%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU134+2 : 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 : n010.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 08:45:07 AM UTC 2026
% Result : Theorem 0.13s 5.66s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 28 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 25 ( 11 ~; 9 |; 2 &)
% ( 3 <=>; 0 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l32_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(t37_xboole_1,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(assume_negation,[status(cth)],[t37_xboole_1]) ).
cnf(c_83,plain,
( subset(A,B)
| set_difference(A,B) != empty_set ),
inference(clausify,[status(thm)],[l32_xboole_1]) ).
cnf(c_84,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(clausify,[status(thm)],[l32_xboole_1]) ).
fof(nnf_46,plain,
? [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) != empty_set )
& ( subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1_neg]) ).
fof(sk_t37_xboole_1_neg,plain,
( ( ~ subset(sK0,sK1)
| set_difference(sK0,sK1) != empty_set )
& ( subset(sK0,sK1)
| set_difference(sK0,sK1) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_46]) ).
cnf(c_115,negated_conjecture,
( subset(sK0,sK1)
| set_difference(sK0,sK1) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t37_xboole_1_neg]) ).
cnf(c_116,negated_conjecture,
( ~ subset(sK0,sK1)
| set_difference(sK0,sK1) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t37_xboole_1_neg]) ).
cnf(c_1107,negated_conjecture,
( set_difference(sK0,sK1) = empty_set
| set_difference(sK0,sK1) = empty_set ),
inference(resolve,[status(thm)],[c_115,c_84]) ).
cnf(c_720,negated_conjecture,
set_difference(sK0,sK1) = empty_set,
inference(copy,[status(thm)],[c_1107]) ).
cnf(c_721,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_720,c_116]) ).
cnf(c_1108,negated_conjecture,
set_difference(sK0,sK1) != empty_set,
inference(resolve,[status(thm)],[c_83,c_721]) ).
cnf(c_1106,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_720,c_1108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU134+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.57 % Computer : n010.cluster.edu
% 0.10/5.57 % Model : x86_64 x86_64
% 0.10/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.57 % Memory : 8046.5625MB
% 0.10/5.57 % OS : Linux 6.8.0-71-generic
% 0.10/5.57 % CPULimit : 300
% 0.10/5.57 % WCLimit : 300
% 0.10/5.57 % DateTime : Sat Sep 26 08:38:52 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.58 % Process 2929807 was started by sandbox2 on n010,
% 0.10/5.58 % Sat Sep 26 08:38:52 2026
% 0.10/5.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.59
% 0.10/5.59 % From the command line: assign(max_seconds, 300).
% 0.13/5.66
% 0.13/5.66 % SZS status Theorem for theBenchmark
% 0.13/5.66
% 0.13/5.66 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.13/5.66 % Length of proof is 9.
% 0.13/5.66 % Level of proof is 4.
% 0.13/5.66 % Maximum clause weight is 18.000.
% 0.13/5.66 % Given clauses 94.
% 0.13/5.66
% 0.13/5.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------