%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET950+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 : n028.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 05:09:02 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 105 ( 33 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 128 ( 54 ~; 49 |; 21 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 90 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t103_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
~ ( subset(X1,cartesian_product2(X2,X3))
& in(X4,X1)
& ! [X5,X6] :
~ ( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_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(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(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(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(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( subset(X1,cartesian_product2(X2,X3))
& in(X4,X1)
& ! [X5,X6] :
~ ( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
inference(assume_negation,[status(cth)],[t103_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
! [X72,X73] :
( subset(esk9_0,cartesian_product2(esk10_0,esk11_0))
& in(esk12_0,esk9_0)
& ( ~ in(X72,esk10_0)
| ~ in(X73,esk11_0)
| esk12_0 != ordered_pair(X72,X73) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X61,X62] : ordered_pair(X61,X62) = unordered_pair(unordered_pair(X61,X62),singleton(X61)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X38,X39,X40,X41,X44,X45,X46,X47,X48,X49,X51,X52] :
( ( in(esk1_4(X38,X39,X40,X41),X38)
| ~ in(X41,X40)
| X40 != cartesian_product2(X38,X39) )
& ( in(esk2_4(X38,X39,X40,X41),X39)
| ~ in(X41,X40)
| X40 != cartesian_product2(X38,X39) )
& ( X41 = ordered_pair(esk1_4(X38,X39,X40,X41),esk2_4(X38,X39,X40,X41))
| ~ in(X41,X40)
| X40 != cartesian_product2(X38,X39) )
& ( ~ in(X45,X38)
| ~ in(X46,X39)
| X44 != ordered_pair(X45,X46)
| in(X44,X40)
| X40 != cartesian_product2(X38,X39) )
& ( ~ in(esk3_3(X47,X48,X49),X49)
| ~ in(X51,X47)
| ~ in(X52,X48)
| esk3_3(X47,X48,X49) != ordered_pair(X51,X52)
| X49 = cartesian_product2(X47,X48) )
& ( in(esk4_3(X47,X48,X49),X47)
| in(esk3_3(X47,X48,X49),X49)
| X49 = cartesian_product2(X47,X48) )
& ( in(esk5_3(X47,X48,X49),X48)
| in(esk3_3(X47,X48,X49),X49)
| X49 = cartesian_product2(X47,X48) )
& ( esk3_3(X47,X48,X49) = ordered_pair(esk4_3(X47,X48,X49),esk5_3(X47,X48,X49))
| in(esk3_3(X47,X48,X49),X49)
| X49 = cartesian_product2(X47,X48) ) ),
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_9,negated_conjecture,
( ~ in(X1,esk10_0)
| ~ in(X2,esk11_0)
| esk12_0 != ordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X36,X37] : unordered_pair(X36,X37) = unordered_pair(X37,X36),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( X1 = ordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( esk12_0 != unordered_pair(unordered_pair(X1,X2),singleton(X1))
| ~ in(X2,esk11_0)
| ~ in(X1,esk10_0) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( X1 = unordered_pair(unordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1)),singleton(esk1_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( unordered_pair(singleton(X1),unordered_pair(X1,X2)) != esk12_0
| ~ in(X2,esk11_0)
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( unordered_pair(singleton(esk1_4(X1,X2,cartesian_product2(X1,X2),X3)),unordered_pair(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),esk2_4(X1,X2,cartesian_product2(X1,X2),X3))) = X3
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14])]) ).
cnf(c_0_18,plain,
( in(esk2_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(esk2_4(X1,X2,cartesian_product2(X1,X2),esk12_0),esk11_0)
| ~ in(esk1_4(X1,X2,cartesian_product2(X1,X2),esk12_0),esk10_0)
| ~ in(esk12_0,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
( in(esk1_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_22,plain,
! [X55,X56,X57,X58,X59] :
( ( ~ subset(X55,X56)
| ~ in(X57,X55)
| in(X57,X56) )
& ( in(esk6_2(X58,X59),X58)
| subset(X58,X59) )
& ( ~ in(esk6_2(X58,X59),X59)
| subset(X58,X59) ) ),
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_23,negated_conjecture,
( ~ in(esk1_4(X1,esk11_0,cartesian_product2(X1,esk11_0),esk12_0),esk10_0)
| ~ in(esk12_0,cartesian_product2(X1,esk11_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( in(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
subset(esk9_0,cartesian_product2(esk10_0,esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk12_0,cartesian_product2(esk10_0,esk11_0)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,cartesian_product2(esk10_0,esk11_0))
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
in(esk12_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET950+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n028.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 02:40:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------