%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU120+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 : n011.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 08:45:04 AM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 5 unt; 0 def)
% Number of atoms : 63 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 32 ~; 21 |; 15 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 21 !; 6 ?)
% 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(t4_xboole_0,conjecture,
! [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(t4_xboole_0_neg,negated_conjecture,
~ ! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
inference(assume_negation,[status(cth)],[t4_xboole_0]) ).
fof(nnf_3,plain,
! [A] :
( ( ? [B] : in(B,A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(sk_d1_xboole_0_sk,plain,
! [A] :
( ( in(sK0(A),A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_3]) ).
fof(sk_d1_xboole_0,plain,
( ! [VAR_0] :
( in(sK0(VAR_0),VAR_0)
| empty_set = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ in(VAR_1,VAR_0)
| empty_set != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_xboole_0_sk]) ).
cnf(c_16,plain,
( ~ in(B,A)
| empty_set != A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_17,plain,
( in(sK0(A),A)
| empty_set = A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_24,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_25,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
fof(nnf_13,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_neg]) ).
fof(sk_t4_xboole_0_neg_sk,plain,
( ( disjoint(sK1,sK2)
& in(sK3,set_intersection2(sK1,sK2)) )
| ( ! [X0] : ~ in(X0,set_intersection2(sK1,sK2))
& ~ disjoint(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_13]) ).
fof(sk_t4_xboole_0_neg,plain,
( ! [VAR_0] :
( disjoint(sK1,sK2)
| ~ in(VAR_0,set_intersection2(sK1,sK2)) )
& ! [VAR_0] :
( in(sK3,set_intersection2(sK1,sK2))
| ~ in(VAR_0,set_intersection2(sK1,sK2)) )
& ( in(sK3,set_intersection2(sK1,sK2))
| ~ disjoint(sK1,sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_t4_xboole_0_neg_sk]) ).
cnf(c_34,negated_conjecture,
( in(sK3,set_intersection2(sK1,sK2))
| ~ disjoint(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0_neg]) ).
cnf(c_36,negated_conjecture,
( disjoint(sK1,sK2)
| ~ in(A,set_intersection2(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0_neg]) ).
cnf(c_45,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_16]) ).
cnf(c_201,negated_conjecture,
( empty_set = set_intersection2(sK1,sK2)
| disjoint(sK1,sK2) ),
inference(resolve,[status(thm)],[c_36,c_17]) ).
cnf(c_112,negated_conjecture,
( set_intersection2(sK1,sK2) = empty_set
| disjoint(sK1,sK2) ),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_202,plain,
( set_intersection2(sK1,sK2) = empty_set
| set_intersection2(sK1,sK2) = empty_set ),
inference(resolve,[status(thm)],[c_112,c_24]) ).
cnf(c_193,plain,
set_intersection2(sK1,sK2) = empty_set,
inference(copy,[status(thm)],[c_202]) ).
cnf(c_203,negated_conjecture,
( in(sK3,empty_set)
| ~ disjoint(sK1,sK2) ),
inference(paramod,[status(thm)],[c_193,c_34]) ).
cnf(c_198,negated_conjecture,
~ disjoint(sK1,sK2),
inference(resolve,[status(thm)],[c_45,c_203]) ).
cnf(c_204,plain,
disjoint(sK1,sK2),
inference(resolve,[status(thm)],[c_193,c_25]) ).
cnf(c_200,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_198,c_204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n011.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 08:37:13 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.43 % Process 66584 was started by sandbox2 on n011,
% 0.14/0.43 % Sat Sep 26 08:37:13 2026
% 0.14/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.44
% 0.14/0.44 % 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 0.01 (+ 0.01) seconds.
% 0.14/0.47 % Length of proof is 14.
% 0.14/0.47 % Level of proof is 5.
% 0.14/0.47 % Maximum clause weight is 8.000.
% 0.14/0.47 % Given clauses 58.
% 0.14/0.47
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------