%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET656+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 : n031.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 3.53s 3.05s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 193 ( 8 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 241 ( 95 ~; 94 |; 18 &)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 2 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p21,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',p21) ).
fof(p20,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',p20) ).
fof(p30,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
fof(p13,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',p13) ).
fof(p19,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',p19) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(prove_relset_1_18,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> intersection(X3,cross_product(X1,X2)) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_18) ).
fof(p17,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',p17) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
=> intersection(X1,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(c_0_9,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)],[p21]) ).
fof(c_0_10,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p20]) ).
fof(c_0_11,plain,
! [X133,X134] :
( ( ~ ilf_type(X133,member_type(X134))
| member(X133,X134)
| empty(X134)
| ~ ilf_type(X134,set_type)
| ~ ilf_type(X133,set_type) )
& ( ~ member(X133,X134)
| ilf_type(X133,member_type(X134))
| empty(X134)
| ~ ilf_type(X134,set_type)
| ~ ilf_type(X133,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_12,plain,
! [X163] : ilf_type(X163,set_type),
inference(variable_rename,[status(thm)],[p30]) ).
fof(c_0_13,plain,
! [X116,X117] :
( ( ~ ilf_type(X117,subset_type(X116))
| ilf_type(X117,member_type(power_set(X116)))
| ~ ilf_type(X117,set_type)
| ~ ilf_type(X116,set_type) )
& ( ~ ilf_type(X117,member_type(power_set(X116)))
| ilf_type(X117,subset_type(X116))
| ~ 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)],[p13])])])]) ).
fof(c_0_14,plain,
! [X132] :
( ( ~ empty(power_set(X132))
| ~ ilf_type(X132,set_type) )
& ( ilf_type(power_set(X132),set_type)
| ~ ilf_type(X132,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_15,plain,
! [X128,X129,X130] :
( ( ~ member(X128,power_set(X129))
| ~ ilf_type(X130,set_type)
| ~ member(X130,X128)
| member(X130,X129)
| ~ ilf_type(X129,set_type)
| ~ ilf_type(X128,set_type) )
& ( ilf_type(esk9_2(X128,X129),set_type)
| member(X128,power_set(X129))
| ~ ilf_type(X129,set_type)
| ~ ilf_type(X128,set_type) )
& ( member(esk9_2(X128,X129),X128)
| member(X128,power_set(X129))
| ~ ilf_type(X129,set_type)
| ~ ilf_type(X128,set_type) )
& ( ~ member(esk9_2(X128,X129),X129)
| member(X128,power_set(X129))
| ~ ilf_type(X129,set_type)
| ~ ilf_type(X128,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)],[p19])])])])]) ).
cnf(c_0_16,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_11]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,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_13]) ).
cnf(c_0_19,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,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_15]) ).
cnf(c_0_21,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_16,c_0_17]),c_0_17])]) ).
cnf(c_0_22,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_18,c_0_17]),c_0_17])]) ).
cnf(c_0_23,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17])]) ).
fof(c_0_24,plain,
! [X97,X98,X99,X100] :
( ( ~ ilf_type(X99,subset_type(cross_product(X97,X98)))
| ilf_type(X99,relation_type(X97,X98))
| ~ ilf_type(X98,set_type)
| ~ ilf_type(X97,set_type) )
& ( ~ ilf_type(X100,relation_type(X97,X98))
| ilf_type(X100,subset_type(cross_product(X97,X98)))
| ~ 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)],[p6])])])]) ).
cnf(c_0_25,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_20,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_26,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,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_24]) ).
fof(c_0_28,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> intersection(X3,cross_product(X1,X2)) = X3 ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_18]) ).
fof(c_0_29,plain,
! [X123,X124,X125] :
( ( ~ subset(X123,X124)
| ~ ilf_type(X125,set_type)
| ~ member(X125,X123)
| member(X125,X124)
| ~ ilf_type(X124,set_type)
| ~ ilf_type(X123,set_type) )
& ( ilf_type(esk8_2(X123,X124),set_type)
| subset(X123,X124)
| ~ ilf_type(X124,set_type)
| ~ ilf_type(X123,set_type) )
& ( member(esk8_2(X123,X124),X123)
| subset(X123,X124)
| ~ ilf_type(X124,set_type)
| ~ ilf_type(X123,set_type) )
& ( ~ member(esk8_2(X123,X124),X124)
| subset(X123,X124)
| ~ ilf_type(X124,set_type)
| ~ ilf_type(X123,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)],[p17])])])])]) ).
cnf(c_0_30,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,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_27,c_0_17]),c_0_17])]) ).
fof(c_0_32,negated_conjecture,
( ilf_type(esk16_0,set_type)
& ilf_type(esk17_0,set_type)
& ilf_type(esk18_0,relation_type(esk16_0,esk17_0))
& intersection(esk18_0,cross_product(esk16_0,esk17_0)) != esk18_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_33,plain,
! [X81,X82] :
( ~ ilf_type(X81,set_type)
| ~ ilf_type(X82,set_type)
| ~ subset(X81,X82)
| intersection(X81,X82) = X81 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ member(esk8_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
ilf_type(esk18_0,relation_type(esk16_0,esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( intersection(X1,X2) = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( subset(X1,X2)
| ~ member(esk8_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17]),c_0_17])]) ).
cnf(c_0_39,negated_conjecture,
( member(X1,cross_product(esk16_0,esk17_0))
| ~ member(X1,esk18_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( member(esk8_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,negated_conjecture,
intersection(esk18_0,cross_product(esk16_0,esk17_0)) != esk18_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_17]),c_0_17])]) ).
cnf(c_0_43,negated_conjecture,
( subset(X1,cross_product(esk16_0,esk17_0))
| ~ member(esk8_2(X1,cross_product(esk16_0,esk17_0)),esk18_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( member(esk8_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_17]),c_0_17])]) ).
cnf(c_0_45,negated_conjecture,
~ subset(esk18_0,cross_product(esk16_0,esk17_0)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET656+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n031.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:33:08 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 3.53/3.05 % Version : CSE_E---1.7
% 3.53/3.05 % Problem : theBenchmark.p
% 3.53/3.05 % SZS status Theorem for theBenchmark.p
% 3.53/3.05 % SZS output start CNFRefutation
% See solution above
% 3.53/3.06 % Total time : 2.367s
%------------------------------------------------------------------------------