%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:36:38 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 3 sgn 17 !; 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(associativity_of_union,axiom,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
file('theBenchmark.p',associativity_of_union) ).
fof(union_intersection,axiom,
! [B,C] : union(B,intersection(B,C)) = B,
file('theBenchmark.p',union_intersection) ).
fof(union_intersection_difference,axiom,
! [B,C] : union(intersection(B,C),difference(B,C)) = B,
file('theBenchmark.p',union_intersection_difference) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th95,conjecture,
! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
file('theBenchmark.p',prove_th95) ).
fof(prove_th95_neg,negated_conjecture,
~ ! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
inference(assume_negation,[status(cth)],[prove_th95]) ).
cnf(c_15,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(clausify,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_16,plain,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,plain,
union(union(A,B),C) = union(A,union(B,C)),
inference(clausify,[status(thm)],[associativity_of_union]) ).
cnf(c_18,plain,
union(A,intersection(A,B)) = A,
inference(clausify,[status(thm)],[union_intersection]) ).
cnf(c_19,plain,
union(intersection(A,B),difference(A,B)) = A,
inference(clausify,[status(thm)],[union_intersection_difference]) ).
cnf(c_29,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
cnf(c_30,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
fof(nnf_14,plain,
? [B,C] : union(symmetric_difference(B,C),intersection(B,C)) != union(B,C),
inference(fof_nnf,[status(thm)],[prove_th95_neg]) ).
fof(sk_prove_th95_neg,plain,
union(symmetric_difference(sK0,sK1),intersection(sK0,sK1)) != union(sK0,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_14]) ).
cnf(c_40,negated_conjecture,
union(symmetric_difference(sK0,sK1),intersection(sK0,sK1)) != union(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th95_neg]) ).
cnf(c_120,negated_conjecture,
union(union(difference(sK0,sK1),difference(sK1,sK0)),intersection(sK0,sK1)) != union(sK0,sK1),
inference(paramod,[status(thm)],[c_16,c_40]) ).
cnf(c_41,negated_conjecture,
union(intersection(sK0,sK1),union(difference(sK0,sK1),difference(sK1,sK0))) != union(sK0,sK1),
inference(paramod,[status(thm)],[c_29,c_120]) ).
cnf(c_121,plain,
union(A,B) = union(A,union(intersection(A,C),B)),
inference(paramod,[status(thm)],[c_18,c_17]) ).
cnf(c_44,plain,
union(A,union(intersection(A,B),C)) = union(A,C),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_122,plain,
union(A,B) = union(intersection(A,C),union(difference(A,C),B)),
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_46,plain,
union(intersection(A,B),union(difference(A,B),C)) = union(A,C),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_47,negated_conjecture,
union(sK0,difference(sK1,sK0)) != union(sK0,sK1),
inference(paramod,[status(thm)],[c_46,c_41]) ).
cnf(c_55,plain,
union(intersection(A,B),difference(B,A)) = B,
inference(paramod,[status(thm)],[c_30,c_19]) ).
cnf(c_123,plain,
union(A,B) = union(A,difference(B,A)),
inference(paramod,[status(thm)],[c_55,c_44]) ).
cnf(c_118,plain,
union(A,difference(B,A)) = union(A,B),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_119,plain,
$false,
inference(resolve,[status(thm)],[c_118,c_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:01:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2578984 was started by sandbox2 on n014,
% 0.13/0.36 % Sat Sep 26 08:01:02 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 22.
% 0.13/0.39 % Level of proof is 5.
% 0.13/0.39 % Maximum clause weight is 15.000.
% 0.13/0.39 % Given clauses 31.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------