%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU130+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 : 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 08:45:06 AM UTC 2026
% Result : Theorem 0.16s 0.54s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 33 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 6 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 2 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t17_xboole_1,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,axiom,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t28_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t28_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
inference(assume_negation,[status(cth)],[t28_xboole_1]) ).
cnf(c_43,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_70,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_73,plain,
subset(set_intersection2(A,B),A),
inference(clausify,[status(thm)],[t17_xboole_1]) ).
cnf(c_74,plain,
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t19_xboole_1]) ).
fof(nnf_37,plain,
? [A,B] :
( set_intersection2(A,B) != A
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1_neg]) ).
fof(sk_t28_xboole_1_neg,plain,
( set_intersection2(sK0,sK1) != sK0
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_37]) ).
cnf(c_91,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t28_xboole_1_neg]) ).
cnf(c_92,negated_conjecture,
set_intersection2(sK0,sK1) != sK0,
inference(split_conjunct,[status(thm)],[sk_t28_xboole_1_neg]) ).
cnf(c_874,negated_conjecture,
( ~ subset(set_intersection2(sK0,sK1),sK0)
| ~ subset(sK0,set_intersection2(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_92]) ).
cnf(c_435,negated_conjecture,
~ subset(sK0,set_intersection2(sK0,sK1)),
inference(resolve,[status(thm)],[c_874,c_73]) ).
cnf(c_875,negated_conjecture,
( subset(sK0,set_intersection2(A,sK1))
| ~ subset(sK0,A) ),
inference(resolve,[status(thm)],[c_74,c_91]) ).
cnf(c_876,negated_conjecture,
~ subset(sK0,sK0),
inference(resolve,[status(thm)],[c_875,c_435]) ).
cnf(c_873,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_70,c_876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU130+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:39:53 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2466632 was started by sandbox on n003,
% 0.16/0.43 % Sat Sep 26 08:39:53 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.54
% 0.16/0.54 % SZS status Theorem for theBenchmark
% 0.16/0.54
% 0.16/0.54 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.16/0.54 % Length of proof is 13.
% 0.16/0.54 % Level of proof is 3.
% 0.16/0.54 % Maximum clause weight is 21.000.
% 0.16/0.54 % Given clauses 90.
% 0.16/0.54
% 0.16/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------