%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET962+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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 05:09:03 PM UTC 2026
% Result : Theorem 1.14s 1.67s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 68 ( 20 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 27 |; 5 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 4 sgn 25 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t115_zfmisc_1,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X1) = cartesian_product2(X2,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_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(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_5,plain,
! [X32,X33,X34,X35] :
( ( in(X32,X34)
| ~ in(ordered_pair(X32,X33),cartesian_product2(X34,X35)) )
& ( in(X33,X35)
| ~ in(ordered_pair(X32,X33),cartesian_product2(X34,X35)) )
& ( ~ in(X32,X34)
| ~ in(X33,X35)
| in(ordered_pair(X32,X33),cartesian_product2(X34,X35)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_6,plain,
! [X28,X29] : ordered_pair(X28,X29) = unordered_pair(unordered_pair(X28,X29),singleton(X28)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X1) = cartesian_product2(X2,X2)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t115_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,plain,
! [X26,X27] : unordered_pair(X26,X27) = unordered_pair(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_11,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_12,negated_conjecture,
( cartesian_product2(esk3_0,esk3_0) = cartesian_product2(esk4_0,esk4_0)
& esk3_0 != esk4_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,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_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,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_11,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
cartesian_product2(esk3_0,esk3_0) = cartesian_product2(esk4_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk4_0))
| ~ in(X2,esk3_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,plain,
! [X40,X41] :
( ( ~ in(esk5_2(X40,X41),X40)
| ~ in(esk5_2(X40,X41),X41)
| X40 = X41 )
& ( in(esk5_2(X40,X41),X40)
| in(esk5_2(X40,X41),X41)
| X40 = X41 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( in(esk5_2(X1,X2),X1)
| in(esk5_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( esk3_0 = X1
| in(esk5_2(esk3_0,X1),esk4_0)
| in(esk5_2(esk3_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
( in(X1,esk3_0)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ in(esk5_2(X1,X2),X1)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
in(esk5_2(esk3_0,esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_22]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( in(X1,esk3_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),cartesian_product2(esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_28,negated_conjecture,
~ in(esk5_2(esk3_0,esk4_0),esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET962+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.00/0.10 % 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
% 0.08/0.30 % Computer : n012.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Tue May 5 02:40:16 EDT 2026
% 0.08/0.30 % CPUTime :
% 0.08/0.30 % start to proof: theBenchmark
% 1.14/1.67 % Version : CSE_E---1.7
% 1.14/1.67 % Problem : theBenchmark.p
% 1.14/1.67 % SZS status Theorem for theBenchmark.p
% 1.14/1.67 % SZS output start CNFRefutation
% See solution above
% 1.14/1.67 % Total time : 1.361s
%------------------------------------------------------------------------------