%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:36:40 AM UTC 2026
% Result : Theorem 0.09s 5.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 32 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 6 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('theBenchmark.p',symmetric_difference_defn) ).
fof(intersect_with_union,axiom,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
file('theBenchmark.p',intersect_with_union) ).
fof(intersection_and_union_disjoint,axiom,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('theBenchmark.p',intersection_and_union_disjoint) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(prove_intersection_and_symmetric_difference_disjoint,conjecture,
! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
file('theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(prove_intersection_and_symmetric_difference_disjoint_neg,negated_conjecture,
~ ! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(assume_negation,[status(cth)],[prove_intersection_and_symmetric_difference_disjoint]) ).
cnf(c_13,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(clausify,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_14,plain,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_15,plain,
( intersect(A,C)
| intersect(A,B)
| ~ intersect(A,union(B,C)) ),
inference(clausify,[status(thm)],[intersect_with_union]) ).
cnf(c_18,plain,
disjoint(intersection(A,B),difference(A,B)),
inference(clausify,[status(thm)],[intersection_and_union_disjoint]) ).
cnf(c_25,plain,
( ~ intersect(A,B)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
cnf(c_26,plain,
( intersect(A,B)
| disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
cnf(c_28,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
fof(nnf_12,plain,
? [B,C] : ~ disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(fof_nnf,[status(thm)],[prove_intersection_and_symmetric_difference_disjoint_neg]) ).
fof(sk_prove_intersection_and_symmetric_difference_disjoint_neg,plain,
~ disjoint(intersection(sK0,sK1),symmetric_difference(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_12]) ).
cnf(c_35,negated_conjecture,
~ disjoint(intersection(sK0,sK1),symmetric_difference(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_intersection_and_symmetric_difference_disjoint_neg]) ).
cnf(c_36,negated_conjecture,
~ disjoint(intersection(sK0,sK1),union(difference(sK0,sK1),difference(sK1,sK0))),
inference(paramod,[status(thm)],[c_14,c_35]) ).
cnf(c_40,plain,
~ intersect(intersection(A,B),difference(A,B)),
inference(resolve,[status(thm)],[c_25,c_18]) ).
cnf(c_68,plain,
intersect(intersection(sK0,sK1),union(difference(sK0,sK1),difference(sK1,sK0))),
inference(resolve,[status(thm)],[c_36,c_26]) ).
cnf(c_77,plain,
~ intersect(intersection(A,B),difference(B,A)),
inference(paramod,[status(thm)],[c_28,c_40]) ).
cnf(c_83,plain,
( intersect(intersection(A,B),C)
| ~ intersect(intersection(A,B),union(difference(A,B),C)) ),
inference(resolve,[status(thm)],[c_15,c_40]) ).
cnf(c_81,plain,
~ intersect(intersection(A,B),union(difference(A,B),difference(B,A))),
inference(resolve,[status(thm)],[c_83,c_77]) ).
cnf(c_82,plain,
$false,
inference(resolve,[status(thm)],[c_81,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n015.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 08:05:03 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.36 % Process 3522385 was started by sandbox on n015,
% 0.09/5.36 % Sat Sep 26 08:05:03 2026
% 0.09/5.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.38
% 0.09/5.38 % SZS status Theorem for theBenchmark
% 0.09/5.38
% 0.09/5.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/5.38 % Length of proof is 20.
% 0.09/5.38 % Level of proof is 5.
% 0.09/5.38 % Maximum clause weight is 11.000.
% 0.09/5.38 % Given clauses 27.
% 0.09/5.38
% 0.09/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------