%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:45:10 AM UTC 2026
% Result : Theorem 29.46s 4.16s
% Output : CNFRefutation 29.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 20 unt; 0 def)
% Number of atoms : 161 ( 76 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 150 ( 58 ~; 71 |; 11 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 2 sgn 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(l4_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l4_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).
cnf(c_69,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_72,plain,
( subset(B,A)
| A != B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_74,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
fof(nnf_8,plain,
! [A] :
( ( ? [B] : in(B,A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(sk_d1_xboole_0_sk,plain,
! [A] :
( ( in(sK0(A),A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_8]) ).
fof(sk_d1_xboole_0,plain,
( ! [VAR_0] :
( in(sK0(VAR_0),VAR_0)
| empty_set = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ in(VAR_1,VAR_0)
| empty_set != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_xboole_0_sk]) ).
cnf(c_80,plain,
( in(sK0(A),A)
| empty_set = A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_81,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_93,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[d3_tarski]) ).
cnf(c_111,plain,
( B != A
| ~ proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_112,plain,
( B = A
| ~ subset(A,B)
| proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_118,plain,
~ proper_subset(A,A),
inference(clausify,[status(thm)],[irreflexivity_r2_xboole_0]) ).
cnf(c_121,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
cnf(c_139,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
cnf(c_159,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
fof(nnf_66,plain,
? [A,B] :
( ( ( singleton(B) != A
& empty_set != A )
| ~ subset(A,singleton(B)) )
& ( singleton(B) = A
| empty_set = A
| subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[l4_zfmisc_1_neg]) ).
fof(sk_l4_zfmisc_1_neg_sk,plain,
( ( ( singleton(sK2) != sK1
& empty_set != sK1 )
| ~ subset(sK1,singleton(sK2)) )
& ( singleton(sK2) = sK1
| empty_set = sK1
| subset(sK1,singleton(sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_66]) ).
fof(sk_l4_zfmisc_1_neg,plain,
( ( singleton(sK2) != sK1
| ~ subset(sK1,singleton(sK2)) )
& ( empty_set != sK1
| ~ subset(sK1,singleton(sK2)) )
& ( singleton(sK2) = sK1
| empty_set = sK1
| subset(sK1,singleton(sK2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_l4_zfmisc_1_neg_sk]) ).
cnf(c_167,negated_conjecture,
( singleton(sK2) = sK1
| empty_set = sK1
| subset(sK1,singleton(sK2)) ),
inference(split_conjunct,[status(thm)],[sk_l4_zfmisc_1_neg]) ).
cnf(c_11221,negated_conjecture,
( singleton(sK2) = sK1
| empty_set = sK1
| subset(sK1,unordered_pair(sK2,sK2)) ),
inference(paramod,[status(thm)],[c_159,c_167]) ).
cnf(c_11222,negated_conjecture,
( unordered_pair(sK2,sK2) = sK1
| empty_set = sK1
| subset(sK1,unordered_pair(sK2,sK2)) ),
inference(paramod,[status(thm)],[c_159,c_11221]) ).
cnf(c_168,negated_conjecture,
( unordered_pair(sK2,sK2) = sK1
| sK1 = empty_set
| subset(sK1,unordered_pair(sK2,sK2)) ),
inference(copy,[status(thm)],[c_11222]) ).
cnf(c_169,negated_conjecture,
( empty_set != sK1
| ~ subset(sK1,singleton(sK2)) ),
inference(split_conjunct,[status(thm)],[sk_l4_zfmisc_1_neg]) ).
cnf(c_11223,negated_conjecture,
( empty_set != sK1
| ~ subset(sK1,unordered_pair(sK2,sK2)) ),
inference(paramod,[status(thm)],[c_159,c_169]) ).
cnf(c_170,negated_conjecture,
( sK1 != empty_set
| ~ subset(sK1,unordered_pair(sK2,sK2)) ),
inference(copy,[status(thm)],[c_11223]) ).
cnf(c_171,negated_conjecture,
( singleton(sK2) != sK1
| ~ subset(sK1,singleton(sK2)) ),
inference(split_conjunct,[status(thm)],[sk_l4_zfmisc_1_neg]) ).
cnf(c_11224,negated_conjecture,
( singleton(sK2) != sK1
| ~ subset(sK1,unordered_pair(sK2,sK2)) ),
inference(paramod,[status(thm)],[c_159,c_171]) ).
cnf(c_172,negated_conjecture,
( unordered_pair(sK2,sK2) != sK1
| ~ subset(sK1,unordered_pair(sK2,sK2)) ),
inference(paramod,[status(thm)],[c_159,c_11224]) ).
cnf(c_209,plain,
( ~ in(A,B)
| subset(unordered_pair(A,A),B) ),
inference(paramod,[status(thm)],[c_159,c_121]) ).
cnf(c_225,plain,
( A = B
| A = C
| ~ in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_81,c_69]) ).
cnf(c_227,plain,
( A = B
| ~ in(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_225]) ).
cnf(c_11225,plain,
( A = empty_set
| proper_subset(empty_set,A) ),
inference(resolve,[status(thm)],[c_139,c_112]) ).
cnf(c_622,plain,
( empty_set = A
| proper_subset(empty_set,A) ),
inference(copy,[status(thm)],[c_11225]) ).
cnf(c_11226,negated_conjecture,
( ~ subset(unordered_pair(sK2,sK2),sK1)
| sK1 = unordered_pair(sK2,sK2)
| unordered_pair(sK2,sK2) = sK1
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_168,c_74]) ).
cnf(c_11227,negated_conjecture,
( ~ subset(unordered_pair(sK2,sK2),sK1)
| unordered_pair(sK2,sK2) = sK1
| unordered_pair(sK2,sK2) = sK1
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_11226]) ).
cnf(c_892,negated_conjecture,
( ~ subset(unordered_pair(sK2,sK2),sK1)
| unordered_pair(sK2,sK2) = sK1
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_11227]) ).
cnf(c_11228,negated_conjecture,
( subset(sK1,unordered_pair(sK2,sK2))
| sK1 = empty_set
| subset(sK1,unordered_pair(sK2,sK2)) ),
inference(resolve,[status(thm)],[c_168,c_72]) ).
cnf(c_905,negated_conjecture,
( sK1 = empty_set
| subset(sK1,unordered_pair(sK2,sK2)) ),
inference(copy,[status(thm)],[c_11228]) ).
cnf(c_11229,plain,
( sK1 != empty_set
| ~ subset(empty_set,unordered_pair(sK2,sK2))
| proper_subset(empty_set,sK1) ),
inference(paramod,[status(thm)],[c_622,c_170]) ).
cnf(c_2480,plain,
( sK1 != empty_set
| proper_subset(empty_set,sK1) ),
inference(resolve,[status(thm)],[c_139,c_11229]) ).
cnf(c_11230,plain,
( A = empty_set
| proper_subset(empty_set,A) ),
inference(copy,[status(thm)],[c_622]) ).
cnf(c_11231,plain,
( proper_subset(empty_set,sK1)
| proper_subset(empty_set,sK1) ),
inference(resolve,[status(thm)],[c_2480,c_11230]) ).
cnf(c_3397,plain,
proper_subset(empty_set,sK1),
inference(copy,[status(thm)],[c_11231]) ).
cnf(c_3400,plain,
sK1 != empty_set,
inference(resolve,[status(thm)],[c_3397,c_111]) ).
cnf(c_11232,plain,
( proper_subset(empty_set,empty_set)
| in(sK0(sK1),sK1) ),
inference(paramod,[status(thm)],[c_80,c_3397]) ).
cnf(c_3402,plain,
in(sK0(sK1),sK1),
inference(resolve,[status(thm)],[c_118,c_11232]) ).
cnf(c_3432,negated_conjecture,
subset(sK1,unordered_pair(sK2,sK2)),
inference(resolve,[status(thm)],[c_3400,c_905]) ).
cnf(c_3433,negated_conjecture,
( ~ subset(unordered_pair(sK2,sK2),sK1)
| unordered_pair(sK2,sK2) = sK1 ),
inference(resolve,[status(thm)],[c_3400,c_892]) ).
cnf(c_3505,negated_conjecture,
unordered_pair(sK2,sK2) != sK1,
inference(resolve,[status(thm)],[c_3432,c_172]) ).
cnf(c_3517,negated_conjecture,
~ subset(unordered_pair(sK2,sK2),sK1),
inference(resolve,[status(thm)],[c_3505,c_3433]) ).
cnf(c_3810,plain,
subset(unordered_pair(sK0(sK1),sK0(sK1)),sK1),
inference(resolve,[status(thm)],[c_3402,c_209]) ).
cnf(c_3826,plain,
( in(sK0(sK1),A)
| ~ subset(sK1,A) ),
inference(resolve,[status(thm)],[c_3402,c_93]) ).
cnf(c_10966,plain,
in(sK0(sK1),unordered_pair(sK2,sK2)),
inference(resolve,[status(thm)],[c_3826,c_3432]) ).
cnf(c_10983,plain,
sK0(sK1) = sK2,
inference(resolve,[status(thm)],[c_10966,c_227]) ).
cnf(c_11233,plain,
subset(unordered_pair(sK2,sK0(sK1)),sK1),
inference(paramod,[status(thm)],[c_10983,c_3810]) ).
cnf(c_11234,plain,
subset(unordered_pair(sK2,sK2),sK1),
inference(paramod,[status(thm)],[c_10983,c_11233]) ).
cnf(c_11220,plain,
$false,
inference(resolve,[status(thm)],[c_3517,c_11234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:45:16 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 457230 was started by sandbox on n016,
% 0.08/0.37 % Sat Sep 26 08:45:16 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 29.46/4.16
% 29.46/4.16 % SZS status Theorem for theBenchmark
% 29.46/4.16
% 29.46/4.16 % Proof 1 at 2.63 (+ 1.09) seconds.
% 29.46/4.16 % Length of proof is 48.
% 29.46/4.16 % Level of proof is 9.
% 29.46/4.16 % Maximum clause weight is 18.000.
% 29.46/4.16 % Given clauses 411.
% 29.46/4.16
% 29.46/4.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------