%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET622+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 : n009.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 08:36:39 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_intersection,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('theBenchmark.p',associativity_of_intersection) ).
fof(difference_difference_union2,axiom,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
file('theBenchmark.p',difference_difference_union2) ).
fof(symmetric_difference_and_difference,axiom,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
file('theBenchmark.p',symmetric_difference_and_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_th98,conjecture,
! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
file('theBenchmark.p',prove_th98) ).
fof(prove_th98_neg,negated_conjecture,
~ ! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(assume_negation,[status(cth)],[prove_th98]) ).
cnf(c_16,plain,
intersection(intersection(A,B),C) = intersection(A,intersection(B,C)),
inference(clausify,[status(thm)],[associativity_of_intersection]) ).
cnf(c_17,plain,
union(difference(A,B),intersection(A,C)) = difference(A,difference(B,C)),
inference(clausify,[status(thm)],[difference_difference_union2]) ).
cnf(c_18,plain,
symmetric_difference(A,B) = difference(union(A,B),intersection(A,B)),
inference(clausify,[status(thm)],[symmetric_difference_and_difference]) ).
cnf(c_33,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
cnf(c_34,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
fof(nnf_15,plain,
? [B,C,D] : union(difference(B,union(C,D)),intersection(intersection(B,C),D)) != difference(B,symmetric_difference(C,D)),
inference(fof_nnf,[status(thm)],[prove_th98_neg]) ).
fof(sk_prove_th98_neg,plain,
union(difference(sK0,union(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)) != difference(sK0,symmetric_difference(sK1,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2)],[nnf_15]) ).
cnf(c_44,negated_conjecture,
union(difference(sK0,union(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)) != difference(sK0,symmetric_difference(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_th98_neg]) ).
cnf(c_60,negated_conjecture,
union(difference(sK0,union(sK1,sK2)),intersection(sK2,intersection(sK0,sK1))) != difference(sK0,symmetric_difference(sK1,sK2)),
inference(paramod,[status(thm)],[c_34,c_44]) ).
cnf(c_61,negated_conjecture,
union(intersection(sK2,intersection(sK0,sK1)),difference(sK0,union(sK1,sK2))) != difference(sK0,symmetric_difference(sK1,sK2)),
inference(paramod,[status(thm)],[c_33,c_60]) ).
cnf(c_45,negated_conjecture,
union(intersection(sK2,intersection(sK0,sK1)),difference(sK0,union(sK1,sK2))) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(paramod,[status(thm)],[c_18,c_61]) ).
cnf(c_55,plain,
union(intersection(A,B),difference(A,C)) = difference(A,difference(C,B)),
inference(paramod,[status(thm)],[c_33,c_17]) ).
cnf(c_62,plain,
intersection(intersection(A,B),C) = intersection(B,intersection(A,C)),
inference(paramod,[status(thm)],[c_34,c_16]) ).
cnf(c_57,plain,
intersection(A,intersection(B,C)) = intersection(B,intersection(A,C)),
inference(paramod,[status(thm)],[c_16,c_62]) ).
cnf(c_63,negated_conjecture,
union(intersection(sK0,intersection(sK2,sK1)),difference(sK0,union(sK1,sK2))) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(paramod,[status(thm)],[c_57,c_45]) ).
cnf(c_64,negated_conjecture,
union(intersection(sK0,intersection(sK1,sK2)),difference(sK0,union(sK1,sK2))) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(paramod,[status(thm)],[c_34,c_63]) ).
cnf(c_65,negated_conjecture,
difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))) != difference(sK0,difference(union(sK1,sK2),intersection(sK1,sK2))),
inference(paramod,[status(thm)],[c_55,c_64]) ).
cnf(c_59,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 08:00:59 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.14/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.38 % Process 3769652 was started by sandbox on n009,
% 0.14/0.38 % Sat Sep 26 08:00:59 2026
% 0.14/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.41 % Length of proof is 16.
% 0.14/0.41 % Level of proof is 3.
% 0.14/0.41 % Maximum clause weight is 21.000.
% 0.14/0.41 % Given clauses 18.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------