%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET886+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 : n017.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 05:08:54 PM UTC 2026
% Result : Theorem 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 15 unt; 0 def)
% Number of atoms : 31 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 4 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t27_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> unordered_pair(X1,X2) = singleton(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
fof(t26_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [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] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> unordered_pair(X1,X2) = singleton(X3) ),
inference(assume_negation,[status(cth)],[t27_zfmisc_1]) ).
fof(c_0_5,plain,
! [X22,X23,X24] :
( ~ subset(unordered_pair(X22,X23),singleton(X24))
| X22 = X24 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_zfmisc_1])]) ).
fof(c_0_6,plain,
! [X28] : unordered_pair(X28,X28) = singleton(X28),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,negated_conjecture,
( subset(unordered_pair(esk3_0,esk4_0),singleton(esk5_0))
& unordered_pair(esk3_0,esk4_0) != singleton(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( X1 = X3
| ~ subset(unordered_pair(X1,X2),singleton(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X17,X18] : unordered_pair(X17,X18) = unordered_pair(X18,X17),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( X1 = X3
| ~ subset(unordered_pair(X1,X2),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),unordered_pair(esk5_0,esk5_0)),
inference(rw,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
unordered_pair(esk3_0,esk4_0) != singleton(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
esk5_0 = esk3_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
unordered_pair(esk5_0,esk5_0) != unordered_pair(esk3_0,esk4_0),
inference(rw,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ subset(unordered_pair(X3,X1),unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),unordered_pair(esk3_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_16]),c_0_16]) ).
cnf(c_0_20,negated_conjecture,
unordered_pair(esk3_0,esk4_0) != unordered_pair(esk3_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16]),c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk4_0 = esk3_0,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET886+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n017.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 02:37:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------