%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET902+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 05:08:56 PM UTC 2026
% Result : Theorem 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 18 unt; 0 def)
% Number of atoms : 70 ( 58 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 32 ~; 19 |; 17 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t43_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(l1_zfmisc_1,axiom,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(c_0_6,plain,
! [X40,X41] : subset(X40,set_union2(X40,X41)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_7,plain,
! [X24,X25] : set_union2(X24,X25) = set_union2(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
inference(assume_negation,[status(cth)],[t43_zfmisc_1]) ).
cnf(c_0_9,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( singleton(esk3_0) = set_union2(esk4_0,esk5_0)
& ( esk4_0 != singleton(esk3_0)
| esk5_0 != singleton(esk3_0) )
& ( esk4_0 != empty_set
| esk5_0 != singleton(esk3_0) )
& ( esk4_0 != singleton(esk3_0)
| esk5_0 != empty_set ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X32,X33] :
( ( ~ subset(X32,singleton(X33))
| X32 = empty_set
| X32 = singleton(X33) )
& ( X32 != empty_set
| subset(X32,singleton(X33)) )
& ( X32 != singleton(X33)
| subset(X32,singleton(X33)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
cnf(c_0_13,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
singleton(esk3_0) = set_union2(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subset(esk5_0,singleton(esk3_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
subset(esk4_0,singleton(esk3_0)),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( esk4_0 != empty_set
| esk5_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( singleton(esk3_0) = esk5_0
| esk5_0 = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( esk4_0 != singleton(esk3_0)
| esk5_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( singleton(esk3_0) = esk4_0
| esk4_0 = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( esk4_0 != singleton(esk3_0)
| esk5_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
( esk5_0 = empty_set
| esk4_0 != empty_set ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk4_0 = empty_set
| esk5_0 != empty_set ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( esk4_0 = empty_set
| esk5_0 != esk4_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
fof(c_0_26,plain,
! [X30] : set_union2(X30,X30) = X30,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(c_0_27,plain,
! [X31] : singleton(X31) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_28,negated_conjecture,
( set_union2(empty_set,esk4_0) = singleton(esk3_0)
| esk4_0 != empty_set ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_10]) ).
cnf(c_0_29,negated_conjecture,
esk4_0 = empty_set,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_29])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET902+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
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 5 02:39:13 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Theorem for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------