%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET617+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 : n008.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 0.08s 0.49s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 22 ~; 10 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 11 !; 1 ?)
% 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(union_empty_set,axiom,
! [B] : union(B,empty_set) = B,
file('theBenchmark.p',union_empty_set) ).
fof(no_difference_with_empty_set1,axiom,
! [B] : difference(B,empty_set) = B,
file('theBenchmark.p',no_difference_with_empty_set1) ).
fof(no_difference_with_empty_set2,axiom,
! [B] : difference(empty_set,B) = empty_set,
file('theBenchmark.p',no_difference_with_empty_set2) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_symmetric_difference,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(prove_th92,conjecture,
! [B] :
( symmetric_difference(empty_set,B) = B
& symmetric_difference(B,empty_set) = B ),
file('theBenchmark.p',prove_th92) ).
fof(prove_th92_neg,negated_conjecture,
~ ! [B] :
( symmetric_difference(empty_set,B) = B
& symmetric_difference(B,empty_set) = B ),
inference(assume_negation,[status(cth)],[prove_th92]) ).
fof(nnf_13,plain,
? [B] :
( symmetric_difference(empty_set,B) != B
| symmetric_difference(B,empty_set) != B ),
inference(fof_nnf,[status(thm)],[prove_th92_neg]) ).
fof(sk_prove_th92_neg,plain,
( symmetric_difference(empty_set,sK0) != sK0
| symmetric_difference(sK0,empty_set) != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_13]) ).
cnf(c_17,negated_conjecture,
( symmetric_difference(empty_set,sK0) != sK0
| symmetric_difference(sK0,empty_set) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_prove_th92_neg]) ).
cnf(c_26,plain,
symmetric_difference(A,B) = symmetric_difference(B,A),
inference(clausify,[status(thm)],[commutativity_of_symmetric_difference]) ).
cnf(c_27,plain,
union(A,B) = union(B,A),
inference(clausify,[status(thm)],[commutativity_of_union]) ).
cnf(c_32,plain,
difference(empty_set,A) = empty_set,
inference(clausify,[status(thm)],[no_difference_with_empty_set2]) ).
cnf(c_33,plain,
difference(A,empty_set) = A,
inference(clausify,[status(thm)],[no_difference_with_empty_set1]) ).
cnf(c_34,plain,
union(A,empty_set) = A,
inference(clausify,[status(thm)],[union_empty_set]) ).
cnf(c_35,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(clausify,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_36,plain,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
inference(copy,[status(thm)],[c_35]) ).
cnf(c_54,negated_conjecture,
( symmetric_difference(empty_set,sK0) != sK0
| symmetric_difference(empty_set,sK0) != sK0 ),
inference(paramod,[status(thm)],[c_26,c_17]) ).
cnf(c_55,negated_conjecture,
( symmetric_difference(empty_set,sK0) != sK0
| union(difference(empty_set,sK0),difference(sK0,empty_set)) != sK0 ),
inference(paramod,[status(thm)],[c_36,c_54]) ).
cnf(c_56,negated_conjecture,
( symmetric_difference(empty_set,sK0) != sK0
| union(empty_set,difference(sK0,empty_set)) != sK0 ),
inference(paramod,[status(thm)],[c_32,c_55]) ).
cnf(c_57,negated_conjecture,
( symmetric_difference(empty_set,sK0) != sK0
| union(empty_set,sK0) != sK0 ),
inference(paramod,[status(thm)],[c_33,c_56]) ).
cnf(c_58,negated_conjecture,
( union(difference(empty_set,sK0),difference(sK0,empty_set)) != sK0
| union(empty_set,sK0) != sK0 ),
inference(paramod,[status(thm)],[c_36,c_57]) ).
cnf(c_59,negated_conjecture,
( union(empty_set,difference(sK0,empty_set)) != sK0
| union(empty_set,sK0) != sK0 ),
inference(paramod,[status(thm)],[c_32,c_58]) ).
cnf(c_60,negated_conjecture,
( union(empty_set,sK0) != sK0
| union(empty_set,sK0) != sK0 ),
inference(paramod,[status(thm)],[c_33,c_59]) ).
cnf(c_37,negated_conjecture,
union(empty_set,sK0) != sK0,
inference(copy,[status(thm)],[c_60]) ).
cnf(c_61,plain,
A = union(empty_set,A),
inference(paramod,[status(thm)],[c_34,c_27]) ).
cnf(c_52,plain,
union(empty_set,A) = A,
inference(copy,[status(thm)],[c_61]) ).
cnf(c_53,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.44 % Computer : n008.cluster.edu
% 0.08/0.44 % Model : x86_64 x86_64
% 0.08/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.44 % Memory : 8046.5625MB
% 0.08/0.44 % OS : Linux 6.8.0-71-generic
% 0.08/0.44 % CPULimit : 300
% 0.08/0.44 % WCLimit : 300
% 0.08/0.44 % DateTime : Sat Sep 26 08:01:09 UTC 2026
% 0.08/0.45 % CPUTime :
% 0.08/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.45 % Process 3150191 was started by sandbox on n008,
% 0.08/0.45 % Sat Sep 26 08:01:09 2026
% 0.08/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.46
% 0.08/0.46 % From the command line: assign(max_seconds, 300).
% 0.08/0.49
% 0.08/0.49 % SZS status Theorem for theBenchmark
% 0.08/0.49
% 0.08/0.49 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.49 % Length of proof is 18.
% 0.08/0.49 % Level of proof is 4.
% 0.08/0.49 % Maximum clause weight is 11.000.
% 0.08/0.49 % Given clauses 17.
% 0.08/0.49
% 0.08/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------