%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU160+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 : n009.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 08:45:14 AM UTC 2026
% Result : Theorem 6.71s 1.34s
% Output : CNFRefutation 6.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 128 ( 60 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 121 ( 41 ~; 58 |; 14 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 : 54 ( 4 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_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(t39_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t39_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(assume_negation,[status(cth)],[t39_zfmisc_1]) ).
cnf(c_94,plain,
( subset(B,A)
| A != B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_101,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
fof(nnf_13,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_13]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_129,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_153,plain,
( B != A
| ~ proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_154,plain,
( B = A
| ~ subset(A,B)
| proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_171,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[l4_zfmisc_1]) ).
cnf(c_193,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
cnf(c_216,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
fof(nnf_88,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)],[t39_zfmisc_1_neg]) ).
fof(sk_t39_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_88]) ).
fof(sk_t39_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_t39_zfmisc_1_neg_sk]) ).
cnf(c_227,negated_conjecture,
( singleton(sK2) = sK1
| empty_set = sK1
| subset(sK1,singleton(sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t39_zfmisc_1_neg]) ).
cnf(c_228,negated_conjecture,
( singleton(sK2) = sK1
| sK1 = empty_set
| subset(sK1,singleton(sK2)) ),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_229,negated_conjecture,
( empty_set != sK1
| ~ subset(sK1,singleton(sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t39_zfmisc_1_neg]) ).
cnf(c_230,negated_conjecture,
( sK1 != empty_set
| ~ subset(sK1,singleton(sK2)) ),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_231,negated_conjecture,
( singleton(sK2) != sK1
| ~ subset(sK1,singleton(sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t39_zfmisc_1_neg]) ).
cnf(c_899,plain,
( empty_set != A
| subset(A,B) ),
inference(resolve,[status(thm)],[c_129,c_101]) ).
cnf(c_4778,plain,
( A = empty_set
| proper_subset(empty_set,A) ),
inference(resolve,[status(thm)],[c_193,c_154]) ).
cnf(c_2290,plain,
( empty_set = A
| proper_subset(empty_set,A) ),
inference(copy,[status(thm)],[c_4778]) ).
cnf(c_4779,negated_conjecture,
( singleton(sK2) = sK1
| empty_set = sK1
| singleton(sK2) = sK1
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_228,c_171]) ).
cnf(c_4780,negated_conjecture,
( singleton(sK2) = sK1
| sK1 = empty_set
| singleton(sK2) = sK1
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_4779]) ).
cnf(c_4781,negated_conjecture,
( singleton(sK2) = sK1
| singleton(sK2) = sK1
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_4780]) ).
cnf(c_2728,negated_conjecture,
( singleton(sK2) = sK1
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_4781]) ).
cnf(c_4782,negated_conjecture,
( subset(sK1,singleton(sK2))
| sK1 = empty_set
| subset(sK1,singleton(sK2)) ),
inference(resolve,[status(thm)],[c_228,c_94]) ).
cnf(c_2741,negated_conjecture,
( sK1 = empty_set
| subset(sK1,singleton(sK2)) ),
inference(copy,[status(thm)],[c_4782]) ).
cnf(c_2743,plain,
( sK1 != empty_set
| ~ subset(sK1,unordered_pair(sK2,sK2)) ),
inference(paramod,[status(thm)],[c_216,c_230]) ).
cnf(c_3979,plain,
( subset(A,B)
| proper_subset(empty_set,A) ),
inference(resolve,[status(thm)],[c_2290,c_899]) ).
cnf(c_4199,plain,
( sK1 != empty_set
| proper_subset(empty_set,sK1) ),
inference(resolve,[status(thm)],[c_3979,c_2743]) ).
cnf(c_4783,plain,
( A = empty_set
| proper_subset(empty_set,A) ),
inference(copy,[status(thm)],[c_2290]) ).
cnf(c_4784,plain,
( proper_subset(empty_set,sK1)
| proper_subset(empty_set,sK1) ),
inference(resolve,[status(thm)],[c_4199,c_4783]) ).
cnf(c_4770,plain,
proper_subset(empty_set,sK1),
inference(copy,[status(thm)],[c_4784]) ).
cnf(c_4772,plain,
sK1 != empty_set,
inference(resolve,[status(thm)],[c_4770,c_153]) ).
cnf(c_4775,negated_conjecture,
subset(sK1,singleton(sK2)),
inference(resolve,[status(thm)],[c_4772,c_2741]) ).
cnf(c_4776,negated_conjecture,
singleton(sK2) = sK1,
inference(resolve,[status(thm)],[c_4772,c_2728]) ).
cnf(c_4785,negated_conjecture,
singleton(sK2) != sK1,
inference(resolve,[status(thm)],[c_4775,c_231]) ).
cnf(c_4777,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4776,c_4785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:42:14 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3877715 was started by sandbox on n009,
% 0.17/0.44 % Sat Sep 26 08:42:14 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 6.71/1.34
% 6.71/1.34 % SZS status Theorem for theBenchmark
% 6.71/1.34
% 6.71/1.34 % Proof 1 at 0.66 (+ 0.18) seconds.
% 6.71/1.34 % Length of proof is 33.
% 6.71/1.34 % Level of proof is 8.
% 6.71/1.34 % Maximum clause weight is 21.000.
% 6.71/1.34 % Given clauses 241.
% 6.71/1.34
% 6.71/1.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------