%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU139+1 : 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 : n003.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 08:45:08 AM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 32 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 6 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(t60_xboole_1,conjecture,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t60_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
inference(assume_negation,[status(cth)],[t60_xboole_1]) ).
cnf(c_10,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_11,plain,
( subset(A,B)
| ~ proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_12,plain,
( B != A
| ~ proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
fof(nnf_6,plain,
? [A,B] :
( proper_subset(B,A)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1_neg]) ).
fof(sk_t60_xboole_1_neg,plain,
( proper_subset(sK1,sK0)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_6]) ).
cnf(c_16,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t60_xboole_1_neg]) ).
cnf(c_17,negated_conjecture,
proper_subset(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t60_xboole_1_neg]) ).
cnf(c_24,negated_conjecture,
( ~ subset(sK1,sK0)
| sK0 = sK1 ),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_19,negated_conjecture,
( ~ subset(sK1,sK0)
| sK1 = sK0 ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_25,negated_conjecture,
sK0 != sK1,
inference(resolve,[status(thm)],[c_17,c_12]) ).
cnf(c_20,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_25]) ).
cnf(c_21,plain,
subset(sK1,sK0),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_26,negated_conjecture,
~ subset(sK1,sK0),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_23,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_21,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU139+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:40:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2468167 was started by sandbox on n003,
% 0.11/0.37 % Sat Sep 26 08:40:54 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 12.
% 0.15/0.39 % Level of proof is 3.
% 0.15/0.39 % Maximum clause weight is 9.000.
% 0.15/0.39 % Given clauses 11.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------