%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET008+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 : n017.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 05:06:47 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 15 unt; 0 def)
% Number of atoms : 84 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 84 ( 36 ~; 30 |; 11 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 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 : 72 ( 7 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
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(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(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_intersection_difference_empty_set,conjecture,
! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_9,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_10,plain,
! [X26,X27,X28] :
( ( member(X28,X26)
| ~ member(X28,intersection(X26,X27)) )
& ( member(X28,X27)
| ~ member(X28,intersection(X26,X27)) )
& ( ~ member(X28,X26)
| ~ member(X28,X27)
| member(X28,intersection(X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_11,plain,
! [X44,X45,X46] :
( ( ~ empty(X44)
| ~ member(X45,X44) )
& ( member(esk2_1(X46),X46)
| empty(X46) ) ),
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_7])])])])]) ).
fof(c_0_12,plain,
! [X32] : ~ member(X32,empty_set),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X48,X49,X50,X51,X52,X53] :
( ( ~ member(X50,X48)
| member(X50,X49)
| X48 != X49 )
& ( ~ member(X51,X49)
| member(X51,X48)
| X48 != X49 )
& ( ~ member(esk3_2(X52,X53),X52)
| ~ member(esk3_2(X52,X53),X53)
| X52 = X53 )
& ( member(esk3_2(X52,X53),X52)
| member(esk3_2(X52,X53),X53)
| X52 = X53 ) ),
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(c_0_14,plain,
! [X29,X30,X31] :
( ( member(X31,X29)
| ~ member(X31,difference(X29,X30)) )
& ( ~ member(X31,X30)
| ~ member(X31,difference(X29,X30)) )
& ( ~ member(X31,X29)
| member(X31,X30)
| member(X31,difference(X29,X30)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
inference(assume_negation,[status(cth)],[prove_intersection_difference_empty_set]) ).
cnf(c_0_18,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( member(esk3_2(X1,X2),X1)
| member(esk3_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( empty(intersection(X1,X2))
| member(esk2_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_23,negated_conjecture,
intersection(difference(esk4_0,esk5_0),esk5_0) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_24,plain,
! [X35,X36] : intersection(X35,X36) = intersection(X36,X35),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_25,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,plain,
( empty_set = X1
| member(esk3_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( empty(intersection(X1,difference(X2,X3)))
| ~ member(esk2_1(intersection(X1,difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( empty(intersection(X1,X2))
| member(esk2_1(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
intersection(difference(esk4_0,esk5_0),esk5_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
empty(intersection(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
intersection(esk5_0,difference(esk4_0,esk5_0)) != empty_set,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
intersection(X1,difference(X2,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET008+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.15/0.32 % Computer : n017.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:02:43 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------