%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU119+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 : n004.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 08:45:03 AM UTC 2026
% Result : Theorem 1.03s 0.50s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 156 ( 34 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 183 ( 67 ~; 76 |; 36 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 0-3 aty)
% Number of variables : 83 ( 3 sgn 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_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(t3_xboole_0,conjecture,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_0_neg,negated_conjecture,
~ ! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
inference(assume_negation,[status(cth)],[t3_xboole_0]) ).
cnf(c_14,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_15,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
fof(nnf_4,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| in(D,C) ) )
| set_intersection2(A,B) = C )
& ( ! [X0] :
( ( ~ in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_intersection2(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(sk_d3_xboole_0_sk,plain,
! [A,B,C] :
( ( ( ( ~ in(sK0(A,B,C),B)
| ~ in(sK0(A,B,C),A)
| ~ in(sK0(A,B,C),C) )
& ( ( in(sK0(A,B,C),B)
& in(sK0(A,B,C),A) )
| in(sK0(A,B,C),C) ) )
| set_intersection2(A,B) = C )
& ( ! [X0] :
( ( ~ in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_intersection2(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_4]) ).
fof(sk_d3_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_1)
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK0(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK0(VAR_0,VAR_1,VAR_2),VAR_0)
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| ~ in(VAR_3,VAR_0)
| in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_3,VAR_1)
| ~ in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_3,VAR_0)
| ~ in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_xboole_0_sk]) ).
cnf(c_19,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_20,plain,
( in(sK0(A,B,C),A)
| in(sK0(A,B,C),C)
| set_intersection2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_21,plain,
( in(sK0(A,B,C),B)
| in(sK0(A,B,C),C)
| set_intersection2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_23,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_24,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
fof(nnf_12,plain,
? [A,B] :
( ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
| ( ! [X0] :
( ~ in(X0,B)
| ~ in(X0,A) )
& ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0_neg]) ).
fof(sk_t3_xboole_0_neg_sk,plain,
( ( disjoint(sK1,sK2)
& in(sK3,sK2)
& in(sK3,sK1) )
| ( ! [X0] :
( ~ in(X0,sK2)
| ~ in(X0,sK1) )
& ~ disjoint(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_12]) ).
fof(sk_t3_xboole_0_neg,plain,
( ! [VAR_0] :
( disjoint(sK1,sK2)
| ~ in(VAR_0,sK2)
| ~ in(VAR_0,sK1) )
& ! [VAR_0] :
( in(sK3,sK2)
| ~ in(VAR_0,sK2)
| ~ in(VAR_0,sK1) )
& ! [VAR_0] :
( in(sK3,sK1)
| ~ in(VAR_0,sK2)
| ~ in(VAR_0,sK1) )
& ( in(sK3,sK2)
| ~ disjoint(sK1,sK2) )
& ( in(sK3,sK1)
| ~ disjoint(sK1,sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_t3_xboole_0_neg_sk]) ).
cnf(c_30,negated_conjecture,
( in(sK3,sK1)
| ~ disjoint(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t3_xboole_0_neg]) ).
cnf(c_31,negated_conjecture,
( in(sK3,sK2)
| ~ disjoint(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t3_xboole_0_neg]) ).
cnf(c_34,negated_conjecture,
( disjoint(sK1,sK2)
| ~ in(A,sK2)
| ~ in(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t3_xboole_0_neg]) ).
cnf(c_42,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_15]) ).
cnf(c_360,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_15]) ).
cnf(c_64,plain,
( in(sK0(A,B,empty_set),A)
| set_intersection2(A,B) = empty_set ),
inference(resolve,[status(thm)],[c_360,c_20]) ).
cnf(c_361,negated_conjecture,
( in(sK0(A,sK1,B),B)
| set_intersection2(A,sK1) = B
| disjoint(sK1,sK2)
| ~ in(sK0(A,sK1,B),sK2) ),
inference(resolve,[status(thm)],[c_34,c_21]) ).
cnf(c_362,negated_conjecture,
( set_intersection2(sK2,sK1) = empty_set
| in(sK0(sK2,sK1,empty_set),empty_set)
| set_intersection2(sK2,sK1) = empty_set
| disjoint(sK1,sK2) ),
inference(resolve,[status(thm)],[c_361,c_64]) ).
cnf(c_363,negated_conjecture,
( set_intersection2(sK2,sK1) = empty_set
| in(sK0(sK2,sK1,empty_set),empty_set)
| set_intersection2(sK1,sK2) = empty_set
| disjoint(sK1,sK2) ),
inference(paramod,[status(thm)],[c_14,c_362]) ).
cnf(c_364,negated_conjecture,
( set_intersection2(sK1,sK2) = empty_set
| in(sK0(sK2,sK1,empty_set),empty_set)
| set_intersection2(sK1,sK2) = empty_set
| disjoint(sK1,sK2) ),
inference(paramod,[status(thm)],[c_14,c_363]) ).
cnf(c_365,negated_conjecture,
( in(sK0(sK2,sK1,empty_set),empty_set)
| set_intersection2(sK1,sK2) = empty_set
| disjoint(sK1,sK2) ),
inference(copy,[status(thm)],[c_364]) ).
cnf(c_288,negated_conjecture,
( set_intersection2(sK1,sK2) = empty_set
| disjoint(sK1,sK2) ),
inference(resolve,[status(thm)],[c_42,c_365]) ).
cnf(c_366,plain,
( set_intersection2(sK1,sK2) = empty_set
| set_intersection2(sK1,sK2) = empty_set ),
inference(resolve,[status(thm)],[c_288,c_23]) ).
cnf(c_296,plain,
set_intersection2(sK1,sK2) = empty_set,
inference(copy,[status(thm)],[c_366]) ).
cnf(c_304,plain,
disjoint(sK1,sK2),
inference(resolve,[status(thm)],[c_296,c_24]) ).
cnf(c_315,negated_conjecture,
in(sK3,sK2),
inference(resolve,[status(thm)],[c_304,c_31]) ).
cnf(c_316,negated_conjecture,
in(sK3,sK1),
inference(resolve,[status(thm)],[c_304,c_30]) ).
cnf(c_367,plain,
( ~ in(A,sK2)
| ~ in(A,sK1)
| in(A,empty_set) ),
inference(resolve,[status(thm)],[c_19,c_296]) ).
cnf(c_368,plain,
( ~ in(A,sK2)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_367,c_42]) ).
cnf(c_369,negated_conjecture,
~ in(sK3,sK1),
inference(resolve,[status(thm)],[c_368,c_315]) ).
cnf(c_359,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_316,c_369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:37:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1261882 was started by sandbox on n004,
% 0.09/0.36 % Sat Sep 26 08:37:21 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 1.03/0.50
% 1.03/0.50 % Assigning unary symbol f1 kb_weight 0 and highest precedence (13).
% 1.03/0.50
% 1.03/0.50 % SZS status Theorem for theBenchmark
% 1.03/0.50
% 1.03/0.50 % Proof 1 at 0.09 (+ 0.05) seconds.
% 1.03/0.50 % Length of proof is 23.
% 1.03/0.50 % Level of proof is 7.
% 1.03/0.50 % Maximum clause weight is 27.000.
% 1.03/0.50 % Given clauses 80.
% 1.03/0.50
% 1.03/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------