%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET146+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 : n020.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 05:07:26 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 48 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 45 ( 19 ~; 17 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_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(prove_th61,conjecture,
! [X1] : intersection(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th61) ).
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(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_5,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_6,plain,
! [X25] : ~ member(X25,empty_set),
inference(variable_rename,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X41,X42,X43,X44,X45,X46] :
( ( ~ member(X43,X41)
| member(X43,X42)
| X41 != X42 )
& ( ~ member(X44,X42)
| member(X44,X41)
| X41 != X42 )
& ( ~ member(esk3_2(X45,X46),X45)
| ~ member(esk3_2(X45,X46),X46)
| X45 = X46 )
& ( member(esk3_2(X45,X46),X45)
| member(esk3_2(X45,X46),X46)
| X45 = X46 ) ),
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_8,negated_conjecture,
~ ! [X1] : intersection(X1,empty_set) = empty_set,
inference(assume_negation,[status(cth)],[prove_th61]) ).
fof(c_0_9,plain,
! [X22,X23,X24] :
( ( member(X24,X22)
| ~ member(X24,intersection(X22,X23)) )
& ( member(X24,X23)
| ~ member(X24,intersection(X22,X23)) )
& ( ~ member(X24,X22)
| ~ member(X24,X23)
| member(X24,intersection(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_10,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(esk3_2(X1,X2),X1)
| member(esk3_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
intersection(esk4_0,empty_set) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X28,X29] : intersection(X28,X29) = intersection(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( empty_set = X1
| member(esk3_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
intersection(esk4_0,empty_set) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( intersection(X1,X2) = empty_set
| member(esk3_2(empty_set,intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
intersection(empty_set,esk4_0) != empty_set,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
intersection(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET146+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
% 0.17/0.33 % Computer : n020.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 02:12:35 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------