%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET684+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 : n010.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 05:08:19 PM UTC 2026
% Result : Theorem 1.41s 1.76s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 114 ( 18 unt; 0 def)
% Number of atoms : 485 ( 4 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 641 ( 270 ~; 261 |; 47 &)
% ( 10 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-5 aty)
% Number of variables : 254 ( 17 sgn 87 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p7,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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(p29,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(p17,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/sandbox2/benchmark/theBenchmark.p',p17) ).
fof(p9,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(p22,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/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(p5,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',p5) ).
fof(p26,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',p26) ).
fof(prove_relset_1_51,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ( ~ empty(X3)
& ilf_type(X3,set_type) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( ilf_type(X8,member_type(X2))
& member(ordered_pair(X6,X8),X4)
& member(ordered_pair(X8,X7),X5) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_51) ).
fof(p15,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',p15) ).
fof(p2,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',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ! [X4] :
( ilf_type(X4,binary_relation_type)
=> ( member(ordered_pair(X1,X2),compose(X3,X4))
<=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X1,X5),X3)
& member(ordered_pair(X5,X2),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> compose5(X1,X2,X3,X4,X5) = compose(X4,X5) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(c_0_13,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)],[p7]) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_15,plain,
! [X116,X117] :
( ( ~ ilf_type(X116,member_type(X117))
| member(X116,X117)
| empty(X117)
| ~ ilf_type(X117,set_type)
| ~ ilf_type(X116,set_type) )
& ( ~ member(X116,X117)
| ilf_type(X116,member_type(X117))
| empty(X117)
| ~ ilf_type(X117,set_type)
| ~ ilf_type(X116,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_16,plain,
! [X171] : ilf_type(X171,set_type),
inference(variable_rename,[status(thm)],[p29]) ).
fof(c_0_17,plain,
! [X134,X135] :
( ( ~ ilf_type(X135,subset_type(X134))
| ilf_type(X135,member_type(power_set(X134)))
| ~ ilf_type(X135,set_type)
| ~ ilf_type(X134,set_type) )
& ( ~ ilf_type(X135,member_type(power_set(X134)))
| ilf_type(X135,subset_type(X134))
| ~ 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)],[p17])])])]) ).
fof(c_0_18,plain,
! [X149] :
( ( ~ empty(power_set(X149))
| ~ ilf_type(X149,set_type) )
& ( ilf_type(power_set(X149),set_type)
| ~ ilf_type(X149,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p9]) ).
fof(c_0_20,plain,
! [X145,X146,X147] :
( ( ~ member(X145,power_set(X146))
| ~ ilf_type(X147,set_type)
| ~ member(X147,X145)
| member(X147,X146)
| ~ ilf_type(X146,set_type)
| ~ ilf_type(X145,set_type) )
& ( ilf_type(esk8_2(X145,X146),set_type)
| member(X145,power_set(X146))
| ~ ilf_type(X146,set_type)
| ~ ilf_type(X145,set_type) )
& ( member(esk8_2(X145,X146),X145)
| member(X145,power_set(X146))
| ~ ilf_type(X146,set_type)
| ~ ilf_type(X145,set_type) )
& ( ~ member(esk8_2(X145,X146),X146)
| member(X145,power_set(X146))
| ~ ilf_type(X146,set_type)
| ~ ilf_type(X145,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_21,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_15]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X120,X121] :
( ( ~ empty(X120)
| ~ ilf_type(X121,set_type)
| ~ member(X121,X120)
| ~ ilf_type(X120,set_type) )
& ( ilf_type(esk4_1(X120),set_type)
| empty(X120)
| ~ ilf_type(X120,set_type) )
& ( member(esk4_1(X120),X120)
| empty(X120)
| ~ ilf_type(X120,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)],[c_0_19])])])])]) ).
cnf(c_0_26,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_20]) ).
cnf(c_0_27,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_21,c_0_22]),c_0_22])]) ).
cnf(c_0_28,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_23,c_0_22]),c_0_22])]) ).
cnf(c_0_29,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22])]) ).
fof(c_0_30,plain,
! [X109,X110,X111,X112] :
( ( ~ ilf_type(X111,subset_type(cross_product(X109,X110)))
| ilf_type(X111,relation_type(X109,X110))
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,set_type) )
& ( ~ ilf_type(X112,relation_type(X109,X110))
| ilf_type(X112,subset_type(cross_product(X109,X110)))
| ~ ilf_type(X110,set_type)
| ~ ilf_type(X109,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])]) ).
cnf(c_0_31,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X158,X159,X160] :
( ~ ilf_type(X158,set_type)
| ~ ilf_type(X159,set_type)
| ~ ilf_type(X160,subset_type(cross_product(X158,X159)))
| relation_like(X160) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])]) ).
cnf(c_0_33,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_26,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_34,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,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]) ).
fof(c_0_36,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ( ~ empty(X3)
& ilf_type(X3,set_type) )
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,relation_type(X2,X3))
=> ! [X6] :
( ilf_type(X6,member_type(X1))
=> ! [X7] :
( ilf_type(X7,member_type(X3))
=> ( member(ordered_pair(X6,X7),compose5(X1,X2,X3,X4,X5))
<=> ? [X8] :
( ilf_type(X8,member_type(X2))
& member(ordered_pair(X6,X8),X4)
& member(ordered_pair(X8,X7),X5) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_51])]) ).
cnf(c_0_37,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_38,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_39,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_22]),c_0_22])]) ).
cnf(c_0_40,plain,
( member(X1,power_set(X2))
| ~ member(esk8_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_41,plain,
( member(esk8_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_42,plain,
! [X132] :
( ( relation_like(X132)
| ~ ilf_type(X132,binary_relation_type)
| ~ ilf_type(X132,set_type) )
& ( ilf_type(X132,set_type)
| ~ ilf_type(X132,binary_relation_type)
| ~ ilf_type(X132,set_type) )
& ( ~ relation_like(X132)
| ~ ilf_type(X132,set_type)
| ilf_type(X132,binary_relation_type)
| ~ ilf_type(X132,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])]) ).
cnf(c_0_43,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_32]) ).
fof(c_0_44,plain,
! [X97,X98,X99,X100,X101] :
( ( member(X99,X97)
| ~ member(ordered_pair(X99,X100),X101)
| ~ ilf_type(X101,relation_type(X97,X98))
| ~ ilf_type(X100,set_type)
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type)
| ~ ilf_type(X97,set_type) )
& ( member(X100,X98)
| ~ member(ordered_pair(X99,X100),X101)
| ~ ilf_type(X101,relation_type(X97,X98))
| ~ ilf_type(X100,set_type)
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type)
| ~ ilf_type(X97,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_45,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_46,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_35,c_0_22]),c_0_22])]) ).
fof(c_0_47,negated_conjecture,
! [X179] :
( ~ empty(esk12_0)
& ilf_type(esk12_0,set_type)
& ~ empty(esk13_0)
& ilf_type(esk13_0,set_type)
& ~ empty(esk14_0)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk12_0,esk13_0))
& ilf_type(esk16_0,relation_type(esk13_0,esk14_0))
& ilf_type(esk17_0,member_type(esk12_0))
& ilf_type(esk18_0,member_type(esk14_0))
& ( ~ member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| ~ ilf_type(X179,member_type(esk13_0))
| ~ member(ordered_pair(esk17_0,X179),esk15_0)
| ~ member(ordered_pair(X179,esk18_0),esk16_0) )
& ( ilf_type(esk19_0,member_type(esk13_0))
| member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) )
& ( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) )
& ( member(ordered_pair(esk19_0,esk18_0),esk16_0)
| member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])])]) ).
cnf(c_0_48,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_22]),c_0_22])]) ).
cnf(c_0_49,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_22]),c_0_22])]),c_0_39]) ).
cnf(c_0_50,plain,
( member(X1,power_set(X2))
| ~ member(esk8_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_22]),c_0_22])]) ).
cnf(c_0_51,plain,
( member(esk8_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_22]),c_0_22])]) ).
cnf(c_0_52,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_42]) ).
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_43,c_0_22]),c_0_22])]) ).
cnf(c_0_54,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_44]) ).
cnf(c_0_55,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
ilf_type(esk15_0,relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_58,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0))
| ~ ilf_type(X1,member_type(esk13_0))
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_62,plain,
! [X91,X92,X93,X94,X96] :
( ( ilf_type(esk1_4(X91,X92,X93,X94),set_type)
| ~ member(ordered_pair(X91,X92),compose(X93,X94))
| ~ ilf_type(X94,binary_relation_type)
| ~ ilf_type(X93,binary_relation_type)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( member(ordered_pair(X91,esk1_4(X91,X92,X93,X94)),X93)
| ~ member(ordered_pair(X91,X92),compose(X93,X94))
| ~ ilf_type(X94,binary_relation_type)
| ~ ilf_type(X93,binary_relation_type)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( member(ordered_pair(esk1_4(X91,X92,X93,X94),X92),X94)
| ~ member(ordered_pair(X91,X92),compose(X93,X94))
| ~ ilf_type(X94,binary_relation_type)
| ~ ilf_type(X93,binary_relation_type)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ~ ilf_type(X96,set_type)
| ~ member(ordered_pair(X91,X96),X93)
| ~ member(ordered_pair(X96,X92),X94)
| member(ordered_pair(X91,X92),compose(X93,X94))
| ~ ilf_type(X94,binary_relation_type)
| ~ ilf_type(X93,binary_relation_type)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,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_63,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_52]) ).
cnf(c_0_64,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_65,negated_conjecture,
ilf_type(esk16_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_66,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_54,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_67,negated_conjecture,
( member(X1,cross_product(esk12_0,esk13_0))
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_22]),c_0_22])]) ).
cnf(c_0_69,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_70,plain,
! [X161,X162,X163,X164,X165] :
( ~ ilf_type(X161,set_type)
| ~ ilf_type(X162,set_type)
| ~ ilf_type(X163,set_type)
| ~ ilf_type(X164,relation_type(X161,X162))
| ~ ilf_type(X165,relation_type(X162,X163))
| compose5(X161,X162,X163,X164,X165) = compose(X164,X165) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
cnf(c_0_71,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
( member(ordered_pair(esk1_4(X1,X2,X3,X4),X2),X4)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_22])]) ).
cnf(c_0_74,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_75,negated_conjecture,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),esk15_0)
| ~ ilf_type(cross_product(esk12_0,esk13_0),relation_type(X4,X2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,plain,
( compose5(X1,X2,X3,X4,X5) = compose(X4,X5)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X5,relation_type(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_49]) ).
cnf(c_0_79,plain,
( member(ordered_pair(esk1_4(X1,X2,X3,X4),X2),X4)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_22]),c_0_22])]) ).
cnf(c_0_80,negated_conjecture,
ilf_type(esk16_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( member(X1,esk13_0)
| ~ member(ordered_pair(X2,X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
( member(ordered_pair(X1,esk1_4(X1,X2,X3,X4)),X3)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_83,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
cnf(c_0_84,plain,
( compose5(X1,X2,X3,X4,X5) = compose(X4,X5)
| ~ ilf_type(X5,relation_type(X2,X3))
| ~ ilf_type(X4,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_85,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_86,plain,
( member(ordered_pair(X2,X4),compose(X3,X5))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ member(ordered_pair(X1,X4),X5)
| ~ ilf_type(X5,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_87,negated_conjecture,
( member(ordered_pair(esk17_0,esk19_0),esk15_0)
| ~ member(ordered_pair(esk17_0,esk1_4(X1,esk18_0,X2,esk16_0)),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),compose(X2,esk16_0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]),c_0_81]) ).
cnf(c_0_88,plain,
( member(ordered_pair(X1,esk1_4(X1,X2,X3,X4)),X3)
| ~ member(ordered_pair(X1,X2),compose(X3,X4))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_22]),c_0_22])]) ).
cnf(c_0_89,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_73,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0))
| member(ordered_pair(esk17_0,esk19_0),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_84]),c_0_65]),c_0_56])]) ).
cnf(c_0_91,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_44]) ).
cnf(c_0_92,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_85]) ).
cnf(c_0_93,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(ordered_pair(X1,X5),X3)
| ~ member(ordered_pair(X5,X2),X4)
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_94,negated_conjecture,
member(ordered_pair(esk17_0,esk19_0),esk15_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_80])]),c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( member(ordered_pair(esk19_0,esk18_0),esk16_0)
| member(ordered_pair(esk17_0,esk18_0),compose5(esk12_0,esk13_0,esk14_0,esk15_0,esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_96,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_91,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_97,negated_conjecture,
( member(X1,cross_product(esk13_0,esk14_0))
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_65]) ).
cnf(c_0_98,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| ~ member(ordered_pair(esk17_0,esk1_4(X1,esk18_0,X2,esk16_0)),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),compose(X2,esk16_0))
| ~ ilf_type(esk1_4(X1,esk18_0,X2,esk16_0),member_type(esk13_0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_79]),c_0_80])]) ).
cnf(c_0_99,negated_conjecture,
( ~ member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0))
| ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_84]),c_0_65]),c_0_56])]) ).
cnf(c_0_100,negated_conjecture,
( member(ordered_pair(esk17_0,X1),compose(esk15_0,X2))
| ~ member(ordered_pair(esk19_0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_89])]) ).
cnf(c_0_101,negated_conjecture,
( member(ordered_pair(esk19_0,esk18_0),esk16_0)
| ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),esk16_0)
| ~ ilf_type(cross_product(esk13_0,esk14_0),relation_type(X2,X4)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( ilf_type(esk19_0,member_type(esk13_0))
| ~ member(ordered_pair(esk17_0,esk1_4(X1,esk18_0,X2,esk16_0)),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),compose(X2,esk16_0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_49]),c_0_81]) ).
cnf(c_0_104,negated_conjecture,
( member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0))
| ilf_type(esk19_0,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_84]),c_0_65]),c_0_56])]) ).
cnf(c_0_105,negated_conjecture,
( ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_80])]),c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( member(X1,esk13_0)
| ~ member(ordered_pair(X1,X2),esk16_0) ),
inference(spm,[status(thm)],[c_0_102,c_0_76]) ).
cnf(c_0_107,negated_conjecture,
ilf_type(esk19_0,member_type(esk13_0)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_88]),c_0_89]),c_0_80])]),c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( ~ member(ordered_pair(X1,esk18_0),esk16_0)
| ~ member(ordered_pair(esk17_0,X1),esk15_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_49]),c_0_106]) ).
cnf(c_0_109,negated_conjecture,
( member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0))
| member(ordered_pair(esk19_0,esk18_0),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_84]),c_0_65]),c_0_56])]) ).
cnf(c_0_110,negated_conjecture,
~ member(ordered_pair(esk19_0,esk18_0),esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_107]),c_0_94])]) ).
cnf(c_0_111,negated_conjecture,
( ~ member(ordered_pair(esk17_0,esk1_4(X1,esk18_0,X2,esk16_0)),esk15_0)
| ~ member(ordered_pair(X1,esk18_0),compose(X2,esk16_0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_79]),c_0_80])]) ).
cnf(c_0_112,negated_conjecture,
member(ordered_pair(esk17_0,esk18_0),compose(esk15_0,esk16_0)),
inference(sr,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_88]),c_0_112]),c_0_89]),c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET684+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 : n010.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 02:31:21 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.41/1.76 % Version : CSE_E---1.7
% 1.41/1.76 % Problem : theBenchmark.p
% 1.41/1.76 % SZS status Theorem for theBenchmark.p
% 1.41/1.76 % SZS output start CNFRefutation
% See solution above
% 1.41/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------