%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU140+1 : 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 08:45:08 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 36 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 4 |; 6 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(t26_xboole_1,axiom,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t63_xboole_1,conjecture,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t63_xboole_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
inference(assume_negation,[status(cth)],[t63_xboole_1]) ).
cnf(c_20,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_21,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_28,plain,
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t26_xboole_1]) ).
cnf(c_30,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[t3_xboole_1]) ).
fof(nnf_17,plain,
? [A,B,C] :
( ~ disjoint(A,C)
& disjoint(B,C)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1_neg]) ).
fof(sk_t63_xboole_1_neg,plain,
( ~ disjoint(sK0,sK2)
& disjoint(sK1,sK2)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_17]) ).
cnf(c_34,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t63_xboole_1_neg]) ).
cnf(c_35,negated_conjecture,
disjoint(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t63_xboole_1_neg]) ).
cnf(c_36,negated_conjecture,
~ disjoint(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t63_xboole_1_neg]) ).
cnf(c_44,negated_conjecture,
subset(set_intersection2(sK0,A),set_intersection2(sK1,A)),
inference(resolve,[status(thm)],[c_28,c_34]) ).
cnf(c_46,negated_conjecture,
set_intersection2(sK1,sK2) = empty_set,
inference(resolve,[status(thm)],[c_20,c_35]) ).
cnf(c_48,negated_conjecture,
set_intersection2(sK0,sK2) != empty_set,
inference(resolve,[status(thm)],[c_21,c_36]) ).
cnf(c_58,plain,
empty_set != set_intersection2(sK0,sK2),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_51,plain,
~ subset(set_intersection2(sK0,sK2),empty_set),
inference(resolve,[status(thm)],[c_30,c_58]) ).
cnf(c_59,plain,
subset(set_intersection2(sK0,sK2),empty_set),
inference(paramod,[status(thm)],[c_46,c_44]) ).
cnf(c_57,plain,
$false,
inference(resolve,[status(thm)],[c_51,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU140+1 : 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 : n010.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
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 08:39:16 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 2930820 was started by sandbox2 on n010,
% 0.17/0.43 % Sat Sep 26 08:39:16 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 16.
% 0.17/0.45 % Level of proof is 4.
% 0.17/0.45 % Maximum clause weight is 10.000.
% 0.17/0.45 % Given clauses 33.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------