%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET949+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 05:09:01 PM UTC 2026
% Result : Theorem 1.15s 1.72s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 59 ( 31 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 68 ( 29 ~; 25 |; 12 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 61 ( 6 sgn 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t102_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( in(X1,cartesian_product2(X2,X3))
& ! [X4,X5] : ordered_pair(X4,X5) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( in(X1,cartesian_product2(X2,X3))
& ! [X4,X5] : ordered_pair(X4,X5) != X1 ),
inference(assume_negation,[status(cth)],[t102_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
! [X58,X59] :
( in(esk8_0,cartesian_product2(esk9_0,esk10_0))
& ordered_pair(X58,X59) != esk8_0 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X49,X50] : ordered_pair(X49,X50) = unordered_pair(unordered_pair(X49,X50),singleton(X49)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,plain,
! [X32,X33,X34,X35,X38,X39,X40,X41,X42,X43,X45,X46] :
( ( in(esk1_4(X32,X33,X34,X35),X32)
| ~ in(X35,X34)
| X34 != cartesian_product2(X32,X33) )
& ( in(esk2_4(X32,X33,X34,X35),X33)
| ~ in(X35,X34)
| X34 != cartesian_product2(X32,X33) )
& ( X35 = ordered_pair(esk1_4(X32,X33,X34,X35),esk2_4(X32,X33,X34,X35))
| ~ in(X35,X34)
| X34 != cartesian_product2(X32,X33) )
& ( ~ in(X39,X32)
| ~ in(X40,X33)
| X38 != ordered_pair(X39,X40)
| in(X38,X34)
| X34 != cartesian_product2(X32,X33) )
& ( ~ in(esk3_3(X41,X42,X43),X43)
| ~ in(X45,X41)
| ~ in(X46,X42)
| esk3_3(X41,X42,X43) != ordered_pair(X45,X46)
| X43 = cartesian_product2(X41,X42) )
& ( in(esk4_3(X41,X42,X43),X41)
| in(esk3_3(X41,X42,X43),X43)
| X43 = cartesian_product2(X41,X42) )
& ( in(esk5_3(X41,X42,X43),X42)
| in(esk3_3(X41,X42,X43),X43)
| X43 = cartesian_product2(X41,X42) )
& ( esk3_3(X41,X42,X43) = ordered_pair(esk4_3(X41,X42,X43),esk5_3(X41,X42,X43))
| in(esk3_3(X41,X42,X43),X43)
| X43 = cartesian_product2(X41,X42) ) ),
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_8,negated_conjecture,
ordered_pair(X1,X2) != esk8_0,
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,plain,
! [X30,X31] : unordered_pair(X30,X31) = unordered_pair(X31,X30),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_11,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_7]) ).
cnf(c_0_12,negated_conjecture,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) != esk8_0,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,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_11,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
unordered_pair(singleton(X1),unordered_pair(X1,X2)) != esk8_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,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_14,c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
in(esk8_0,cartesian_product2(esk9_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
~ in(esk8_0,cartesian_product2(X1,X2)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_17,c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET949+1 : TPTP v9.2.1. Released v3.2.0.
% 0.06/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8042.1875MB
% 0.08/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Tue May 5 02:39:46 EDT 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % start to proof: theBenchmark
% 1.15/1.72 % Version : CSE_E---1.7
% 1.15/1.72 % Problem : theBenchmark.p
% 1.15/1.72 % SZS status Theorem for theBenchmark.p
% 1.15/1.72 % SZS output start CNFRefutation
% See solution above
% 1.15/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------