%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU137+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 : n013.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 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 19 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t39_xboole_1,axiom,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t45_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t45_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
inference(assume_negation,[status(cth)],[t45_xboole_1]) ).
cnf(c_92,plain,
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t12_xboole_1]) ).
cnf(c_105,plain,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(clausify,[status(thm)],[t39_xboole_1]) ).
fof(nnf_49,plain,
? [A,B] :
( set_union2(A,set_difference(B,A)) != B
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t45_xboole_1_neg]) ).
fof(sk_t45_xboole_1_neg,plain,
( set_union2(sK0,set_difference(sK1,sK0)) != sK1
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_49]) ).
cnf(c_120,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t45_xboole_1_neg]) ).
cnf(c_121,negated_conjecture,
set_union2(sK0,set_difference(sK1,sK0)) != sK1,
inference(split_conjunct,[status(thm)],[sk_t45_xboole_1_neg]) ).
cnf(c_836,plain,
set_union2(sK0,sK1) = sK1,
inference(resolve,[status(thm)],[c_120,c_92]) ).
cnf(c_845,plain,
set_union2(sK0,sK1) != sK1,
inference(paramod,[status(thm)],[c_105,c_121]) ).
cnf(c_844,plain,
$false,
inference(resolve,[status(thm)],[c_836,c_845]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU137+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:38:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2352396 was started by sandbox2 on n013,
% 0.09/0.37 % Sat Sep 26 08:38:23 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.47
% 0.14/0.47 % SZS status Theorem for theBenchmark
% 0.14/0.47
% 0.14/0.47 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.14/0.47 % Length of proof is 9.
% 0.14/0.47 % Level of proof is 3.
% 0.14/0.47 % Maximum clause weight is 24.000.
% 0.14/0.47 % Given clauses 72.
% 0.14/0.47
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------