%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET585+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 : n025.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 0.27s 1.61s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 33
% Syntax : Number of formulae : 71 ( 28 unt; 0 def)
% Number of atoms : 162 ( 51 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 161 ( 70 ~; 73 |; 11 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 170 ( 8 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_subset_of_union,conjecture,
! [X1,X2,X3] : subset(intersection(X1,X2),union(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_subset_of_union) ).
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(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_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(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(transitivity_of_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subset) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(i_0_11,negated_conjecture,
~ ! [X1,X2,X3] : subset(intersection(X1,X2),union(X1,X3)),
inference(assume_negation,[status(cth)],[prove_intersection_subset_of_union]) ).
fof(i_0_12,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( ~ member(X57,X55)
| member(X57,X56)
| X55 != X56 )
& ( ~ member(X58,X56)
| member(X58,X55)
| X55 != X56 )
& ( ~ member(esk2_2(X59,X60),X59)
| ~ member(esk2_2(X59,X60),X60)
| X59 = X60 )
& ( member(esk2_2(X59,X60),X59)
| member(esk2_2(X59,X60),X60)
| X59 = X60 ) ),
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_13,plain,
! [X38,X39,X40] :
( ( ~ member(X40,union(X38,X39))
| member(X40,X38)
| member(X40,X39) )
& ( ~ member(X40,X38)
| member(X40,union(X38,X39)) )
& ( ~ member(X40,X39)
| member(X40,union(X38,X39)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(i_0_14,plain,
! [X41,X42,X43] :
( ( member(X43,X41)
| ~ member(X43,intersection(X41,X42)) )
& ( member(X43,X42)
| ~ member(X43,intersection(X41,X42)) )
& ( ~ member(X43,X41)
| ~ member(X43,X42)
| member(X43,intersection(X41,X42)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(i_0_15,negated_conjecture,
~ subset(intersection(esk3_0,esk4_0),union(esk3_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_11])])]) ).
fof(i_0_16,plain,
! [X44,X45,X46,X47,X48] :
( ( ~ subset(X44,X45)
| ~ member(X46,X44)
| member(X46,X45) )
& ( member(esk1_2(X47,X48),X47)
| subset(X47,X48) )
& ( ~ member(esk1_2(X47,X48),X48)
| subset(X47,X48) ) ),
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_17,plain,
! [X31,X32,X33] :
( ~ subset(X31,X32)
| ~ subset(X32,X33)
| subset(X31,X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_subset])]) ).
fof(i_0_18,plain,
! [X36,X37] : subset(intersection(X36,X37),X36),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
fof(i_0_19,plain,
! [X34,X35] : subset(X34,union(X34,X35)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
fof(i_0_20,plain,
! [X52,X53] : intersection(X52,X53) = intersection(X53,X52),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(i_0_21,plain,
! [X50,X51] : union(X50,X51) = union(X51,X50),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(i_0_22,plain,
! [X54] : subset(X54,X54),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(i_0_23,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_24,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_25,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_26,negated_conjecture,
~ subset(intersection(esk3_0,esk4_0),union(esk3_0,esk5_0)),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_27,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_28,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_29,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_30,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_31,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_32,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_33,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_34,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_35,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_36,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_37,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_38,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_39,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_40,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_41,axiom,
X1 = X1 ).
cnf(i_0_42,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_43,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_44,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| intersection(X1,X3) = intersection(X2,X3) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| intersection(X3,X1) = intersection(X3,X2) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_41_001,axiom,
X1 = X1 ).
cnf(i_0_42_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_43_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_44_004,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_45_005,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_46_006,axiom,
( X1 != X2
| intersection(X1,X3) = intersection(X2,X3) ) ).
cnf(i_0_47_007,axiom,
( X1 != X2
| intersection(X3,X1) = intersection(X3,X2) ) ).
cnf(i_0_48_008,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_49_009,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_50_010,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_51_011,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_52,plain,
~ subset(intersection(esk3_0,esk4_0),intersection(union(esk3_0,esk5_0),X1)),
inference(scs_inference,[],[i_0_26,i_0_36,i_0_34]) ).
cnf(i_0_53,plain,
subset(intersection(X1,X2),X1),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_54,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_55,plain,
~ subset(intersection(esk4_0,esk3_0),union(esk3_0,esk5_0)),
inference(scs_inference,[],[i_0_26,i_0_38,i_0_36,i_0_34,i_0_50]) ).
cnf(i_0_56,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_57,plain,
~ subset(intersection(esk3_0,esk4_0),union(esk5_0,esk3_0)),
inference(scs_inference,[],[i_0_26,i_0_38,i_0_39,i_0_36,i_0_34,i_0_50,i_0_51]) ).
cnf(i_0_58,plain,
union(X1,X2) = union(X2,X1),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_59,plain,
$false,
inference(scs_inference,[],[i_0_26,i_0_37,i_0_36,i_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET585+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
% 0.16/0.33 % Computer : n025.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 02:28:43 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.27/1.61 % Version : CSE_E---1.7
% 0.27/1.61 % Problem : theBenchmark.p
% 0.27/1.61 % SZS status Theorem for theBenchmark.p
% 0.27/1.61 % SZS output start CNFRefutation
% See solution above
% 0.27/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------