%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET876+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 05:08:53 PM UTC 2026
% Result : Theorem 0.28s 1.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 23)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(l28_zfmisc_1,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(t17_zfmisc_1,conjecture,
! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_7,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_8,plain,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_9,negated_conjecture,
~ ! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
inference(assume_negation,[status(cth)],[t17_zfmisc_1]) ).
fof(i_0_10,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_11,plain,
! [X19,X20,X21,X22,X23,X24] :
( ( ~ in(X21,X20)
| X21 = X19
| X20 != singleton(X19) )
& ( X22 != X19
| in(X22,X20)
| X20 != singleton(X19) )
& ( ~ in(esk1_2(X23,X24),X24)
| esk1_2(X23,X24) != X23
| X24 = singleton(X23) )
& ( in(esk1_2(X23,X24),X24)
| esk1_2(X23,X24) = X23
| X24 = singleton(X23) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).
fof(i_0_12,plain,
! [X17,X18] :
( ~ in(X17,X18)
| ~ in(X18,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])]) ).
fof(i_0_13,plain,
! [X30,X31] :
( ~ disjoint(X30,X31)
| disjoint(X31,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_14,plain,
! [X26,X27] :
( in(X26,X27)
| disjoint(singleton(X26),X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])]) ).
fof(i_0_15,negated_conjecture,
( esk4_0 != esk5_0
& ~ disjoint(singleton(esk4_0),singleton(esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])])]) ).
fof(i_0_16,plain,
~ empty(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_10])]) ).
fof(i_0_17,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_18,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_19,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_20,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_21,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_22,plain,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_23,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_24,negated_conjecture,
~ disjoint(singleton(esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_25,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_26,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_27,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_28,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_29,axiom,
X1 = X1 ).
cnf(i_0_30,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_31,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_32,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_33,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_34,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_29_001,axiom,
X1 = X1 ).
cnf(i_0_30_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_31_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_32_004,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_33_005,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_34_006,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_35_007,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_36_008,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_37_009,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_38_010,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_39_011,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_40,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(equality_inference,[],[23]) ).
cnf(i_0_41,plain,
in(esk4_0,singleton(esk5_0)),
inference(scs_inference,[],[i_0_24,i_0_22]) ).
cnf(i_0_42,plain,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_43,plain,
$false,
inference(scs_inference,[],[i_0_24,i_0_28,i_0_22,i_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET876+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 02:36:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.28/1.62 % Version : CSE_E---1.7
% 0.28/1.62 % Problem : theBenchmark.p
% 0.28/1.62 % SZS status Theorem for theBenchmark.p
% 0.28/1.62 % SZS output start CNFRefutation
% See solution above
% 0.28/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------