%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET964+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n008.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 05:09:03 PM UTC 2026
% Result : Theorem 1.30s 1.93s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 158 ( 34 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 171 ( 67 ~; 76 |; 21 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 135 ( 18 sgn 53 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t117_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( X1 != empty_set
& ( subset(cartesian_product2(X2,X1),cartesian_product2(X3,X1))
| subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3)) )
& ~ subset(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
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(l55_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',l55_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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
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(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( X1 != empty_set
& ( subset(cartesian_product2(X2,X1),cartesian_product2(X3,X1))
| subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3)) )
& ~ subset(X2,X3) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t117_zfmisc_1])]) ).
fof(c_0_8,plain,
! [X62,X63,X64,X65,X66] :
( ( ~ subset(X62,X63)
| ~ in(X64,X62)
| in(X64,X63) )
& ( in(esk7_2(X65,X66),X65)
| subset(X65,X66) )
& ( ~ in(esk7_2(X65,X66),X66)
| subset(X65,X66) ) ),
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])])])])])]) ).
fof(c_0_9,negated_conjecture,
( esk10_0 != empty_set
& ( subset(cartesian_product2(esk11_0,esk10_0),cartesian_product2(esk12_0,esk10_0))
| subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0)) )
& ~ subset(esk11_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X72,X73,X74,X75] :
( ( in(X72,X74)
| ~ in(ordered_pair(X72,X73),cartesian_product2(X74,X75)) )
& ( in(X73,X75)
| ~ in(ordered_pair(X72,X73),cartesian_product2(X74,X75)) )
& ( ~ in(X72,X74)
| ~ in(X73,X75)
| in(ordered_pair(X72,X73),cartesian_product2(X74,X75)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_11,plain,
! [X68,X69] : ordered_pair(X68,X69) = unordered_pair(unordered_pair(X68,X69),singleton(X68)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_12,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( subset(cartesian_product2(esk11_0,esk10_0),cartesian_product2(esk12_0,esk10_0))
| subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_17,negated_conjecture,
( subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0))
| in(X1,cartesian_product2(esk12_0,esk10_0))
| ~ in(X1,cartesian_product2(esk11_0,esk10_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
! [X41,X42,X43] :
( ( X41 != empty_set
| ~ in(X42,X41) )
& ( in(esk1_1(X43),X43)
| X43 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_20,plain,
! [X39,X40] : unordered_pair(X39,X40) = unordered_pair(X40,X39),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk12_0,esk10_0))
| ~ in(X2,esk10_0)
| ~ in(X1,esk11_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
esk10_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
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_21,c_0_15]) ).
cnf(c_0_27,negated_conjecture,
( subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_1(esk10_0))),cartesian_product2(esk12_0,esk10_0))
| ~ in(X1,esk11_0) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
( in(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,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_25]) ).
cnf(c_0_30,negated_conjecture,
( subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0))
| subset(esk11_0,X1)
| in(unordered_pair(singleton(esk7_2(esk11_0,X1)),unordered_pair(esk7_2(esk11_0,X1),esk1_1(esk10_0))),cartesian_product2(esk12_0,esk10_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
( subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0))
| subset(esk11_0,X1)
| in(esk7_2(esk11_0,X1),esk12_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
~ subset(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_35,plain,
! [X45,X46,X47,X48,X51,X52,X53,X54,X55,X56,X58,X59] :
( ( in(esk2_4(X45,X46,X47,X48),X45)
| ~ in(X48,X47)
| X47 != cartesian_product2(X45,X46) )
& ( in(esk3_4(X45,X46,X47,X48),X46)
| ~ in(X48,X47)
| X47 != cartesian_product2(X45,X46) )
& ( X48 = ordered_pair(esk2_4(X45,X46,X47,X48),esk3_4(X45,X46,X47,X48))
| ~ in(X48,X47)
| X47 != cartesian_product2(X45,X46) )
& ( ~ in(X52,X45)
| ~ in(X53,X46)
| X51 != ordered_pair(X52,X53)
| in(X51,X47)
| X47 != cartesian_product2(X45,X46) )
& ( ~ in(esk4_3(X54,X55,X56),X56)
| ~ in(X58,X54)
| ~ in(X59,X55)
| esk4_3(X54,X55,X56) != ordered_pair(X58,X59)
| X56 = cartesian_product2(X54,X55) )
& ( in(esk5_3(X54,X55,X56),X54)
| in(esk4_3(X54,X55,X56),X56)
| X56 = cartesian_product2(X54,X55) )
& ( in(esk6_3(X54,X55,X56),X55)
| in(esk4_3(X54,X55,X56),X56)
| X56 = cartesian_product2(X54,X55) )
& ( esk4_3(X54,X55,X56) = ordered_pair(esk5_3(X54,X55,X56),esk6_3(X54,X55,X56))
| in(esk4_3(X54,X55,X56),X56)
| X56 = cartesian_product2(X54,X55) ) ),
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)],[d2_zfmisc_1])])])])])]) ).
cnf(c_0_36,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_31,c_0_15]) ).
cnf(c_0_37,negated_conjecture,
subset(cartesian_product2(esk10_0,esk11_0),cartesian_product2(esk10_0,esk12_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_39,plain,
( in(esk2_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_41,negated_conjecture,
( in(X1,cartesian_product2(esk10_0,esk12_0))
| ~ in(X1,cartesian_product2(esk10_0,esk11_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_37]) ).
cnf(c_0_42,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( in(X1,esk12_0)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),cartesian_product2(esk10_0,esk11_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_46,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( in(X1,esk12_0)
| ~ in(X1,esk11_0)
| ~ in(X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
( in(esk5_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,plain,
cartesian_product2(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_50,negated_conjecture,
( subset(esk11_0,X1)
| in(esk7_2(esk11_0,X1),esk12_0)
| ~ in(X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_28]) ).
cnf(c_0_51,plain,
( X1 = empty_set
| in(esk4_3(empty_set,X2,X1),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_48]),c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( subset(esk11_0,X1)
| in(esk7_2(esk11_0,X1),esk12_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_24]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_52]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.22 % Problem : SET964+1 : TPTP v9.2.1. Released v3.2.0.
% 0.03/0.22 % 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
% 0.12/0.44 % Computer : n008.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8042.1875MB
% 0.12/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Tue May 5 02:40:44 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 1.30/1.93 % Version : CSE_E---1.7
% 1.30/1.93 % Problem : theBenchmark.p
% 1.30/1.93 % SZS status Theorem for theBenchmark.p
% 1.30/1.93 % SZS output start CNFRefutation
% See solution above
% 1.30/1.94 % Total time : 1.384s
%------------------------------------------------------------------------------