%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU162+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 : n012.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 08:45:15 AM UTC 2026
% Result : Theorem 61.98s 14.41s
% Output : CNFRefutation 61.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 65 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 23 ~; 20 |; 4 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 8 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(l28_zfmisc_1,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
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(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t83_xboole_1,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t65_zfmisc_1,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t65_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(assume_negation,[status(cth)],[t65_zfmisc_1]) ).
cnf(c_146,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_169,plain,
( disjoint(singleton(A),B)
| in(A,B) ),
inference(clausify,[status(thm)],[l28_zfmisc_1]) ).
cnf(c_186,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_187,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
cnf(c_209,plain,
( in(B,C)
| ~ subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
cnf(c_228,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
cnf(c_234,plain,
( set_difference(A,B) = A
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[t83_xboole_1]) ).
fof(nnf_90,plain,
? [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) != A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) = A ) ),
inference(fof_nnf,[status(thm)],[t65_zfmisc_1_neg]) ).
fof(sk_t65_zfmisc_1_neg,plain,
( ( in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) != sK0 )
& ( ~ in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) = sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_90]) ).
cnf(c_242,negated_conjecture,
( ~ in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) = sK0 ),
inference(split_conjunct,[status(thm)],[sk_t65_zfmisc_1_neg]) ).
cnf(c_243,negated_conjecture,
( ~ in(sK1,sK0)
| set_difference(sK0,unordered_pair(sK1,sK1)) = sK0 ),
inference(paramod,[status(thm)],[c_228,c_242]) ).
cnf(c_244,negated_conjecture,
( in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_t65_zfmisc_1_neg]) ).
cnf(c_245,negated_conjecture,
( in(sK1,sK0)
| set_difference(sK0,unordered_pair(sK1,sK1)) != sK0 ),
inference(paramod,[status(thm)],[c_228,c_244]) ).
cnf(c_302,plain,
( disjoint(unordered_pair(A,A),B)
| in(A,B) ),
inference(paramod,[status(thm)],[c_228,c_169]) ).
cnf(c_918,plain,
in(A,unordered_pair(B,A)),
inference(resolve,[status(thm)],[c_209,c_186]) ).
cnf(c_2097,plain,
( disjoint(B,unordered_pair(A,A))
| in(A,B) ),
inference(resolve,[status(thm)],[c_302,c_187]) ).
cnf(c_2269,plain,
( ~ in(C,D)
| set_difference(A,unordered_pair(B,C)) != D ),
inference(resolve,[status(thm)],[c_918,c_146]) ).
cnf(c_4300,plain,
( set_difference(B,unordered_pair(A,A)) = B
| in(A,B) ),
inference(resolve,[status(thm)],[c_2097,c_234]) ).
cnf(c_23729,negated_conjecture,
( set_difference(sK0,unordered_pair(sK1,sK1)) = sK0
| set_difference(sK0,unordered_pair(sK1,sK1)) = sK0 ),
inference(resolve,[status(thm)],[c_4300,c_243]) ).
cnf(c_23690,negated_conjecture,
set_difference(sK0,unordered_pair(sK1,sK1)) = sK0,
inference(copy,[status(thm)],[c_23729]) ).
cnf(c_23730,negated_conjecture,
( in(sK1,sK0)
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_23690,c_245]) ).
cnf(c_23693,negated_conjecture,
in(sK1,sK0),
inference(copy,[status(thm)],[c_23730]) ).
cnf(c_23727,plain,
set_difference(A,unordered_pair(B,sK1)) != sK0,
inference(resolve,[status(thm)],[c_23693,c_2269]) ).
cnf(c_23728,plain,
$false,
inference(resolve,[status(thm)],[c_23727,c_23690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.56 % Computer : n012.cluster.edu
% 0.09/5.56 % Model : x86_64 x86_64
% 0.09/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.56 % Memory : 8046.5625MB
% 0.09/5.56 % OS : Linux 6.8.0-71-generic
% 0.09/5.56 % CPULimit : 300
% 0.09/5.56 % WCLimit : 300
% 0.09/5.56 % DateTime : Sat Sep 26 08:42:31 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.57 % Process 169065 was started by sandbox2 on n012,
% 0.09/5.57 % Sat Sep 26 08:42:31 2026
% 0.09/5.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.59
% 0.09/5.59 % From the command line: assign(max_seconds, 300).
% 61.98/14.41
% 61.98/14.41 % given #500 (F,wt=10): 3845 set_difference(A,unordered_pair(B,c1)) != set_union2(powerset(C),D). [resolve(3824,a,2269,b)].
% 61.98/14.41
% 61.98/14.41 % given #1000 (T,wt=8): 11168 in(f17(c1,powerset(c1)),unordered_pair(c1,A)). [resolve(2915,a,10868,a),rewrite([1032(4)])].
% 61.98/14.41
% 61.98/14.41 % given #1500 (F,wt=9): 15514 -in(set_union2(A,powerset(B)),f17(powerset(c1),c1)). [resolve(5141,a,91,b)].
% 61.98/14.41
% 61.98/14.41 % given #2000 (A,wt=30): 539 union(A) != B | in(C,B) | -in(C,f5(A,D,E)) | set_union2(A,D) = E | in(f5(A,D,E),E) | in(f5(A,D,E),D). [resolve(141,d,118,c)].
% 61.98/14.41
% 61.98/14.41 % given #2500 (T,wt=9): 20429 in(unordered_pair(A,c1),set_union2(powerset(powerset(A)),B)). [resolve(20419,a,1070,a)].
% 61.98/14.41
% 61.98/14.41 % given #3000 (F,wt=9): 23441 -in(unordered_pair(A,c1),f18(powerset(B),powerset(c1))). [resolve(23317,a,91,b)].
% 61.98/14.41
% 61.98/14.41 % SZS status Theorem for theBenchmark
% 61.98/14.41
% 61.98/14.41 % Proof 1 at 6.70 (+ 2.06) seconds.
% 61.98/14.41 % Length of proof is 28.
% 61.98/14.41 % Level of proof is 8.
% 61.98/14.41 % Maximum clause weight is 11.000.
% 61.98/14.41 % Given clauses 3139.
% 61.98/14.41
% 61.98/14.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------