%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET633+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 : n012.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 08:36:41 AM UTC 2026
% Result : Theorem 0.02s 0.32s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 29 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 3 |; 7 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 11 !; 3 ?)
% 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_subset,axiom,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('theBenchmark.p',union_subset) ).
fof(prove_th115,conjecture,
! [B,C,D] :
( ( subset(difference(C,B),D)
& subset(difference(B,C),D) )
=> subset(symmetric_difference(B,C),D) ),
file('theBenchmark.p',prove_th115) ).
fof(prove_th115_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(difference(C,B),D)
& subset(difference(B,C),D) )
=> subset(symmetric_difference(B,C),D) ),
inference(assume_negation,[status(cth)],[prove_th115]) ).
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(union(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[union_subset]) ).
fof(nnf_9,plain,
? [B,C,D] :
( ~ subset(symmetric_difference(B,C),D)
& subset(difference(C,B),D)
& subset(difference(B,C),D) ),
inference(fof_nnf,[status(thm)],[prove_th115_neg]) ).
fof(sk_prove_th115_neg,plain,
( ~ subset(symmetric_difference(sK0,sK1),sK2)
& subset(difference(sK1,sK0),sK2)
& subset(difference(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK2)],[nnf_9]) ).
cnf(c_26,negated_conjecture,
subset(difference(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th115_neg]) ).
cnf(c_27,negated_conjecture,
subset(difference(sK1,sK0),sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th115_neg]) ).
cnf(c_28,negated_conjecture,
~ subset(symmetric_difference(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th115_neg]) ).
cnf(c_29,negated_conjecture,
~ subset(union(difference(sK0,sK1),difference(sK1,sK0)),sK2),
inference(paramod,[status(thm)],[c_11,c_28]) ).
cnf(c_63,negated_conjecture,
( subset(union(A,difference(sK1,sK0)),sK2)
| ~ subset(A,sK2) ),
inference(resolve,[status(thm)],[c_12,c_27]) ).
cnf(c_64,negated_conjecture,
~ subset(difference(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_63,c_29]) ).
cnf(c_62,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET633+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 26 08:01:35 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 81255 was started by sandbox on n012,
% 0.02/0.30 % Sat Sep 26 08:01:35 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.02/0.32
% 0.02/0.32 % SZS status Theorem for theBenchmark
% 0.02/0.32
% 0.02/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.32 % Length of proof is 11.
% 0.02/0.32 % Level of proof is 4.
% 0.02/0.32 % Maximum clause weight is 11.000.
% 0.02/0.32 % Given clauses 17.
% 0.02/0.32
% 0.02/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------