%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET980+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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 : n026.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 05:09:05 PM UTC 2026
% Result : Theorem 1.16s 1.87s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 11 unt; 0 def)
% Number of atoms : 128 ( 44 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 132 ( 54 ~; 61 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 17 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t134_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_5,plain,
! [X42,X43,X44,X45] :
( ( in(X42,X44)
| ~ in(ordered_pair(X42,X43),cartesian_product2(X44,X45)) )
& ( in(X43,X45)
| ~ in(ordered_pair(X42,X43),cartesian_product2(X44,X45)) )
& ( ~ in(X42,X44)
| ~ in(X43,X45)
| in(ordered_pair(X42,X43),cartesian_product2(X44,X45)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_6,plain,
! [X38,X39] : ordered_pair(X38,X39) = unordered_pair(unordered_pair(X38,X39),singleton(X38)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
inference(assume_negation,[status(cth)],[t134_zfmisc_1]) ).
cnf(c_0_8,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
( cartesian_product2(esk4_0,esk5_0) = cartesian_product2(esk6_0,esk7_0)
& esk4_0 != empty_set
& esk5_0 != empty_set
& ( esk4_0 != esk6_0
| esk5_0 != esk7_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
cartesian_product2(esk4_0,esk5_0) = cartesian_product2(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
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_5]) ).
fof(c_0_15,plain,
! [X34,X35,X36] :
( ( X34 != empty_set
| ~ in(X35,X34) )
& ( in(esk1_1(X36),X36)
| X36 = 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_11])])])])]) ).
cnf(c_0_16,negated_conjecture,
( in(X1,esk7_0)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,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_9]) ).
fof(c_0_18,plain,
! [X54,X55] :
( ( ~ in(esk8_2(X54,X55),X54)
| ~ in(esk8_2(X54,X55),X55)
| X54 = X55 )
& ( in(esk8_2(X54,X55),X54)
| in(esk8_2(X54,X55),X55)
| X54 = X55 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_19,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,esk7_0)
| ~ in(X1,esk5_0)
| ~ in(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( in(esk8_2(X1,X2),X1)
| in(esk8_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,negated_conjecture,
( X1 = esk5_0
| in(esk8_2(X1,esk5_0),esk7_0)
| in(esk8_2(X1,esk5_0),X1)
| ~ in(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( empty_set = X1
| in(esk8_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk5_0))
| ~ in(X2,esk7_0)
| ~ in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_29,negated_conjecture,
( X1 = esk5_0
| in(esk8_2(X1,esk5_0),esk7_0)
| in(esk8_2(X1,esk5_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk6_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_13]) ).
cnf(c_0_31,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk7_0)
| ~ in(X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( esk7_0 = esk5_0
| in(esk8_2(esk7_0,esk5_0),esk7_0) ),
inference(ef,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X2,esk5_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_34,negated_conjecture,
esk5_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,negated_conjecture,
( esk7_0 = esk5_0
| in(esk8_2(esk7_0,esk5_0),esk5_0)
| ~ in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( esk7_0 = esk5_0
| in(esk8_2(esk7_0,esk5_0),esk5_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
( X1 = X2
| ~ in(esk8_2(X1,X2),X1)
| ~ in(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_39,negated_conjecture,
( esk7_0 = esk5_0
| in(esk8_2(esk7_0,esk5_0),esk5_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_25]),c_0_26]) ).
cnf(c_0_40,negated_conjecture,
esk7_0 = esk5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk5_0))
| ~ in(X2,esk5_0)
| ~ in(X1,esk6_0) ),
inference(rw,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X2,esk5_0)
| ~ in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk6_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_25]),c_0_34]) ).
cnf(c_0_44,negated_conjecture,
( esk4_0 != esk6_0
| esk5_0 != esk7_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_45,negated_conjecture,
( X1 = esk6_0
| in(esk8_2(X1,esk6_0),esk4_0)
| in(esk8_2(X1,esk6_0),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_21]) ).
cnf(c_0_46,negated_conjecture,
esk6_0 != esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_40])]) ).
cnf(c_0_47,negated_conjecture,
( X1 = esk6_0
| ~ in(esk8_2(X1,esk6_0),esk4_0)
| ~ in(esk8_2(X1,esk6_0),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_48,negated_conjecture,
in(esk8_2(esk4_0,esk6_0),esk4_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_45]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_48])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.20 % Problem : SET980+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.02/0.20 % 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
% 0.11/0.42 % Computer : n026.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8042.1875MB
% 0.11/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Tue May 5 02:41:38 EDT 2026
% 0.11/0.43 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 1.16/1.87 % Version : CSE_E---1.7
% 1.16/1.87 % Problem : theBenchmark.p
% 1.16/1.87 % SZS status Theorem for theBenchmark.p
% 1.16/1.87 % SZS output start CNFRefutation
% See solution above
% 1.16/1.87 % Total time : 1.395s
%------------------------------------------------------------------------------