%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU123+1 : 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 : 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 08:45:04 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 23 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 3 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 10 ( 1 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t3_xboole_1,conjecture,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t3_xboole_1_neg,negated_conjecture,
~ ! [A] :
( subset(A,empty_set)
=> A = empty_set ),
inference(assume_negation,[status(cth)],[t3_xboole_1]) ).
cnf(c_15,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_20,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
fof(nnf_11,plain,
? [A] :
( empty_set != A
& subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1_neg]) ).
fof(sk_t3_xboole_1_neg,plain,
( empty_set != sK0
& subset(sK0,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_11]) ).
cnf(c_24,negated_conjecture,
subset(sK0,empty_set),
inference(split_conjunct,[status(thm)],[sk_t3_xboole_1_neg]) ).
cnf(c_25,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_t3_xboole_1_neg]) ).
cnf(c_26,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_25]) ).
cnf(c_30,plain,
( ~ subset(A,empty_set)
| A = empty_set ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_31,negated_conjecture,
sK0 = empty_set,
inference(resolve,[status(thm)],[c_30,c_24]) ).
cnf(c_29,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU123+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:37:44 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3870695 was started by sandbox2 on n009,
% 0.17/0.44 % Sat Sep 26 08:37:44 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 9.
% 0.17/0.46 % Level of proof is 3.
% 0.17/0.46 % Maximum clause weight is 9.000.
% 0.17/0.46 % Given clauses 13.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------