%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU141+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 : n006.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 6.85s 1.42s
% Output : CNFRefutation 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 20 unt; 0 def)
% Number of atoms : 90 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 35 ~; 27 |; 10 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 5 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_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(l32_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t36_xboole_1,axiom,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t48_xboole_1,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t4_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t60_xboole_1,axiom,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t83_xboole_1,conjecture,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t83_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
inference(assume_negation,[status(cth)],[t83_xboole_1]) ).
cnf(c_64,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_87,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_91,plain,
( B = A
| ~ subset(A,B)
| proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_98,plain,
( subset(A,B)
| set_difference(A,B) != empty_set ),
inference(clausify,[status(thm)],[l32_xboole_1]) ).
cnf(c_111,plain,
set_intersection2(A,empty_set) = empty_set,
inference(clausify,[status(thm)],[t2_boole]) ).
cnf(c_116,plain,
subset(set_difference(A,B),A),
inference(clausify,[status(thm)],[t36_xboole_1]) ).
cnf(c_118,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
cnf(c_125,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t48_xboole_1]) ).
cnf(c_126,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(copy,[status(thm)],[c_125]) ).
fof(nnf_48,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [X0] : in(X0,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(sk_t4_xboole_0_sk,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( in(sK0(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(A,B))],[nnf_48]) ).
fof(sk_t4_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ disjoint(VAR_1,VAR_2)
| ~ in(VAR_0,set_intersection2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),set_intersection2(VAR_0,VAR_1))
| disjoint(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t4_xboole_0_sk]) ).
cnf(c_128,plain,
( in(sK0(A,B),set_intersection2(A,B))
| disjoint(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0]) ).
cnf(c_129,plain,
( in(sK0(A,B),set_difference(A,set_difference(A,B)))
| disjoint(A,B) ),
inference(paramod,[status(thm)],[c_126,c_128]) ).
cnf(c_132,plain,
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t60_xboole_1]) ).
fof(nnf_56,plain,
? [A,B] :
( ( set_difference(A,B) != A
| ~ disjoint(A,B) )
& ( set_difference(A,B) = A
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1_neg]) ).
fof(sk_t83_xboole_1_neg,plain,
( ( set_difference(sK1,sK2) != sK1
| ~ disjoint(sK1,sK2) )
& ( set_difference(sK1,sK2) = sK1
| disjoint(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_56]) ).
cnf(c_139,negated_conjecture,
( set_difference(sK1,sK2) = sK1
| disjoint(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t83_xboole_1_neg]) ).
cnf(c_140,negated_conjecture,
( set_difference(sK1,sK2) != sK1
| ~ disjoint(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t83_xboole_1_neg]) ).
cnf(c_3288,plain,
set_difference(A,set_difference(A,empty_set)) = empty_set,
inference(paramod,[status(thm)],[c_126,c_111]) ).
cnf(c_159,plain,
set_difference(A,A) = empty_set,
inference(paramod,[status(thm)],[c_118,c_3288]) ).
cnf(c_164,plain,
( set_difference(A,set_difference(A,B)) = empty_set
| ~ disjoint(A,B) ),
inference(paramod,[status(thm)],[c_126,c_87]) ).
cnf(c_172,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_64]) ).
cnf(c_656,plain,
~ proper_subset(A,set_difference(A,B)),
inference(resolve,[status(thm)],[c_132,c_116]) ).
cnf(c_3289,plain,
( in(sK0(sK1,sK2),set_difference(sK1,sK1))
| disjoint(sK1,sK2)
| disjoint(sK1,sK2) ),
inference(paramod,[status(thm)],[c_139,c_129]) ).
cnf(c_3290,plain,
( in(sK0(sK1,sK2),empty_set)
| disjoint(sK1,sK2)
| disjoint(sK1,sK2) ),
inference(paramod,[status(thm)],[c_159,c_3289]) ).
cnf(c_3291,plain,
( in(sK0(sK1,sK2),empty_set)
| disjoint(sK1,sK2) ),
inference(copy,[status(thm)],[c_3290]) ).
cnf(c_733,plain,
disjoint(sK1,sK2),
inference(resolve,[status(thm)],[c_172,c_3291]) ).
cnf(c_736,negated_conjecture,
set_difference(sK1,sK2) != sK1,
inference(resolve,[status(thm)],[c_733,c_140]) ).
cnf(c_1541,plain,
set_difference(sK1,set_difference(sK1,sK2)) = empty_set,
inference(resolve,[status(thm)],[c_733,c_164]) ).
cnf(c_3292,plain,
( set_difference(A,B) = A
| ~ subset(A,set_difference(A,B)) ),
inference(resolve,[status(thm)],[c_91,c_656]) ).
cnf(c_1634,negated_conjecture,
~ subset(sK1,set_difference(sK1,sK2)),
inference(resolve,[status(thm)],[c_3292,c_736]) ).
cnf(c_3293,plain,
set_difference(sK1,set_difference(sK1,sK2)) != empty_set,
inference(resolve,[status(thm)],[c_98,c_1634]) ).
cnf(c_3294,plain,
empty_set != empty_set,
inference(paramod,[status(thm)],[c_1541,c_3293]) ).
cnf(c_3287,plain,
$false,
inference(copy,[status(thm)],[c_3294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n006.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % 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 08:39:41 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 842720 was started by sandbox2 on n006,
% 0.17/0.43 % Sat Sep 26 08:39:41 2026
% 0.17/0.43 % 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).
% 6.85/1.42
% 6.85/1.42 % SZS status Theorem for theBenchmark
% 6.85/1.42
% 6.85/1.42 % Proof 1 at 0.54 (+ 0.24) seconds.
% 6.85/1.42 % Length of proof is 34.
% 6.85/1.42 % Level of proof is 7.
% 6.85/1.42 % Maximum clause weight is 20.000.
% 6.85/1.42 % Given clauses 176.
% 6.85/1.42
% 6.85/1.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------