%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET640+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 : n025.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 05:08:12 PM UTC 2026
% Result : Theorem 1.45s 1.78s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 9 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 288 ( 113 ~; 114 |; 21 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 113 ( 2 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p13,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',p13) ).
fof(p12,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',p12) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(p8,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',p8) ).
fof(p11,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',p11) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(prove_relset_1_2,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X3))
=> ( subset(X1,X4)
=> subset(X1,cross_product(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_2) ).
fof(p6,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',p6) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(c_0_10,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)],[p13]) ).
fof(c_0_11,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p12]) ).
fof(c_0_12,plain,
! [X91,X92] :
( ( ~ ilf_type(X91,member_type(X92))
| member(X91,X92)
| empty(X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) )
& ( ~ member(X91,X92)
| ilf_type(X91,member_type(X92))
| empty(X92)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X91,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_13,plain,
! [X109] : ilf_type(X109,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_14,plain,
! [X81,X82] :
( ( ~ ilf_type(X82,subset_type(X81))
| ilf_type(X82,member_type(power_set(X81)))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) )
& ( ~ ilf_type(X82,member_type(power_set(X81)))
| ilf_type(X82,subset_type(X81))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p8])])])]) ).
fof(c_0_15,plain,
! [X90] :
( ( ~ empty(power_set(X90))
| ~ ilf_type(X90,set_type) )
& ( ilf_type(power_set(X90),set_type)
| ~ ilf_type(X90,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_16,plain,
! [X86,X87,X88] :
( ( ~ member(X86,power_set(X87))
| ~ ilf_type(X88,set_type)
| ~ member(X88,X86)
| member(X88,X87)
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( ilf_type(esk6_2(X86,X87),set_type)
| member(X86,power_set(X87))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( member(esk6_2(X86,X87),X86)
| member(X86,power_set(X87))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,set_type) )
& ( ~ member(esk6_2(X86,X87),X87)
| member(X86,power_set(X87))
| ~ ilf_type(X87,set_type)
| ~ ilf_type(X86,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)],[p11])])])])]) ).
cnf(c_0_17,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_12]) ).
cnf(c_0_18,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,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_14]) ).
cnf(c_0_20,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,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_16]) ).
cnf(c_0_22,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_17,c_0_18]),c_0_18])]) ).
cnf(c_0_23,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_19,c_0_18]),c_0_18])]) ).
cnf(c_0_24,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_18])]) ).
fof(c_0_25,plain,
! [X68,X69,X70,X71] :
( ( ~ ilf_type(X70,subset_type(cross_product(X68,X69)))
| ilf_type(X70,relation_type(X68,X69))
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) )
& ( ~ ilf_type(X71,relation_type(X68,X69))
| ilf_type(X71,subset_type(cross_product(X68,X69)))
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).
fof(c_0_26,plain,
! [X56,X57,X58] :
( ~ ilf_type(X56,set_type)
| ~ ilf_type(X57,set_type)
| ~ ilf_type(X58,set_type)
| ~ subset(X56,X57)
| ~ subset(X57,X58)
| subset(X56,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X3))
=> ( subset(X1,X4)
=> subset(X1,cross_product(X2,X3)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_2]) ).
cnf(c_0_28,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_21,c_0_18]),c_0_18]),c_0_18])]) ).
cnf(c_0_29,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,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_25]) ).
fof(c_0_31,plain,
! [X75,X76,X77] :
( ( ~ subset(X75,X76)
| ~ ilf_type(X77,set_type)
| ~ member(X77,X75)
| member(X77,X76)
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,set_type) )
& ( ilf_type(esk4_2(X75,X76),set_type)
| subset(X75,X76)
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,set_type) )
& ( member(esk4_2(X75,X76),X75)
| subset(X75,X76)
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,set_type) )
& ( ~ member(esk4_2(X75,X76),X76)
| subset(X75,X76)
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X75,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)],[p6])])])])]) ).
cnf(c_0_32,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_33,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk13_0,esk14_0))
& subset(esk12_0,esk15_0)
& ~ subset(esk12_0,cross_product(esk13_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[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)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_18]),c_0_18])]) ).
cnf(c_0_36,plain,
( member(X3,X2)
| ~ subset(X1,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_31]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_18]),c_0_18]),c_0_18])]) ).
cnf(c_0_38,negated_conjecture,
subset(esk12_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_18]),c_0_18]),c_0_18])]) ).
cnf(c_0_43,negated_conjecture,
( subset(X1,esk15_0)
| ~ subset(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( member(esk4_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_18]),c_0_18])]) ).
cnf(c_0_46,negated_conjecture,
( member(X1,cross_product(esk13_0,esk14_0))
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,X2)
| ~ subset(X2,esk12_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
( member(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_18]),c_0_18])]) ).
fof(c_0_49,plain,
! [X85] :
( ~ ilf_type(X85,set_type)
| subset(X85,X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])]) ).
cnf(c_0_50,negated_conjecture,
( subset(X1,cross_product(esk13_0,esk14_0))
| ~ member(esk4_2(X1,cross_product(esk13_0,esk14_0)),esk15_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( member(esk4_2(X1,X2),esk15_0)
| subset(X1,X2)
| ~ subset(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
( subset(X1,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
~ subset(esk12_0,cross_product(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_54,negated_conjecture,
( subset(X1,cross_product(esk13_0,esk14_0))
| ~ subset(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
subset(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_18])]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET640+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 : n025.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 02:30:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.45/1.78 % Version : CSE_E---1.7
% 1.45/1.78 % Problem : theBenchmark.p
% 1.45/1.78 % SZS status Theorem for theBenchmark.p
% 1.45/1.78 % SZS output start CNFRefutation
% See solution above
% 1.45/1.79 % Total time : 1.369s
%------------------------------------------------------------------------------