%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET011+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 : n001.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 16.35s 10.27s
% Output : CNFRefutation 16.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 18 unt; 0 def)
% Number of atoms : 120 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 114 ( 47 ~; 49 |; 12 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 141 ( 18 sgn 35 !; 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(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(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(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(prove_difference_difference_intersection,conjecture,
! [X1,X2] : difference(X1,difference(X1,X2)) = intersection(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_difference_intersection) ).
fof(c_0_6,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_7,plain,
! [X26,X27,X28] :
( ( member(X28,X26)
| ~ member(X28,difference(X26,X27)) )
& ( ~ member(X28,X27)
| ~ member(X28,difference(X26,X27)) )
& ( ~ member(X28,X26)
| member(X28,X27)
| member(X28,difference(X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X33,X34,X35,X36,X37] :
( ( ~ subset(X33,X34)
| ~ member(X35,X33)
| member(X35,X34) )
& ( member(esk1_2(X36,X37),X36)
| subset(X36,X37) )
& ( ~ member(esk1_2(X36,X37),X37)
| subset(X36,X37) ) ),
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(c_0_9,plain,
! [X23,X24,X25] :
( ( member(X25,X23)
| ~ member(X25,intersection(X23,X24)) )
& ( member(X25,X24)
| ~ member(X25,intersection(X23,X24)) )
& ( ~ member(X25,X23)
| ~ member(X25,X24)
| member(X25,intersection(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_10,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X31,X32] : intersection(X31,X32) = intersection(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_14,plain,
! [X29,X30] :
( ( subset(X29,X30)
| X29 != X30 )
& ( subset(X30,X29)
| X29 != X30 )
& ( ~ subset(X29,X30)
| ~ subset(X30,X29)
| X29 = X30 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_19,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_23,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_26,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| ~ member(esk1_2(intersection(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_27,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_28,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( X1 = difference(X2,X2)
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_30,plain,
subset(intersection(difference(X1,X2),intersection(X3,X2)),X4),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,plain,
( ~ member(X1,difference(X2,X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_33,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,plain,
intersection(difference(X1,X2),intersection(X3,X2)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_32]) ).
cnf(c_0_36,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_37,plain,
( ~ member(X1,intersection(X2,X3))
| ~ member(X1,difference(X4,X3)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_38,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_39,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_40,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk1_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_41,plain,
( subset(intersection(X1,X2),X3)
| ~ member(esk1_2(intersection(X1,X2),X3),difference(X4,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_11]) ).
cnf(c_0_42,plain,
( subset(intersection(X1,X2),difference(X1,X3))
| member(esk1_2(intersection(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
fof(c_0_43,negated_conjecture,
~ ! [X1,X2] : difference(X1,difference(X1,X2)) = intersection(X1,X2),
inference(assume_negation,[status(cth)],[prove_difference_difference_intersection]) ).
cnf(c_0_44,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_16]) ).
cnf(c_0_45,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk1_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_16]) ).
cnf(c_0_46,plain,
subset(intersection(X1,X2),difference(X1,difference(X3,X2))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_47,negated_conjecture,
difference(esk3_0,difference(esk3_0,esk4_0)) != intersection(esk3_0,esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
cnf(c_0_48,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_46,c_0_19]) ).
cnf(c_0_50,negated_conjecture,
difference(esk3_0,difference(esk3_0,esk4_0)) != intersection(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_51,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_48]),c_0_49])]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET011+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
% 0.14/0.33 % Computer : n001.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 02:04:33 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 16.35/10.27 % Version : CSE_E---1.7
% 16.35/10.27 % Problem : theBenchmark.p
% 16.35/10.27 % SZS status Theorem for theBenchmark.p
% 16.35/10.27 % SZS output start CNFRefutation
% See solution above
% 16.45/10.34 % Total time : 7.383s
%------------------------------------------------------------------------------