%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET599+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 : n005.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 08:36:34 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 3 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn 8 !; 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(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)),
file('theBenchmark.p',subset_of_union) ).
fof(prove_th58,conjecture,
! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
file('theBenchmark.p',prove_th58) ).
fof(prove_th58_neg,negated_conjecture,
~ ! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
inference(assume_negation,[status(cth)],[prove_th58]) ).
cnf(c_10,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(clausify,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_11,plain,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_12,plain,
subset(A,union(A,B)),
inference(clausify,[status(thm)],[subset_of_union]) ).
fof(nnf_9,plain,
? [B,C] : ~ subset(difference(B,C),symmetric_difference(B,C)),
inference(fof_nnf,[status(thm)],[prove_th58_neg]) ).
fof(sk_prove_th58_neg,plain,
~ subset(difference(sK0,sK1),symmetric_difference(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_9]) ).
cnf(c_26,negated_conjecture,
~ subset(difference(sK0,sK1),symmetric_difference(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_th58_neg]) ).
cnf(c_28,negated_conjecture,
~ subset(difference(sK0,sK1),union(difference(sK0,sK1),difference(sK1,sK0))),
inference(paramod,[status(thm)],[c_11,c_26]) ).
cnf(c_27,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_12,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET599+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:58:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1631366 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 07:58:32 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 8.
% 0.09/0.38 % Level of proof is 3.
% 0.09/0.38 % Maximum clause weight is 11.000.
% 0.09/0.38 % Given clauses 0.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------