%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET881+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 : n031.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 0.26s 1.61s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 22)
% Comments :
%------------------------------------------------------------------------------
fof(t22_zfmisc_1,conjecture,
! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(l36_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = empty_set
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
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(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_8,negated_conjecture,
~ ! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
inference(assume_negation,[status(cth)],[t22_zfmisc_1]) ).
fof(i_0_9,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
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,X29,X30] :
( ( ~ in(X26,X25)
| X26 = X23
| X26 = X24
| X25 != unordered_pair(X23,X24) )
& ( X27 != X23
| in(X27,X25)
| X25 != unordered_pair(X23,X24) )
& ( X27 != X24
| in(X27,X25)
| X25 != unordered_pair(X23,X24) )
& ( esk1_3(X28,X29,X30) != X28
| ~ in(esk1_3(X28,X29,X30),X30)
| X30 = unordered_pair(X28,X29) )
& ( esk1_3(X28,X29,X30) != X29
| ~ in(esk1_3(X28,X29,X30),X30)
| X30 = unordered_pair(X28,X29) )
& ( in(esk1_3(X28,X29,X30),X30)
| esk1_3(X28,X29,X30) = X28
| esk1_3(X28,X29,X30) = X29
| X30 = unordered_pair(X28,X29) ) ),
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)],[d2_tarski])])])])])]) ).
fof(i_0_12,negated_conjecture,
set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])])]) ).
fof(i_0_13,plain,
! [X32,X33] :
( ( set_difference(singleton(X32),X33) != empty_set
| in(X32,X33) )
& ( ~ in(X32,X33)
| set_difference(singleton(X32),X33) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l36_zfmisc_1])]) ).
fof(i_0_14,plain,
! [X19,X20] :
( ~ in(X19,X20)
| ~ in(X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])]) ).
fof(i_0_15,plain,
! [X21,X22] : unordered_pair(X21,X22) = unordered_pair(X22,X21),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
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,
( X3 = unordered_pair(X1,X2)
| esk1_3(X1,X2,X3) != X1
| ~ in(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_19,plain,
( X3 = unordered_pair(X1,X2)
| esk1_3(X1,X2,X3) != X2
| ~ in(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_20,plain,
( in(esk1_3(X1,X2,X3),X3)
| esk1_3(X1,X2,X3) = X1
| esk1_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_21,negated_conjecture,
set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_22,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_23,plain,
( in(X1,X2)
| set_difference(singleton(X1),X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_25,plain,
( set_difference(singleton(X1),X2) = empty_set
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_26,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_27,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_28,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_29,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_30,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_32,axiom,
X1 = X1 ).
cnf(i_0_33,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| esk1_3(X1,X3,X4) = esk1_3(X2,X3,X4) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| esk1_3(X3,X1,X4) = esk1_3(X3,X2,X4) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| esk1_3(X3,X4,X1) = esk1_3(X3,X4,X2) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_41,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_32_001,axiom,
X1 = X1 ).
cnf(i_0_33_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_36_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_37_006,axiom,
( X1 != X2
| esk1_3(X1,X3,X4) = esk1_3(X2,X3,X4) ) ).
cnf(i_0_38_007,axiom,
( X1 != X2
| esk1_3(X3,X1,X4) = esk1_3(X3,X2,X4) ) ).
cnf(i_0_39_008,axiom,
( X1 != X2
| esk1_3(X3,X4,X1) = esk1_3(X3,X4,X2) ) ).
cnf(i_0_40_009,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_41_010,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_42_011,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_43_012,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_44_013,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_45,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[22]) ).
cnf(i_0_46,plain,
~ in(esk4_0,unordered_pair(esk4_0,esk5_0)),
inference(scs_inference,[],[i_0_21,i_0_25]) ).
cnf(i_0_47,plain,
( set_difference(singleton(X1),X2) = empty_set
| ~ in(X1,X2) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_48,plain,
esk4_0 != esk5_0,
inference(scs_inference,[],[i_0_21,i_0_28,i_0_25,i_0_26]) ).
cnf(i_0_49,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_50,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_52,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_53,plain,
~ in(esk4_0,unordered_pair(esk5_0,esk4_0)),
inference(scs_inference,[],[i_0_21,i_0_28,i_0_49,i_0_52,i_0_25,i_0_26,i_0_27,i_0_43]) ).
cnf(i_0_54,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_55,plain,
esk2_0 != esk3_0,
inference(scs_inference,[],[i_0_21,i_0_28,i_0_49,i_0_52,i_0_29,i_0_30,i_0_25,i_0_26,i_0_27,i_0_43,i_0_44]) ).
cnf(i_0_56,plain,
~ in(set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_21,i_0_28,i_0_49,i_0_52,i_0_54,i_0_29,i_0_30,i_0_25,i_0_26,i_0_27,i_0_43,i_0_44,i_0_22]) ).
cnf(i_0_57,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_58,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_59,plain,
( X1 != esk4_0
| ~ in(X1,unordered_pair(esk4_0,esk5_0)) ),
inference(scs_inference,[],[i_0_21,i_0_28,i_0_49,i_0_52,i_0_54,i_0_29,i_0_30,i_0_25,i_0_26,i_0_27,i_0_43,i_0_44,i_0_22,i_0_42]) ).
cnf(i_0_60,plain,
~ in(esk4_0,unordered_pair(esk4_0,esk5_0)),
inference(equality_inference,[],[59]) ).
cnf(i_0_62,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_63,plain,
empty_set != esk3_0,
inference(scs_inference,[],[i_0_46,i_0_31,i_0_28,i_0_29,i_0_27,i_0_44]) ).
cnf(i_0_64,plain,
( X1 != set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0))
| ~ in(X1,unordered_pair(empty_set,empty_set)) ),
inference(scs_inference,[],[i_0_46,i_0_56,i_0_31,i_0_28,i_0_29,i_0_27,i_0_44,i_0_42]) ).
cnf(i_0_65,plain,
~ in(set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)),unordered_pair(empty_set,empty_set)),
inference(equality_inference,[],[64]) ).
cnf(i_0_67,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_68,plain,
( X1 != esk4_0
| ~ in(X1,unordered_pair(esk5_0,esk4_0)) ),
inference(scs_inference,[],[i_0_46,i_0_53,i_0_28,i_0_27,i_0_42]) ).
cnf(i_0_69,plain,
~ in(esk4_0,unordered_pair(esk5_0,esk4_0)),
inference(equality_inference,[],[68]) ).
cnf(i_0_71,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_73,plain,
$false,
inference(scs_inference,[],[i_0_46,i_0_28,i_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET881+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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:40:38 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.26/1.61 % Version : CSE_E---1.7
% 0.26/1.61 % Problem : theBenchmark.p
% 0.26/1.61 % SZS status Theorem for theBenchmark.p
% 0.26/1.61 % SZS output start CNFRefutation
% See solution above
% 0.26/1.67 % Total time : 1.271s
%------------------------------------------------------------------------------