%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET618+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 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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 : 13 ( 0 sgn 6 !; 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(idempotency_of_union,axiom,
! [B] : union(B,B) = B,
file('theBenchmark.p',idempotency_of_union) ).
fof(self_difference_is_empty_set,axiom,
! [B] : difference(B,B) = empty_set,
file('theBenchmark.p',self_difference_is_empty_set) ).
fof(prove_th93,conjecture,
! [B] : symmetric_difference(B,B) = empty_set,
file('theBenchmark.p',prove_th93) ).
fof(prove_th93_neg,negated_conjecture,
~ ! [B] : symmetric_difference(B,B) = empty_set,
inference(assume_negation,[status(cth)],[prove_th93]) ).
fof(nnf_12,plain,
? [B] : symmetric_difference(B,B) != empty_set,
inference(fof_nnf,[status(thm)],[prove_th93_neg]) ).
fof(sk_prove_th93_neg,plain,
symmetric_difference(sK0,sK0) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_12]) ).
cnf(c_16,negated_conjecture,
symmetric_difference(sK0,sK0) != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th93_neg]) ).
cnf(c_31,plain,
difference(A,A) = empty_set,
inference(clausify,[status(thm)],[self_difference_is_empty_set]) ).
cnf(c_32,plain,
union(A,A) = A,
inference(clausify,[status(thm)],[idempotency_of_union]) ).
cnf(c_33,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(clausify,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_34,plain,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_36,negated_conjecture,
union(difference(sK0,sK0),difference(sK0,sK0)) != empty_set,
inference(paramod,[status(thm)],[c_34,c_16]) ).
cnf(c_37,negated_conjecture,
union(empty_set,difference(sK0,sK0)) != empty_set,
inference(paramod,[status(thm)],[c_31,c_36]) ).
cnf(c_38,negated_conjecture,
union(empty_set,empty_set) != empty_set,
inference(paramod,[status(thm)],[c_31,c_37]) ).
cnf(c_39,negated_conjecture,
empty_set != empty_set,
inference(paramod,[status(thm)],[c_32,c_38]) ).
cnf(c_35,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:01:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3151523 was started by sandbox on n008,
% 0.08/0.36 % Sat Sep 26 08:01:24 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 10.
% 0.08/0.38 % Level of proof is 3.
% 0.08/0.38 % Maximum clause weight is 11.000.
% 0.08/0.38 % Given clauses 0.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------