%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET959+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 : n014.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 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 79 ( 28 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 81 ( 34 ~; 28 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t112_zfmisc_1,conjecture,
! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_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(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(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_4,negated_conjecture,
~ ! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) )
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t112_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
! [X41,X44,X47,X48] :
( ( ~ in(X41,esk3_0)
| X41 = ordered_pair(esk5_1(X41),esk6_1(X41)) )
& ( ~ in(X44,esk4_0)
| X44 = ordered_pair(esk7_1(X44),esk8_1(X44)) )
& ( ~ in(ordered_pair(X47,X48),esk3_0)
| in(ordered_pair(X47,X48),esk4_0) )
& ( ~ in(ordered_pair(X47,X48),esk4_0)
| in(ordered_pair(X47,X48),esk3_0) )
& esk3_0 != esk4_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,
! [X33,X34] : ordered_pair(X33,X34) = unordered_pair(unordered_pair(X33,X34),singleton(X33)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_7,negated_conjecture,
( in(ordered_pair(X1,X2),esk3_0)
| ~ in(ordered_pair(X1,X2),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X31,X32] : unordered_pair(X31,X32) = unordered_pair(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_10,negated_conjecture,
( X1 = ordered_pair(esk7_1(X1),esk8_1(X1))
| ~ in(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( X1 = unordered_pair(unordered_pair(esk7_1(X1),esk8_1(X1)),singleton(esk7_1(X1)))
| ~ in(X1,esk4_0) ),
inference(rw,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( unordered_pair(singleton(esk7_1(X1)),unordered_pair(esk7_1(X1),esk8_1(X1))) = X1
| ~ in(X1,esk4_0) ),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
fof(c_0_16,plain,
! [X49,X50] :
( ( ~ in(esk9_2(X49,X50),X49)
| ~ in(esk9_2(X49,X50),X50)
| X49 = X50 )
& ( in(esk9_2(X49,X50),X49)
| in(esk9_2(X49,X50),X50)
| X49 = X50 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_17,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( in(esk9_2(X1,X2),X1)
| in(esk9_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( in(ordered_pair(X1,X2),esk4_0)
| ~ in(ordered_pair(X1,X2),esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,negated_conjecture,
( X1 = ordered_pair(esk5_1(X1),esk6_1(X1))
| ~ in(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( esk4_0 = X1
| in(esk9_2(esk4_0,X1),esk3_0)
| in(esk9_2(esk4_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_8]),c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( X1 = unordered_pair(unordered_pair(esk5_1(X1),esk6_1(X1)),singleton(esk5_1(X1)))
| ~ in(X1,esk3_0) ),
inference(rw,[status(thm)],[c_0_20,c_0_8]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ in(esk9_2(X1,X2),X1)
| ~ in(esk9_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
in(esk9_2(esk4_0,esk3_0),esk3_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_21]),c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_28,negated_conjecture,
( unordered_pair(singleton(esk5_1(X1)),unordered_pair(esk5_1(X1),esk6_1(X1))) = X1
| ~ in(X1,esk3_0) ),
inference(rw,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk9_2(esk4_0,esk3_0),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET959+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:40:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------