%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET877+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 : n029.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 0.78s 1.61s
% Output : CNFRefutation 0.88s
% 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(t18_zfmisc_1,conjecture,
! [X1,X2] :
( set_intersection2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_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(l30_zfmisc_1,axiom,
! [X1,X2] :
( set_intersection2(X1,singleton(X2)) = singleton(X2)
=> in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_8,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_9,negated_conjecture,
~ ! [X1,X2] :
( set_intersection2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t18_zfmisc_1]) ).
fof(i_0_10,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_11,plain,
! [X23,X24,X25,X26,X27,X28] :
( ( ~ in(X25,X24)
| X25 = X23
| X24 != singleton(X23) )
& ( X26 != X23
| in(X26,X24)
| X24 != singleton(X23) )
& ( ~ in(esk1_2(X27,X28),X28)
| esk1_2(X27,X28) != X27
| X28 = singleton(X27) )
& ( in(esk1_2(X27,X28),X28)
| esk1_2(X27,X28) = X27
| X28 = singleton(X27) ) ),
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,
! [X31,X32] :
( set_intersection2(X31,singleton(X32)) != singleton(X32)
| in(X32,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l30_zfmisc_1])]) ).
fof(i_0_13,plain,
! [X19,X20] :
( ~ in(X19,X20)
| ~ in(X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])]) ).
fof(i_0_14,plain,
! [X21,X22] : set_intersection2(X21,X22) = set_intersection2(X22,X21),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_15,negated_conjecture,
( set_intersection2(singleton(esk4_0),singleton(esk5_0)) = singleton(esk4_0)
& esk4_0 != esk5_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])])]) ).
fof(i_0_16,plain,
! [X30] : set_intersection2(X30,X30) = X30,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_17,plain,
~ empty(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_10])]) ).
fof(i_0_18,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_19,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_20,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_21,plain,
( in(X2,X1)
| set_intersection2(X1,singleton(X2)) != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_22,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[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,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_14]),
[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,negated_conjecture,
set_intersection2(singleton(esk4_0),singleton(esk5_0)) = singleton(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_27,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_28,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_29,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_30,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_31,axiom,
X1 = X1 ).
cnf(i_0_32,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_33,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_34,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_41,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_31_001,axiom,
X1 = X1 ).
cnf(i_0_32_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_33_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_34_004,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_35_005,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_36_006,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_37_007,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_38_008,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_39_009,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_40_010,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_41_011,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_42,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(equality_inference,[],[23]) ).
cnf(i_0_43,plain,
singleton(esk4_0) = set_intersection2(singleton(esk4_0),singleton(esk5_0)),
inference(scs_inference,[],[i_0_26,i_0_32]) ).
cnf(i_0_44,plain,
in(X1,singleton(X1)),
inference(scs_inference,[],[i_0_26,i_0_27,i_0_32,i_0_21]) ).
cnf(i_0_45,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_46,plain,
( set_intersection2(X1,singleton(X2)) != singleton(X2)
| in(X2,X1) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_47,plain,
~ in(singleton(X1),X1),
inference(scs_inference,[],[i_0_26,i_0_27,i_0_32,i_0_21,i_0_22]) ).
cnf(i_0_48,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_49,plain,
~ in(esk4_0,set_intersection2(singleton(esk5_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_26,i_0_30,i_0_27,i_0_45,i_0_32,i_0_21,i_0_22,i_0_23]) ).
cnf(i_0_50,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_51,plain,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_52,plain,
esk4_0 != set_intersection2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_26,i_0_30,i_0_27,i_0_45,i_0_50,i_0_32,i_0_21,i_0_22,i_0_23,i_0_33]) ).
cnf(i_0_53,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_54,plain,
~ in(set_intersection2(singleton(esk4_0),singleton(esk5_0)),esk4_0),
inference(scs_inference,[],[i_0_26,i_0_30,i_0_27,i_0_45,i_0_50,i_0_32,i_0_21,i_0_22,i_0_23,i_0_33,i_0_39]) ).
cnf(i_0_55,plain,
~ in(singleton(esk4_0),set_intersection2(esk4_0,esk4_0)),
inference(scs_inference,[],[i_0_26,i_0_30,i_0_27,i_0_45,i_0_50,i_0_53,i_0_32,i_0_21,i_0_22,i_0_23,i_0_33,i_0_39,i_0_40]) ).
cnf(i_0_56,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_57,plain,
esk2_0 != esk3_0,
inference(scs_inference,[],[i_0_26,i_0_30,i_0_27,i_0_45,i_0_50,i_0_53,i_0_28,i_0_29,i_0_32,i_0_21,i_0_22,i_0_23,i_0_33,i_0_39,i_0_40,i_0_41]) ).
cnf(i_0_58,plain,
in(set_intersection2(esk4_0,esk4_0),set_intersection2(singleton(esk4_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_26,i_0_30,i_0_27,i_0_45,i_0_50,i_0_53,i_0_56,i_0_28,i_0_29,i_0_32,i_0_21,i_0_22,i_0_23,i_0_33,i_0_39,i_0_40,i_0_41,i_0_25]) ).
cnf(i_0_59,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_60,plain,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_61,plain,
~ in(set_intersection2(singleton(esk4_0),singleton(esk5_0)),set_intersection2(esk4_0,esk4_0)),
inference(scs_inference,[],[i_0_58,i_0_22]) ).
cnf(i_0_62,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_63,plain,
X1 = set_intersection2(X1,X1),
inference(scs_inference,[],[i_0_58,i_0_27,i_0_22,i_0_32]) ).
cnf(i_0_64,plain,
~ in(set_intersection2(esk4_0,esk4_0),set_intersection2(singleton(esk5_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_58,i_0_49,i_0_27,i_0_22,i_0_32,i_0_39]) ).
cnf(i_0_65,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_66,plain,
~ in(singleton(singleton(esk4_0)),set_intersection2(singleton(esk4_0),singleton(esk5_0))),
inference(scs_inference,[],[i_0_26,i_0_58,i_0_49,i_0_47,i_0_27,i_0_22,i_0_32,i_0_39,i_0_40]) ).
cnf(i_0_67,plain,
~ in(singleton(X1),X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_68,plain,
singleton(singleton(esk4_0)) != esk4_0,
inference(scs_inference,[],[i_0_26,i_0_66,i_0_25]) ).
cnf(i_0_69,plain,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_70,plain,
~ in(set_intersection2(esk4_0,esk4_0),singleton(esk5_0)),
inference(scs_inference,[],[i_0_26,i_0_63,i_0_64,i_0_66,i_0_25,i_0_40]) ).
cnf(i_0_71,plain,
X1 = set_intersection2(X1,X1),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_72,plain,
~ in(esk4_0,singleton(esk5_0)),
inference(scs_inference,[],[i_0_26,i_0_63,i_0_71,i_0_64,i_0_66,i_0_25,i_0_40,i_0_39]) ).
cnf(i_0_73,plain,
X1 = set_intersection2(X1,X1),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_74,plain,
set_intersection2(singleton(esk5_0),singleton(esk4_0)) = singleton(esk4_0),
inference(scs_inference,[],[i_0_24,i_0_26,i_0_33]) ).
cnf(i_0_75,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_76,plain,
~ in(singleton(singleton(esk4_0)),set_intersection2(singleton(esk5_0),singleton(esk4_0))),
inference(scs_inference,[],[i_0_24,i_0_75,i_0_26,i_0_66,i_0_33,i_0_40]) ).
cnf(i_0_77,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_78,plain,
~ in(set_intersection2(singleton(esk5_0),singleton(esk4_0)),esk4_0),
inference(scs_inference,[],[i_0_24,i_0_75,i_0_77,i_0_26,i_0_54,i_0_66,i_0_33,i_0_40,i_0_39]) ).
cnf(i_0_79,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_80,plain,
$false,
inference(scs_inference,[],[i_0_24,i_0_75,i_0_77,i_0_26,i_0_72,i_0_54,i_0_66,i_0_33,i_0_40,i_0_39,i_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET877+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
% 0.16/0.32 % Computer : n029.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:38:59 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.78/1.61 % Version : CSE_E---1.7
% 0.78/1.61 % Problem : theBenchmark.p
% 0.78/1.61 % SZS status Theorem for theBenchmark.p
% 0.78/1.61 % SZS output start CNFRefutation
% See solution above
% 0.88/1.71 % Total time : 1.271s
%------------------------------------------------------------------------------