%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET581+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n016.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 05:08:02 PM UTC 2026
% Result : Theorem 0.22s 1.63s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 25)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th24,conjecture,
! [X1,X2,X3] :
( ( member(X1,X2)
& member(X1,X3) )
=> not_equal(intersection(X2,X3),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th24) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(i_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( member(X1,X2)
& member(X1,X3) )
=> not_equal(intersection(X2,X3),empty_set) ),
inference(assume_negation,[status(cth)],[prove_th24]) ).
fof(i_0_8,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(i_0_9,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(i_0_10,plain,
! [X24,X25,X26,X27,X28,X29] :
( ( ~ member(X26,X24)
| member(X26,X25)
| X24 != X25 )
& ( ~ member(X27,X25)
| member(X27,X24)
| X24 != X25 )
& ( ~ member(esk1_2(X28,X29),X28)
| ~ member(esk1_2(X28,X29),X29)
| X28 = X29 )
& ( member(esk1_2(X28,X29),X28)
| member(esk1_2(X28,X29),X29)
| 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)],[equal_member_defn])])])])])]) ).
fof(i_0_11,plain,
! [X20,X21,X22] :
( ( member(X22,X20)
| ~ member(X22,intersection(X20,X21)) )
& ( member(X22,X21)
| ~ member(X22,intersection(X20,X21)) )
& ( ~ member(X22,X20)
| ~ member(X22,X21)
| member(X22,intersection(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(i_0_12,negated_conjecture,
( member(esk3_0,esk4_0)
& member(esk3_0,esk5_0)
& ~ not_equal(intersection(esk4_0,esk5_0),empty_set) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])])]) ).
fof(i_0_13,plain,
! [X35,X36,X37] :
( ( ~ empty(X35)
| ~ member(X36,X35) )
& ( member(esk2_1(X37),X37)
| empty(X37) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])])])])]) ).
fof(i_0_14,plain,
! [X33,X34] : intersection(X33,X34) = intersection(X34,X33),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(i_0_15,plain,
! [X31,X32] :
( ( ~ not_equal(X31,X32)
| X31 != X32 )
& ( X31 = X32
| not_equal(X31,X32) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[not_equal_defn])]) ).
fof(i_0_16,plain,
! [X23] : ~ member(X23,empty_set),
inference(variable_rename,[status(thm)],[i_0_9]) ).
cnf(i_0_17,plain,
( X1 = X2
| ~ member(esk1_2(X1,X2),X1)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_18,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_19,plain,
( member(esk1_2(X1,X2),X1)
| member(esk1_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_20,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_21,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_22,negated_conjecture,
~ not_equal(intersection(esk4_0,esk5_0),empty_set),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_23,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_25,plain,
( ~ not_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_26,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_27,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_28,plain,
( X1 = X2
| not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_29,negated_conjecture,
member(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_30,negated_conjecture,
member(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_12]),
[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
| intersection(X1,X3) = intersection(X2,X3) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| intersection(X3,X1) = intersection(X3,X2) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| ~ not_equal(X1,X3)
| not_equal(X2,X3) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| ~ not_equal(X3,X1)
| not_equal(X3,X2) ) ).
cnf(i_0_40,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
| intersection(X1,X3) = intersection(X2,X3) ) ).
cnf(i_0_35_005,axiom,
( X1 != X2
| intersection(X3,X1) = intersection(X3,X2) ) ).
cnf(i_0_36_006,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_37_007,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_38_008,axiom,
( X1 != X2
| ~ not_equal(X1,X3)
| not_equal(X2,X3) ) ).
cnf(i_0_39_009,axiom,
( X1 != X2
| ~ not_equal(X3,X1)
| not_equal(X3,X2) ) ).
cnf(i_0_40_010,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_41,plain,
~ not_equal(X1,X1),
inference(equality_inference,[],[25]) ).
cnf(i_0_42,plain,
intersection(esk4_0,esk5_0) = empty_set,
inference(scs_inference,[],[i_0_22,i_0_28]) ).
cnf(i_0_43,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_44,plain,
~ not_equal(intersection(X1,X2),intersection(X2,X1)),
inference(scs_inference,[],[i_0_22,i_0_24,i_0_28,i_0_25]) ).
cnf(i_0_45,plain,
( X1 != X2
| ~ not_equal(X1,X2) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_46,plain,
empty(empty_set),
inference(scs_inference,[],[i_0_22,i_0_27,i_0_24,i_0_28,i_0_25,i_0_26]) ).
cnf(i_0_47,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_48,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_49,plain,
empty_set = intersection(esk4_0,esk5_0),
inference(scs_inference,[],[i_0_22,i_0_27,i_0_24,i_0_28,i_0_25,i_0_26,i_0_32]) ).
cnf(i_0_50,plain,
~ member(X1,intersection(esk4_0,esk5_0)),
inference(scs_inference,[],[i_0_22,i_0_27,i_0_47,i_0_24,i_0_28,i_0_25,i_0_26,i_0_32,i_0_37]) ).
cnf(i_0_51,plain,
~ not_equal(intersection(esk5_0,esk4_0),empty_set),
inference(scs_inference,[],[i_0_22,i_0_27,i_0_47,i_0_24,i_0_28,i_0_25,i_0_26,i_0_32,i_0_37,i_0_38]) ).
cnf(i_0_52,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_53,plain,
intersection(esk5_0,esk4_0) = empty_set,
inference(scs_inference,[],[i_0_22,i_0_27,i_0_47,i_0_24,i_0_52,i_0_28,i_0_25,i_0_26,i_0_32,i_0_37,i_0_38,i_0_33]) ).
cnf(i_0_54,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_55,plain,
empty(intersection(esk4_0,esk5_0)),
inference(scs_inference,[],[i_0_22,i_0_27,i_0_47,i_0_24,i_0_52,i_0_28,i_0_25,i_0_26,i_0_32,i_0_37,i_0_38,i_0_33,i_0_40]) ).
cnf(i_0_56,plain,
$false,
inference(scs_inference,[],[i_0_22,i_0_29,i_0_30,i_0_27,i_0_47,i_0_24,i_0_52,i_0_28,i_0_25,i_0_26,i_0_32,i_0_37,i_0_38,i_0_33,i_0_40,i_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET581+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n016.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 02:28:36 EDT 2026
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % start to proof: theBenchmark
% 0.22/1.63 % Version : CSE_E---1.7
% 0.22/1.63 % Problem : theBenchmark.p
% 0.22/1.63 % SZS status Theorem for theBenchmark.p
% 0.22/1.63 % SZS output start CNFRefutation
% See solution above
% 0.22/1.68 % Total time : 1.272s
%------------------------------------------------------------------------------