%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU150+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : 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 05:10:48 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 6 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t9_zfmisc_1,conjecture,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(t8_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
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] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
inference(assume_negation,[status(cth)],[t9_zfmisc_1]) ).
fof(c_0_5,lemma,
! [X316,X317,X318] :
( singleton(X316) != unordered_pair(X317,X318)
| X316 = X317 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(c_0_6,lemma,
! [X301] : unordered_pair(X301,X301) = singleton(X301),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,negated_conjecture,
( singleton(esk14_0) = unordered_pair(esk15_0,esk16_0)
& esk15_0 != esk16_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
singleton(esk14_0) = unordered_pair(esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
unordered_pair(esk15_0,esk16_0) = unordered_pair(esk14_0,esk14_0),
inference(rw,[status(thm)],[c_0_10,c_0_9]) ).
fof(c_0_13,plain,
! [X151,X152] : unordered_pair(X151,X152) = unordered_pair(X152,X151),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,negated_conjecture,
( esk14_0 = X1
| unordered_pair(esk15_0,esk16_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
esk14_0 = esk15_0,
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_17,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
unordered_pair(esk15_0,esk16_0) = unordered_pair(esk15_0,esk15_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_16]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( X1 = esk16_0
| unordered_pair(X1,X1) != unordered_pair(esk15_0,esk15_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
esk15_0 != esk16_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU150+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:45:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------