%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET701+4 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 65.24s 38.36s
% Output : CNFRefutation 65.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 81 ( 27 unt; 0 def)
% Number of atoms : 180 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 171 ( 72 ~; 70 |; 18 &)
% ( 8 <=>; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 154 ( 25 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(thI35,conjecture,
! [X1,X2,X6,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),intersection(X6,difference(X4,X6))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI35) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(c_0_7,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
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,
! [X49,X50,X51] :
( ( member(X49,X50)
| ~ member(X49,intersection(X50,X51)) )
& ( member(X49,X51)
| ~ member(X49,intersection(X50,X51)) )
& ( ~ member(X49,X50)
| ~ member(X49,X51)
| member(X49,intersection(X50,X51)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
fof(c_0_10,plain,
! [X39,X40,X41,X42,X43] :
( ( ~ subset(X39,X40)
| ~ member(X41,X39)
| member(X41,X40) )
& ( member(esk1_2(X42,X43),X42)
| subset(X42,X43) )
& ( ~ member(esk1_2(X42,X43),X43)
| subset(X42,X43) ) ),
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,
! [X55] : ~ member(X55,empty_set),
inference(variable_rename,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X56,X57,X58] :
( ( member(X56,X58)
| ~ member(X56,difference(X58,X57)) )
& ( ~ member(X56,X57)
| ~ member(X56,difference(X58,X57)) )
& ( ~ member(X56,X58)
| member(X56,X57)
| member(X56,difference(X58,X57)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X45,X46] :
( ( subset(X45,X46)
| ~ equal_set(X45,X46) )
& ( subset(X46,X45)
| ~ equal_set(X45,X46) )
& ( ~ subset(X45,X46)
| ~ subset(X46,X45)
| equal_set(X45,X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_16,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_22,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1,X2,X6,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),intersection(X6,difference(X4,X6))) ) ),
inference(assume_negation,[status(cth)],[thI35]) ).
cnf(c_0_25,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,plain,
( equal_set(X1,empty_set)
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_29,negated_conjecture,
( subset(esk4_0,esk7_0)
& subset(esk5_0,esk7_0)
& ( ~ subset(esk4_0,esk5_0)
| ~ subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) )
& ( subset(esk4_0,esk5_0)
| subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_30,plain,
( member(X1,X2)
| ~ equal_set(X3,X2)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
equal_set(intersection(X1,difference(X2,X1)),empty_set),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( subset(esk4_0,esk5_0)
| subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
~ member(X1,intersection(X2,difference(X3,X2))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_16]) ).
cnf(c_0_34,negated_conjecture,
( member(X1,intersection(esk6_0,difference(esk7_0,esk6_0)))
| subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk7_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
fof(c_0_35,plain,
! [X47,X48] :
( ( ~ member(X47,power_set(X48))
| subset(X47,X48) )
& ( ~ subset(X47,X48)
| member(X47,power_set(X48)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
cnf(c_0_36,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
( subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk7_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,negated_conjecture,
subset(esk4_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,negated_conjecture,
subset(esk5_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_43,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_14]) ).
cnf(c_0_44,negated_conjecture,
( subset(esk4_0,esk5_0)
| ~ member(X1,difference(esk7_0,esk5_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_46,negated_conjecture,
( member(X1,esk7_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( member(X1,esk7_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_40]) ).
cnf(c_0_48,plain,
( equal_set(X1,X2)
| ~ member(X2,power_set(X1))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_49,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_50,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_25]) ).
cnf(c_0_52,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_53,negated_conjecture,
( member(esk1_2(difference(esk5_0,X1),X2),esk7_0)
| subset(difference(esk5_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_54,plain,
( subset(X1,X2)
| ~ equal_set(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_55,plain,
( equal_set(empty_set,X1)
| ~ member(X1,power_set(empty_set)) ),
inference(spm,[status(thm)],[c_0_48,c_0_21]) ).
cnf(c_0_56,plain,
member(difference(X1,X1),power_set(X2)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( member(esk1_2(difference(esk4_0,X1),X2),esk5_0)
| subset(difference(esk4_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_43]) ).
cnf(c_0_58,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_52,c_0_45]) ).
cnf(c_0_59,negated_conjecture,
subset(difference(esk5_0,esk7_0),X1),
inference(spm,[status(thm)],[c_0_42,c_0_53]) ).
cnf(c_0_60,plain,
( equal_set(X1,difference(X2,X2))
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_50]) ).
cnf(c_0_61,plain,
( member(X1,X2)
| ~ equal_set(X2,X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
cnf(c_0_62,plain,
equal_set(empty_set,difference(X1,X1)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
subset(difference(esk4_0,esk5_0),X1),
inference(spm,[status(thm)],[c_0_42,c_0_57]) ).
cnf(c_0_64,plain,
( member(esk1_2(intersection(X1,X2),difference(X1,X3)),X3)
| subset(intersection(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[c_0_58,c_0_23]) ).
cnf(c_0_65,negated_conjecture,
( equal_set(X1,difference(esk5_0,esk7_0))
| ~ subset(X1,difference(esk5_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
equal_set(difference(esk5_0,esk7_0),difference(X1,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_59]) ).
cnf(c_0_67,plain,
~ member(X1,difference(X2,X2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_16]) ).
cnf(c_0_68,negated_conjecture,
( equal_set(X1,difference(esk4_0,esk5_0))
| ~ subset(X1,difference(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_63]) ).
cnf(c_0_69,plain,
subset(intersection(X1,difference(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
equal_set(difference(esk4_0,esk5_0),difference(esk5_0,esk7_0)),
inference(spm,[status(thm)],[c_0_65,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
~ member(X1,difference(esk5_0,esk7_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_66]),c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( member(esk1_2(esk4_0,X1),esk5_0)
| subset(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_14]) ).
cnf(c_0_73,negated_conjecture,
equal_set(intersection(esk4_0,difference(X1,esk5_0)),difference(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
~ member(X1,difference(esk4_0,esk5_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_70]),c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_76,negated_conjecture,
subset(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_52,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
~ member(X1,intersection(esk4_0,difference(X2,esk5_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_73]),c_0_74]) ).
cnf(c_0_78,negated_conjecture,
~ subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_79,negated_conjecture,
subset(intersection(esk4_0,difference(X1,esk5_0)),X2),
inference(spm,[status(thm)],[c_0_77,c_0_14]) ).
cnf(c_0_80,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET701+4 : TPTP v9.2.1. Released v2.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n008.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 02:32:28 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 65.24/38.36 % Version : CSE_E---1.7
% 65.24/38.36 % Problem : theBenchmark.p
% 65.24/38.36 % SZS status Theorem for theBenchmark.p
% 65.24/38.36 % SZS output start CNFRefutation
% See solution above
% 65.54/38.63 % Total time : 28.429s
%------------------------------------------------------------------------------