%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU262+1 : TPTP v9.2.1. Released v3.3.0.
% 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 05:11:17 PM UTC 2026
% Result : Theorem 15.88s 11.01s
% Output : CNFRefutation 16.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 11 unt; 0 def)
% Number of atoms : 172 ( 24 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 193 ( 80 ~; 84 |; 15 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 152 ( 15 sgn 66 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t12_relset_1,conjecture,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(c_0_10,plain,
! [X134,X135] :
( ( ~ element(X134,powerset(X135))
| subset(X134,X135) )
& ( ~ subset(X134,X135)
| element(X134,powerset(X135)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_11,plain,
! [X104,X105,X106] :
( ~ relation_of2_as_subset(X106,X104,X105)
| element(X106,powerset(cartesian_product2(X104,X105))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_12,plain,
! [X123,X124,X125,X126] :
( ( in(X123,X125)
| ~ in(ordered_pair(X123,X124),cartesian_product2(X125,X126)) )
& ( in(X124,X126)
| ~ in(ordered_pair(X123,X124),cartesian_product2(X125,X126)) )
& ( ~ in(X123,X125)
| ~ in(X124,X126)
| in(ordered_pair(X123,X124),cartesian_product2(X125,X126)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(c_0_13,plain,
! [X102,X103] : ordered_pair(X102,X103) = unordered_pair(unordered_pair(X102,X103),singleton(X102)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_14,plain,
! [X76,X77,X78,X79,X80] :
( ( ~ subset(X76,X77)
| ~ in(X78,X76)
| in(X78,X77) )
& ( in(esk1_2(X79,X80),X79)
| subset(X79,X80) )
& ( ~ in(esk1_2(X79,X80),X80)
| subset(X79,X80) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
inference(assume_negation,[status(cth)],[t12_relset_1]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X74,X75] : unordered_pair(X74,X75) = unordered_pair(X75,X74),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_21,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_23,negated_conjecture,
( relation_of2_as_subset(esk15_0,esk13_0,esk14_0)
& ( ~ subset(relation_dom(esk15_0),esk13_0)
| ~ subset(relation_rng(esk15_0),esk14_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_24,plain,
! [X82,X83,X84,X86,X87,X88,X90] :
( ( ~ in(X84,X83)
| in(ordered_pair(X84,esk2_3(X82,X83,X84)),X82)
| X83 != relation_dom(X82)
| ~ relation(X82) )
& ( ~ in(ordered_pair(X86,X87),X82)
| in(X86,X83)
| X83 != relation_dom(X82)
| ~ relation(X82) )
& ( ~ in(esk3_2(X82,X88),X88)
| ~ in(ordered_pair(esk3_2(X82,X88),X90),X82)
| X88 = relation_dom(X82)
| ~ relation(X82) )
& ( in(esk3_2(X82,X88),X88)
| in(ordered_pair(esk3_2(X82,X88),esk4_2(X82,X88)),X82)
| X88 = relation_dom(X82)
| ~ relation(X82) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_1])])])])])]) ).
fof(c_0_25,plain,
! [X71,X72,X73] :
( ~ element(X73,powerset(cartesian_product2(X71,X72)))
| relation(X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X4,X2,X3)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
relation_of2_as_subset(esk15_0,esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( in(ordered_pair(X1,esk2_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_33,plain,
! [X92,X93,X94,X96,X97,X98,X100] :
( ( ~ in(X94,X93)
| in(ordered_pair(esk5_3(X92,X93,X94),X94),X92)
| X93 != relation_rng(X92)
| ~ relation(X92) )
& ( ~ in(ordered_pair(X97,X96),X92)
| in(X96,X93)
| X93 != relation_rng(X92)
| ~ relation(X92) )
& ( ~ in(esk6_2(X92,X98),X98)
| ~ in(ordered_pair(X100,esk6_2(X92,X98)),X92)
| X98 = relation_rng(X92)
| ~ relation(X92) )
& ( in(esk6_2(X92,X98),X98)
| in(ordered_pair(esk7_2(X92,X98),esk6_2(X92,X98)),X92)
| X98 = relation_rng(X92)
| ~ relation(X92) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_relat_1])])])])])]) ).
cnf(c_0_34,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X4)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( in(X1,cartesian_product2(esk13_0,esk14_0))
| ~ in(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_37,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_39,plain,
( in(ordered_pair(esk5_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( in(X1,esk13_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk15_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_42,negated_conjecture,
relation(esk15_0),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_43,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_44,plain,
( in(unordered_pair(unordered_pair(esk5_3(X3,X2,X1),X1),singleton(esk5_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_39,c_0_19]) ).
cnf(c_0_45,negated_conjecture,
( in(X1,esk13_0)
| X2 != relation_dom(esk15_0)
| ~ in(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
( in(X1,esk14_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),esk15_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_47,plain,
( in(unordered_pair(unordered_pair(X1,esk5_3(X2,X3,X1)),singleton(esk5_3(X2,X3,X1))),X2)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_48,negated_conjecture,
( in(X1,esk13_0)
| ~ in(X1,relation_dom(esk15_0)) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_50,negated_conjecture,
( in(X1,esk14_0)
| X2 != relation_rng(esk15_0)
| ~ in(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42])]) ).
cnf(c_0_51,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,negated_conjecture,
( subset(relation_dom(esk15_0),X1)
| in(esk1_2(relation_dom(esk15_0),X1),esk13_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( in(X1,esk14_0)
| ~ in(X1,relation_rng(esk15_0)) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( ~ subset(relation_dom(esk15_0),esk13_0)
| ~ subset(relation_rng(esk15_0),esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_55,negated_conjecture,
subset(relation_dom(esk15_0),esk13_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( subset(relation_rng(esk15_0),X1)
| in(esk1_2(relation_rng(esk15_0),X1),esk14_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
~ subset(relation_rng(esk15_0),esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_56]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU262+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:53:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 15.88/11.01 % Version : CSE_E---1.7
% 15.88/11.01 % Problem : theBenchmark.p
% 15.88/11.01 % SZS status Theorem for theBenchmark.p
% 15.88/11.01 % SZS output start CNFRefutation
% See solution above
% 16.00/11.06 % Total time : 8.383s
%------------------------------------------------------------------------------