%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET578+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 : n018.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 05:08:01 PM UTC 2026
% Result : Theorem 1.71s 1.86s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 140 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 141 ( 53 ~; 62 |; 16 &)
% ( 7 <=>; 3 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 4 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th19,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& member(X4,X3) ) )
=> X1 = intersection(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th19) ).
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_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(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_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& member(X4,X3) ) )
=> X1 = intersection(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th19]) ).
fof(c_0_7,plain,
! [X30,X31,X32,X33,X34] :
( ( ~ subset(X30,X31)
| ~ member(X32,X30)
| member(X32,X31) )
& ( member(esk1_2(X33,X34),X33)
| subset(X33,X34) )
& ( ~ member(esk1_2(X33,X34),X34)
| subset(X33,X34) ) ),
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_8,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])])]) ).
fof(c_0_9,negated_conjecture,
! [X47] :
( ( member(X47,esk4_0)
| ~ member(X47,esk3_0) )
& ( member(X47,esk5_0)
| ~ member(X47,esk3_0) )
& ( ~ member(X47,esk4_0)
| ~ member(X47,esk5_0)
| member(X47,esk3_0) )
& esk3_0 != intersection(esk4_0,esk5_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,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_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X28,X29] : intersection(X28,X29) = intersection(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_17,negated_conjecture,
( subset(esk3_0,intersection(X1,esk4_0))
| ~ member(esk1_2(esk3_0,intersection(X1,esk4_0)),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
subset(esk3_0,intersection(esk4_0,esk5_0)),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_19]),c_0_13]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_23,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ member(X39,X37)
| member(X39,X38)
| X37 != X38 )
& ( ~ member(X40,X38)
| member(X40,X37)
| X37 != X38 )
& ( ~ member(esk2_2(X41,X42),X41)
| ~ member(esk2_2(X41,X42),X42)
| X41 = X42 )
& ( member(esk2_2(X41,X42),X41)
| member(esk2_2(X41,X42),X42)
| X41 = X42 ) ),
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])])])])])]) ).
cnf(c_0_24,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,intersection(esk4_0,esk5_0))
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_26,plain,
! [X26,X27] :
( ( subset(X26,X27)
| X26 != X27 )
& ( subset(X27,X26)
| X26 != X27 )
& ( ~ subset(X26,X27)
| ~ subset(X27,X26)
| X26 = X27 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_27,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_28,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( subset(X1,intersection(intersection(esk4_0,esk5_0),X1))
| ~ member(esk1_2(X1,intersection(intersection(esk4_0,esk5_0),X1)),esk3_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
subset(esk3_0,intersection(esk4_0,esk3_0)),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_34,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_10,c_0_27]) ).
cnf(c_0_35,plain,
( X1 = intersection(X2,X3)
| member(esk2_2(X1,intersection(X2,X3)),X1)
| member(esk2_2(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
subset(esk3_0,intersection(esk3_0,intersection(esk4_0,esk5_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_13]),c_0_19]) ).
cnf(c_0_37,plain,
( X1 = intersection(X2,X3)
| ~ member(esk2_2(X1,intersection(X2,X3)),X1)
| ~ member(esk2_2(X1,intersection(X2,X3)),X3)
| ~ member(esk2_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_11]) ).
cnf(c_0_38,negated_conjecture,
( intersection(esk4_0,esk3_0) = esk3_0
| ~ subset(intersection(esk4_0,esk3_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_40,plain,
( intersection(X1,X2) = X2
| member(esk2_2(X2,intersection(X1,X2)),X2) ),
inference(ef,[status(thm)],[c_0_35]) ).
cnf(c_0_41,negated_conjecture,
intersection(esk3_0,intersection(esk4_0,esk5_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_36]),c_0_34])]) ).
cnf(c_0_42,negated_conjecture,
esk3_0 != intersection(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_43,negated_conjecture,
( intersection(esk4_0,esk5_0) = intersection(X1,X2)
| ~ member(esk2_2(intersection(esk4_0,esk5_0),intersection(X1,X2)),esk3_0)
| ~ member(esk2_2(intersection(esk4_0,esk5_0),intersection(X1,X2)),X2)
| ~ member(esk2_2(intersection(esk4_0,esk5_0),intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_44,negated_conjecture,
intersection(esk4_0,esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_45,negated_conjecture,
member(esk2_2(intersection(esk4_0,esk5_0),esk3_0),intersection(esk4_0,esk5_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
~ member(esk2_2(intersection(esk4_0,esk5_0),esk3_0),esk3_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_42]),c_0_12]) ).
cnf(c_0_47,plain,
( intersection(X1,X2) = X3
| member(esk2_2(intersection(X1,X2),X3),X3)
| member(esk2_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_48,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk4_0)
| ~ member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_49,negated_conjecture,
member(esk2_2(intersection(esk4_0,esk5_0),esk3_0),esk5_0),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
member(esk2_2(intersection(esk4_0,esk5_0),esk3_0),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET578+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:28:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.18/0.33 % start to proof: theBenchmark
% 1.71/1.86 % Version : CSE_E---1.7
% 1.71/1.86 % Problem : theBenchmark.p
% 1.71/1.86 % SZS status Theorem for theBenchmark.p
% 1.71/1.86 % SZS output start CNFRefutation
% See solution above
% 1.71/1.87 % Total time : 1.371s
%------------------------------------------------------------------------------