%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET700+4 : 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 : n027.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 05:08:21 PM UTC 2026
% Result : Theorem 127.42s 57.60s
% Output : CNFRefutation 127.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 16 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 141 ( 56 ~; 58 |; 17 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 16 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(thI34,conjecture,
! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI34) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(c_0_6,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),X2) ) ),
inference(assume_negation,[status(cth)],[thI34]) ).
fof(c_0_8,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_9,plain,
! [X47,X48,X49] :
( ( member(X47,X48)
| ~ member(X47,intersection(X48,X49)) )
& ( member(X47,X49)
| ~ member(X47,intersection(X48,X49)) )
& ( ~ member(X47,X48)
| ~ member(X47,X49)
| member(X47,intersection(X48,X49)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
fof(c_0_10,plain,
! [X37,X38,X39,X40,X41] :
( ( ~ subset(X37,X38)
| ~ member(X39,X37)
| member(X39,X38) )
& ( member(esk1_2(X40,X41),X40)
| subset(X40,X41) )
& ( ~ member(esk1_2(X40,X41),X41)
| subset(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)],[subset])])])])])]) ).
fof(c_0_11,plain,
! [X53] : ~ member(X53,empty_set),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( subset(esk4_0,esk6_0)
& subset(esk5_0,esk6_0)
& ( ~ subset(esk4_0,esk5_0)
| ~ subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0) )
& ( subset(esk4_0,esk5_0)
| subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_13,plain,
! [X54,X55,X56] :
( ( member(X54,X56)
| ~ member(X54,difference(X56,X55)) )
& ( ~ member(X54,X55)
| ~ member(X54,difference(X56,X55)) )
& ( ~ member(X54,X56)
| member(X54,X55)
| member(X54,difference(X56,X55)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X43,X44] :
( ( subset(X43,X44)
| ~ equal_set(X43,X44) )
& ( subset(X44,X43)
| ~ equal_set(X43,X44) )
& ( ~ subset(X43,X44)
| ~ subset(X44,X43)
| equal_set(X43,X44) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_17,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( subset(esk4_0,esk5_0)
| subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( member(X1,esk5_0)
| subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk6_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
( equal_set(X1,empty_set)
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( subset(intersection(esk4_0,difference(esk6_0,esk5_0)),X1)
| subset(esk4_0,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_15]),c_0_25]) ).
cnf(c_0_29,plain,
( member(X1,X2)
| ~ equal_set(X3,X2)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( equal_set(intersection(esk4_0,difference(esk6_0,esk5_0)),empty_set)
| subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk6_0,esk5_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_17]) ).
cnf(c_0_32,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,negated_conjecture,
subset(esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,negated_conjecture,
( subset(esk4_0,esk5_0)
| ~ member(X1,difference(esk6_0,esk5_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_36,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_37,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_18]) ).
cnf(c_0_39,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_40,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_42,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_43,negated_conjecture,
( member(esk1_2(difference(esk4_0,X1),X2),esk5_0)
| subset(difference(esk4_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( member(esk1_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3))
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
cnf(c_0_45,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_15]) ).
cnf(c_0_46,negated_conjecture,
subset(difference(esk4_0,esk5_0),X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
( member(esk1_2(intersection(X1,X2),difference(X1,X3)),X3)
| subset(intersection(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( equal_set(X1,difference(esk4_0,esk5_0))
| ~ subset(X1,difference(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_46]) ).
cnf(c_0_49,plain,
subset(intersection(X1,difference(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
equal_set(difference(esk4_0,esk5_0),empty_set),
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( member(esk1_2(esk4_0,X1),esk5_0)
| subset(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_15]) ).
cnf(c_0_52,negated_conjecture,
equal_set(intersection(esk4_0,difference(X1,esk5_0)),difference(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
~ member(X1,difference(esk4_0,esk5_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_50]),c_0_17]) ).
cnf(c_0_54,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_55,negated_conjecture,
subset(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
~ member(X1,intersection(esk4_0,difference(X2,esk5_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_52]),c_0_53]) ).
cnf(c_0_57,negated_conjecture,
~ subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
subset(intersection(esk4_0,difference(X1,esk5_0)),X2),
inference(spm,[status(thm)],[c_0_56,c_0_15]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET700+4 : 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
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:32:35 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 127.42/57.60 % Version : CSE_E---1.7
% 127.42/57.60 % Problem : theBenchmark.p
% 127.42/57.60 % SZS status Theorem for theBenchmark.p
% 127.42/57.60 % SZS output start CNFRefutation
% See solution above
% 127.85/58.04 % Total time : 42.895s
%------------------------------------------------------------------------------