%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET618+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 : n023.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 05:08:09 PM UTC 2026
% Result : Theorem 0.27s 1.63s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_19)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th93,conjecture,
! [X1] : symmetric_difference(X1,X1) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th93) ).
fof(commutativity_of_symmetric_difference,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
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(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(idempotency_of_union,axiom,
! [X1] : union(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotency_of_union) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(self_difference_is_empty_set,axiom,
! [X1] : difference(X1,X1) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
fof(i_0_12,negated_conjecture,
~ ! [X1] : symmetric_difference(X1,X1) = empty_set,
inference(assume_negation,[status(cth)],[prove_th93]) ).
fof(i_0_13,plain,
! [X34,X35] : symmetric_difference(X34,X35) = symmetric_difference(X35,X34),
inference(variable_rename,[status(thm)],[commutativity_of_symmetric_difference]) ).
fof(i_0_14,plain,
! [X25,X26] : symmetric_difference(X25,X26) = union(difference(X25,X26),difference(X26,X25)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(i_0_15,negated_conjecture,
symmetric_difference(esk4_0,esk4_0) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])])]) ).
fof(i_0_16,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(i_0_17,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
cnf(i_0_18,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_13]) ).
cnf(i_0_19,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_14]) ).
fof(i_0_20,plain,
! [X36,X37,X38,X39,X40,X41] :
( ( ~ member(X38,X36)
| member(X38,X37)
| X36 != X37 )
& ( ~ member(X39,X37)
| member(X39,X36)
| X36 != X37 )
& ( ~ member(esk1_2(X40,X41),X40)
| ~ member(esk1_2(X40,X41),X41)
| X40 = X41 )
& ( member(esk1_2(X40,X41),X40)
| member(esk1_2(X40,X41),X41)
| X40 = X41 ) ),
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])])])])])]) ).
cnf(i_0_21,negated_conjecture,
symmetric_difference(esk4_0,esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_15]) ).
fof(i_0_22,plain,
! [X43,X44,X45,X46,X47] :
( ( ~ subset(X43,X44)
| ~ member(X45,X43)
| member(X45,X44) )
& ( member(esk2_2(X46,X47),X46)
| subset(X46,X47) )
& ( ~ member(esk2_2(X46,X47),X47)
| subset(X46,X47) ) ),
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)],[subset_defn])])])])])]) ).
fof(i_0_23,plain,
! [X30,X31] :
( ( subset(X30,X31)
| X30 != X31 )
& ( subset(X31,X30)
| X30 != X31 )
& ( ~ subset(X30,X31)
| ~ subset(X31,X30)
| X30 = X31 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
fof(i_0_24,plain,
! [X50,X51,X52] :
( ( ~ empty(X50)
| ~ member(X51,X50) )
& ( member(esk3_1(X52),X52)
| empty(X52) ) ),
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_16])])])])]) ).
fof(i_0_25,plain,
! [X32,X33] : union(X32,X33) = union(X33,X32),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(i_0_26,plain,
! [X29] : ~ member(X29,empty_set),
inference(variable_rename,[status(thm)],[i_0_17]) ).
fof(i_0_27,plain,
! [X27] : union(X27,X27) = X27,
inference(variable_rename,[status(thm)],[idempotency_of_union]) ).
fof(i_0_28,plain,
! [X49] : subset(X49,X49),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
fof(i_0_29,plain,
! [X28] : difference(X28,X28) = empty_set,
inference(variable_rename,[status(thm)],[self_difference_is_empty_set]) ).
cnf(i_0_30,plain,
union(difference(X1,X2),difference(X2,X1)) = union(difference(X2,X1),difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_18,c_0_19]),c_0_19]),
[final] ).
cnf(i_0_31,plain,
( X1 = X2
| ~ member(esk1_2(X1,X2),X1)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_32,negated_conjecture,
union(difference(esk4_0,esk4_0),difference(esk4_0,esk4_0)) != empty_set,
inference(rw,[status(thm)],[i_0_21,c_0_19]),
[final] ).
cnf(i_0_33,plain,
( member(esk1_2(X1,X2),X1)
| member(esk1_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_34,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_35,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_36,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_37,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_38,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_39,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_40,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_41,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_42,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_43,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_44,plain,
union(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_45,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_46,plain,
difference(X1,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_47,axiom,
X1 = X1 ).
cnf(i_0_48,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_49,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_50,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_52,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_53,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_54,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_55,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_56,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_57,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_47_001,axiom,
X1 = X1 ).
cnf(i_0_48_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_49_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_50_004,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_51_005,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_52_006,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_53_007,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_54_008,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_55_009,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_56_010,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_57_011,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_58_012,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_59,plain,
subset(X1,X1),
inference(equality_inference,[],[42]) ).
cnf(i_0_60,plain,
subset(X1,X1),
inference(equality_inference,[],[43]) ).
cnf(i_0_61,plain,
subset(union(X1,X1),X1),
inference(scs_inference,[],[i_0_44,i_0_42]) ).
cnf(i_0_62,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_63,plain,
X1 = union(X1,X1),
inference(scs_inference,[],[i_0_44,i_0_42,i_0_48]) ).
cnf(i_0_64,plain,
subset(X1,union(X1,X1)),
inference(scs_inference,[],[i_0_44,i_0_42,i_0_48,i_0_43]) ).
cnf(i_0_65,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_66,plain,
subset(empty_set,X1),
inference(scs_inference,[],[i_0_41,i_0_44,i_0_42,i_0_48,i_0_43,i_0_36]) ).
cnf(i_0_67,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_68,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_69,plain,
empty(empty_set),
inference(scs_inference,[],[i_0_41,i_0_67,i_0_44,i_0_42,i_0_48,i_0_43,i_0_36,i_0_40]) ).
cnf(i_0_70,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_71,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_72,plain,
union(difference(esk4_0,esk4_0),difference(esk4_0,esk4_0)) != union(empty_set,empty_set),
inference(scs_inference,[],[i_0_32,i_0_41,i_0_67,i_0_44,i_0_42,i_0_48,i_0_43,i_0_36,i_0_40,i_0_49]) ).
cnf(i_0_73,plain,
union(X1,X1) = X1,
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_74,plain,
~ member(X1,union(empty_set,empty_set)),
inference(scs_inference,[],[i_0_32,i_0_41,i_0_67,i_0_70,i_0_44,i_0_73,i_0_42,i_0_48,i_0_43,i_0_36,i_0_40,i_0_49,i_0_55]) ).
cnf(i_0_75,plain,
union(X1,X1) = X1,
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_76,plain,
empty(union(empty_set,empty_set)),
inference(scs_inference,[],[i_0_32,i_0_41,i_0_67,i_0_70,i_0_44,i_0_73,i_0_42,i_0_48,i_0_43,i_0_36,i_0_40,i_0_49,i_0_55,i_0_58]) ).
cnf(i_0_77,plain,
subset(union(X1,X2),union(X2,X1)),
inference(scs_inference,[],[i_0_39,i_0_42]) ).
cnf(i_0_78,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_79,plain,
subset(union(empty_set,empty_set),X1),
inference(scs_inference,[],[i_0_74,i_0_39,i_0_42,i_0_36]) ).
cnf(i_0_80,plain,
~ member(X1,union(empty_set,empty_set)),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_81,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_82,plain,
empty_set = difference(X1,X1),
inference(scs_inference,[],[i_0_74,i_0_39,i_0_46,i_0_42,i_0_36,i_0_48]) ).
cnf(i_0_83,plain,
$false,
inference(scs_inference,[],[i_0_32,i_0_74,i_0_39,i_0_46,i_0_44,i_0_42,i_0_36,i_0_48,i_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET618+3 : TPTP v9.2.1. Released v2.2.0.
% 0.12/0.13 % 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
% 0.15/0.34 % Computer : n023.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:31:09 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 0.27/1.63 % Version : CSE_E---1.7
% 0.27/1.63 % Problem : theBenchmark.p
% 0.27/1.63 % SZS status Theorem for theBenchmark.p
% 0.27/1.63 % SZS output start CNFRefutation
% See solution above
% 0.27/1.69 % Total time : 1.272s
%------------------------------------------------------------------------------