%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET637+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 05:08:12 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 9 unt; 0 def)
% Number of atoms : 119 ( 16 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 125 ( 53 ~; 51 |; 12 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 4 sgn 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(prove_th119,conjecture,
! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th119) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
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,
! [X24,X25,X26] :
( ( member(X26,X24)
| ~ member(X26,intersection(X24,X25)) )
& ( member(X26,X25)
| ~ member(X26,intersection(X24,X25)) )
& ( ~ member(X26,X24)
| ~ member(X26,X25)
| member(X26,intersection(X24,X25)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_10,plain,
! [X47,X48,X49] :
( ( ~ empty(X47)
| ~ member(X48,X47) )
& ( member(esk3_1(X49),X49)
| empty(X49) ) ),
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_11,plain,
! [X33] : ~ member(X33,empty_set),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ member(X36,X34)
| member(X36,X35)
| X34 != X35 )
& ( ~ member(X37,X35)
| member(X37,X34)
| X34 != X35 )
& ( ~ member(esk2_2(X38,X39),X38)
| ~ member(esk2_2(X38,X39),X39)
| X38 = X39 )
& ( member(esk2_2(X38,X39),X38)
| member(esk2_2(X38,X39),X39)
| X38 = X39 ) ),
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_13,plain,
! [X27,X28,X30,X31,X32] :
( ( member(esk1_2(X27,X28),X27)
| ~ intersect(X27,X28) )
& ( member(esk1_2(X27,X28),X28)
| ~ intersect(X27,X28) )
& ( ~ member(X32,X30)
| ~ member(X32,X31)
| intersect(X30,X31) ) ),
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)],[intersect_defn])])])])])]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
inference(assume_negation,[status(cth)],[prove_th119]) ).
cnf(c_0_17,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,negated_conjecture,
( ( ~ intersect(esk4_0,esk5_0)
| ~ not_equal(intersection(esk4_0,esk5_0),empty_set) )
& ( intersect(esk4_0,esk5_0)
| not_equal(intersection(esk4_0,esk5_0),empty_set) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_23,plain,
! [X41,X42] :
( ( ~ not_equal(X41,X42)
| X41 != X42 )
& ( X41 = X42
| not_equal(X41,X42) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[not_equal_defn])]) ).
cnf(c_0_24,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( empty_set = X1
| member(esk2_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( empty(intersection(X1,X2))
| intersect(X3,X2)
| ~ member(esk3_1(intersection(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_28,negated_conjecture,
( ~ intersect(esk4_0,esk5_0)
| ~ not_equal(intersection(esk4_0,esk5_0),empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( X1 = X2
| not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( empty(intersection(X1,X2))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,negated_conjecture,
( intersection(esk4_0,esk5_0) = empty_set
| ~ intersect(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( intersection(X1,X2) = empty_set
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ empty(intersection(X1,X2))
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
intersection(esk4_0,esk5_0) = empty_set,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
empty(empty_set),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_38,plain,
( ~ not_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_40,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,negated_conjecture,
( intersect(esk4_0,esk5_0)
| not_equal(intersection(esk4_0,esk5_0),empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( ~ intersect(X1,esk5_0)
| ~ member(esk1_2(X1,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,negated_conjecture,
intersect(esk4_0,esk5_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_36]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET637+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n011.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 02:30:17 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.368s
%------------------------------------------------------------------------------