%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET611+3 : 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 : n019.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 05:08:07 PM UTC 2026
% Result : Theorem 2.82s 3.15s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 18 unt; 0 def)
% Number of atoms : 145 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 141 ( 59 ~; 58 |; 14 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 11 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(prove_th84,conjecture,
! [X1,X2] :
( intersection(X1,X2) = empty_set
<=> difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th84) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( intersection(X1,X2) = empty_set
<=> difference(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[prove_th84]) ).
fof(c_0_10,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_11,plain,
! [X35,X36,X37] :
( ( member(X37,X35)
| ~ member(X37,difference(X35,X36)) )
& ( ~ member(X37,X36)
| ~ member(X37,difference(X35,X36)) )
& ( ~ member(X37,X35)
| member(X37,X36)
| member(X37,difference(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,negated_conjecture,
( ( intersection(esk5_0,esk6_0) != empty_set
| difference(esk5_0,esk6_0) != esk5_0 )
& ( intersection(esk5_0,esk6_0) = empty_set
| difference(esk5_0,esk6_0) = esk5_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X32,X33,X34] :
( ( member(X34,X32)
| ~ member(X34,intersection(X32,X33)) )
& ( member(X34,X33)
| ~ member(X34,intersection(X32,X33)) )
& ( ~ member(X34,X32)
| ~ member(X34,X33)
| member(X34,intersection(X32,X33)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_14,plain,
! [X57,X58,X59] :
( ( ~ empty(X57)
| ~ member(X58,X57) )
& ( member(esk4_1(X59),X59)
| empty(X59) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| difference(esk5_0,esk6_0) = esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( member(esk4_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
cnf(c_0_20,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| ~ member(X1,esk5_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( empty(intersection(X1,X2))
| member(esk4_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X41,X42] : intersection(X41,X42) = intersection(X42,X41),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_23,plain,
! [X38] : ~ member(X38,empty_set),
inference(variable_rename,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X50,X51,X52,X53,X54] :
( ( ~ subset(X50,X51)
| ~ member(X52,X50)
| member(X52,X51) )
& ( member(esk3_2(X53,X54),X53)
| subset(X53,X54) )
& ( ~ member(esk3_2(X53,X54),X54)
| subset(X53,X54) ) ),
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])])])])])]) ).
cnf(c_0_25,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| empty(intersection(X1,esk5_0))
| ~ member(esk4_1(intersection(X1,esk5_0)),esk6_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X39,X40] :
( ( subset(X39,X40)
| X39 != X40 )
& ( subset(X40,X39)
| X39 != X40 )
& ( ~ subset(X39,X40)
| ~ subset(X40,X39)
| X39 = X40 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_28,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( member(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| empty(intersection(esk5_0,X1))
| ~ member(esk4_1(intersection(esk5_0,X1)),esk6_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| empty(intersection(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_36,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| subset(intersection(esk5_0,esk6_0),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( ~ empty(intersection(X1,X2))
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
intersection(esk5_0,esk6_0) = empty_set,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
empty(empty_set),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_42,negated_conjecture,
( ~ member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_43,negated_conjecture,
( empty(intersection(X1,esk6_0))
| ~ member(esk4_1(intersection(X1,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_44,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_45,negated_conjecture,
( empty(intersection(esk6_0,X1))
| ~ member(esk4_1(intersection(esk6_0,X1)),esk5_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_26]) ).
cnf(c_0_46,plain,
( empty(intersection(X1,difference(X2,X3)))
| member(esk4_1(intersection(X1,difference(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_47,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_48,negated_conjecture,
empty(intersection(esk6_0,difference(esk5_0,X1))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
( subset(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_50,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),difference(X1,X3))
| member(esk3_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_29]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(X1,difference(esk5_0,X2))
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_48]) ).
cnf(c_0_52,plain,
( subset(X1,difference(X1,X2))
| member(esk3_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
( subset(difference(X1,X2),X3)
| member(esk3_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_54,negated_conjecture,
( subset(difference(esk5_0,X1),X2)
| ~ member(esk3_2(difference(esk5_0,X1),X2),esk6_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_55,plain,
subset(X1,difference(X1,empty_set)),
inference(spm,[status(thm)],[c_0_28,c_0_52]) ).
cnf(c_0_56,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_49,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
subset(difference(esk5_0,X1),difference(difference(esk5_0,X1),esk6_0)),
inference(spm,[status(thm)],[c_0_54,c_0_52]) ).
cnf(c_0_58,plain,
difference(X1,empty_set) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_55]),c_0_56])]) ).
cnf(c_0_59,negated_conjecture,
( intersection(esk5_0,esk6_0) != empty_set
| difference(esk5_0,esk6_0) != esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_60,negated_conjecture,
subset(esk5_0,difference(esk5_0,esk6_0)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
difference(esk5_0,esk6_0) != esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_40])]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_60]),c_0_56])]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : SET611+3 : TPTP v9.2.1. Released v2.2.0.
% 0.03/0.21 % 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
% 0.11/0.43 % Computer : n019.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8042.1875MB
% 0.11/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Tue May 5 02:29:29 EDT 2026
% 0.11/0.44 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 2.82/3.15 % Version : CSE_E---1.7
% 2.82/3.15 % Problem : theBenchmark.p
% 2.82/3.15 % SZS status Theorem for theBenchmark.p
% 2.82/3.15 % SZS output start CNFRefutation
% See solution above
% 2.82/3.16 % Total time : 2.383s
%------------------------------------------------------------------------------