type(X119,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p14])])]) ).
cnf(c_0_65,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_56]) ).
cnf(c_0_66,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_57]) ).
cnf(c_0_67,plain,
( subset(union(X1,X2),union(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_27]),c_0_27]),c_0_27]),c_0_27])]) ).
cnf(c_0_68,plain,
( field_of(X1) = union(domain_of(X1),range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_27]),c_0_27])]) ).
cnf(c_0_70,negated_conjecture,
( member(esk2_2(range_of(esk14_0),X1),esk13_0)
| subset(range_of(esk14_0),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( member(esk2_2(domain_of(esk14_0),X1),esk12_0)
| subset(domain_of(esk14_0),X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_72,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_64]) ).
cnf(c_0_73,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_65,c_0_27]),c_0_27])]) ).
cnf(c_0_74,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_66,c_0_27]),c_0_27])]) ).
cnf(c_0_75,negated_conjecture,
~ subset(field_of(esk14_0),union(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_76,plain,
( subset(field_of(X1),union(X2,X3))
| ~ subset(range_of(X1),X3)
| ~ subset(domain_of(X1),X2)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
subset(range_of(esk14_0),esk13_0),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
subset(domain_of(esk14_0),esk12_0),
inference(spm,[status(thm)],[c_0_69,c_0_71]) ).
cnf(c_0_79,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_72]) ).
cnf(c_0_80,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
~ ilf_type(esk14_0,binary_relation_type),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_82,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_27])]) ).
cnf(c_0_83,negated_conjecture,
relation_like(esk14_0),
inference(spm,[status(thm)],[c_0_80,c_0_41]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET657+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 : n016.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 02:31:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.368s
%------------------------------------------------------------------------------