%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:45:17 AM UTC 2026
% Result : Theorem 3.54s 1.02s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 63 ( 39 unt; 0 def)
% Number of atoms : 100 ( 33 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 61 ( 24 ~; 16 |; 7 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 10 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(l50_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t48_xboole_1,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t65_zfmisc_1,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t99_zfmisc_1,axiom,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(l3_subset_1,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_subset_1_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
inference(assume_negation,[status(cth)],[l3_subset_1]) ).
cnf(c_105,plain,
( in(B,A)
| ~ element(B,A)
| empty(A) ),
inference(clausify,[status(thm)],[d2_subset_1]) ).
fof(nnf_103,plain,
? [A,B] :
( ? [C] :
( ~ in(C,A)
& in(C,B) )
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[l3_subset_1_neg]) ).
fof(sk_l3_subset_1_neg,plain,
( ~ in(sK2,sK1)
& in(sK2,sK0)
& element(sK0,powerset(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2)],[nnf_103]) ).
cnf(c_110,negated_conjecture,
element(sK0,powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_l3_subset_1_neg]) ).
cnf(c_115,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_123,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_178,plain,
~ empty(powerset(A)),
inference(clausify,[status(thm)],[fc1_subset_1]) ).
cnf(c_198,plain,
( subset(A,union(B))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[l50_zfmisc_1]) ).
cnf(c_208,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_224,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
cnf(c_227,plain,
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
cnf(c_228,plain,
set_intersection2(A,empty_set) = empty_set,
inference(clausify,[status(thm)],[t2_boole]) ).
cnf(c_238,plain,
( in(A,C)
| ~ subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
cnf(c_240,plain,
( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
cnf(c_242,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
cnf(c_249,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t48_xboole_1]) ).
cnf(c_250,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(copy,[status(thm)],[c_249]) ).
cnf(c_259,plain,
( in(B,A)
| set_difference(A,singleton(B)) = A ),
inference(clausify,[status(thm)],[t65_zfmisc_1]) ).
cnf(c_260,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
cnf(c_272,plain,
union(powerset(A)) = A,
inference(clausify,[status(thm)],[t99_zfmisc_1]) ).
cnf(c_279,negated_conjecture,
in(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_l3_subset_1_neg]) ).
cnf(c_280,negated_conjecture,
~ in(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_l3_subset_1_neg]) ).
cnf(c_285,negated_conjecture,
( in(sK0,powerset(sK1))
| empty(powerset(sK1)) ),
inference(resolve,[status(thm)],[c_110,c_105]) ).
cnf(c_286,negated_conjecture,
in(sK0,powerset(sK1)),
inference(resolve,[status(thm)],[c_178,c_285]) ).
cnf(c_321,plain,
( ~ in(A,B)
| subset(unordered_pair(A,A),B) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_3237,plain,
set_difference(A,set_difference(A,empty_set)) = empty_set,
inference(paramod,[status(thm)],[c_250,c_228]) ).
cnf(c_323,plain,
set_difference(A,A) = empty_set,
inference(paramod,[status(thm)],[c_242,c_3237]) ).
cnf(c_324,plain,
( set_difference(A,set_difference(A,B)) = A
| ~ subset(A,B) ),
inference(paramod,[status(thm)],[c_250,c_227]) ).
cnf(c_3238,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(B,A),
inference(paramod,[status(thm)],[c_250,c_115]) ).
cnf(c_334,plain,
set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)),
inference(paramod,[status(thm)],[c_250,c_3238]) ).
cnf(c_335,plain,
( in(B,A)
| set_difference(A,unordered_pair(B,B)) = A ),
inference(paramod,[status(thm)],[c_260,c_259]) ).
cnf(c_1022,plain,
in(A,unordered_pair(A,B)),
inference(resolve,[status(thm)],[c_238,c_208]) ).
cnf(c_3239,negated_conjecture,
subset(sK0,union(powerset(sK1))),
inference(resolve,[status(thm)],[c_286,c_198]) ).
cnf(c_1276,negated_conjecture,
subset(sK0,sK1),
inference(paramod,[status(thm)],[c_272,c_3239]) ).
cnf(c_1957,plain,
subset(unordered_pair(sK2,sK2),sK0),
inference(resolve,[status(thm)],[c_321,c_279]) ).
cnf(c_2414,plain,
set_difference(sK1,unordered_pair(sK2,sK2)) = sK1,
inference(resolve,[status(thm)],[c_335,c_280]) ).
cnf(c_2760,plain,
( subset(A,sK1)
| ~ subset(A,sK0) ),
inference(resolve,[status(thm)],[c_1276,c_224]) ).
cnf(c_3240,plain,
empty_set != unordered_pair(A,B),
inference(resolve,[status(thm)],[c_1022,c_123]) ).
cnf(c_2910,plain,
unordered_pair(A,B) != empty_set,
inference(copy,[status(thm)],[c_3240]) ).
cnf(c_3203,plain,
subset(unordered_pair(sK2,sK2),sK1),
inference(resolve,[status(thm)],[c_2760,c_1957]) ).
cnf(c_3241,plain,
set_difference(unordered_pair(sK2,sK2),set_difference(unordered_pair(sK2,sK2),sK1)) = unordered_pair(sK2,sK2),
inference(resolve,[status(thm)],[c_3203,c_324]) ).
cnf(c_3242,plain,
set_difference(sK1,set_difference(sK1,unordered_pair(sK2,sK2))) = unordered_pair(sK2,sK2),
inference(paramod,[status(thm)],[c_334,c_3241]) ).
cnf(c_3243,plain,
set_difference(sK1,sK1) = unordered_pair(sK2,sK2),
inference(paramod,[status(thm)],[c_2414,c_3242]) ).
cnf(c_3244,plain,
empty_set = unordered_pair(sK2,sK2),
inference(paramod,[status(thm)],[c_323,c_3243]) ).
cnf(c_3245,plain,
unordered_pair(sK2,sK2) = empty_set,
inference(copy,[status(thm)],[c_3244]) ).
cnf(c_3236,plain,
$false,
inference(resolve,[status(thm)],[c_2910,c_3245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:47:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3617475 was started by sandbox2 on n015,
% 0.09/0.37 % Sat Sep 26 08:47:13 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 3.54/1.02
% 3.54/1.02 % SZS status Theorem for theBenchmark
% 3.54/1.02
% 3.54/1.02 % Proof 1 at 0.42 (+ 0.10) seconds.
% 3.54/1.02 % Length of proof is 51.
% 3.54/1.02 % Level of proof is 7.
% 3.54/1.02 % Maximum clause weight is 11.000.
% 3.54/1.02 % Given clauses 262.
% 3.54/1.02
% 3.54/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------