%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET580+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 : n020.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 08:36:30 AM UTC 2026
% Result : Theorem 3.39s 0.84s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 9 unt; 0 def)
% Number of atoms : 133 ( 2 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 133 ( 47 ~; 70 |; 10 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 48 ( 11 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
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(prove_th23,conjecture,
! [B,C,D] :
( member(B,symmetric_difference(C,D))
<=> ~ ( member(B,C)
<=> member(B,D) ) ),
file('theBenchmark.p',prove_th23) ).
fof(prove_th23_neg,negated_conjecture,
~ ! [B,C,D] :
( member(B,symmetric_difference(C,D))
<=> ~ ( member(B,C)
<=> member(B,D) ) ),
inference(assume_negation,[status(cth)],[prove_th23]) ).
cnf(c_8,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_9,plain,
( ~ member(A,B)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_10,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union_defn]) ).
cnf(c_11,plain,
( member(A,B)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_12,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_13,plain,
( member(A,C)
| ~ member(A,B)
| member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_14,plain,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
inference(clausify,[status(thm)],[symmetric_difference_defn]) ).
fof(nnf_7,plain,
? [B,C,D] :
( ( ( ( ~ member(B,D)
| member(B,C) )
& ( member(B,D)
| ~ member(B,C) ) )
| ~ member(B,symmetric_difference(C,D)) )
& ( ( ( ~ member(B,D)
| ~ member(B,C) )
& ( member(B,D)
| member(B,C) ) )
| member(B,symmetric_difference(C,D)) ) ),
inference(fof_nnf,[status(thm)],[prove_th23_neg]) ).
fof(sk_prove_th23_neg_sk,plain,
( ( ( ( ~ member(sK0,sK2)
| member(sK0,sK1) )
& ( member(sK0,sK2)
| ~ member(sK0,sK1) ) )
| ~ member(sK0,symmetric_difference(sK1,sK2)) )
& ( ( ( ~ member(sK0,sK2)
| ~ member(sK0,sK1) )
& ( member(sK0,sK2)
| member(sK0,sK1) ) )
| member(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_7]) ).
fof(sk_prove_th23_neg,plain,
( ( ~ member(sK0,sK2)
| member(sK0,sK1)
| ~ member(sK0,symmetric_difference(sK1,sK2)) )
& ( member(sK0,sK2)
| ~ member(sK0,sK1)
| ~ member(sK0,symmetric_difference(sK1,sK2)) )
& ( ~ member(sK0,sK2)
| ~ member(sK0,sK1)
| member(sK0,symmetric_difference(sK1,sK2)) )
& ( member(sK0,sK2)
| member(sK0,sK1)
| member(sK0,symmetric_difference(sK1,sK2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_th23_neg_sk]) ).
cnf(c_21,negated_conjecture,
( member(sK0,sK2)
| member(sK0,sK1)
| member(sK0,symmetric_difference(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_prove_th23_neg]) ).
cnf(c_22,negated_conjecture,
( member(sK0,sK2)
| member(sK0,sK1)
| member(sK0,union(difference(sK1,sK2),difference(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_14,c_21]) ).
cnf(c_23,negated_conjecture,
( ~ member(sK0,sK2)
| ~ member(sK0,sK1)
| member(sK0,symmetric_difference(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_prove_th23_neg]) ).
cnf(c_24,negated_conjecture,
( ~ member(sK0,sK2)
| ~ member(sK0,sK1)
| member(sK0,union(difference(sK1,sK2),difference(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_14,c_23]) ).
cnf(c_25,negated_conjecture,
( member(sK0,sK2)
| ~ member(sK0,sK1)
| ~ member(sK0,symmetric_difference(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_prove_th23_neg]) ).
cnf(c_26,negated_conjecture,
( member(sK0,sK2)
| ~ member(sK0,sK1)
| ~ member(sK0,union(difference(sK1,sK2),difference(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_14,c_25]) ).
cnf(c_27,negated_conjecture,
( ~ member(sK0,sK2)
| member(sK0,sK1)
| ~ member(sK0,symmetric_difference(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_prove_th23_neg]) ).
cnf(c_28,negated_conjecture,
( ~ member(sK0,sK2)
| member(sK0,sK1)
| ~ member(sK0,union(difference(sK1,sK2),difference(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_14,c_27]) ).
cnf(c_74,plain,
( member(sK0,difference(sK2,sK1))
| member(sK0,difference(sK1,sK2))
| member(sK0,sK2)
| member(sK0,sK1) ),
inference(resolve,[status(thm)],[c_22,c_8]) ).
cnf(c_1913,plain,
( member(sK0,sK2)
| member(sK0,difference(sK1,sK2))
| member(sK0,sK2)
| member(sK0,sK1) ),
inference(resolve,[status(thm)],[c_74,c_11]) ).
cnf(c_266,plain,
( member(sK0,difference(sK1,sK2))
| member(sK0,sK2)
| member(sK0,sK1) ),
inference(copy,[status(thm)],[c_1913]) ).
cnf(c_1914,plain,
( member(sK0,sK1)
| member(sK0,sK2)
| member(sK0,sK1) ),
inference(resolve,[status(thm)],[c_266,c_11]) ).
cnf(c_270,plain,
( member(sK0,sK2)
| member(sK0,sK1) ),
inference(copy,[status(thm)],[c_1914]) ).
cnf(c_1915,negated_conjecture,
( member(sK0,sK1)
| ~ member(sK0,union(difference(sK1,sK2),difference(sK2,sK1)))
| member(sK0,sK1) ),
inference(resolve,[status(thm)],[c_270,c_28]) ).
cnf(c_271,negated_conjecture,
( ~ member(sK0,union(difference(sK1,sK2),difference(sK2,sK1)))
| member(sK0,sK1) ),
inference(copy,[status(thm)],[c_1915]) ).
cnf(c_273,plain,
( member(sK0,A)
| member(sK0,difference(sK2,A))
| member(sK0,sK1) ),
inference(resolve,[status(thm)],[c_270,c_13]) ).
cnf(c_278,plain,
( member(sK0,difference(sK2,sK1))
| member(sK0,sK1) ),
inference(factor,[status(thm)],[c_273]) ).
cnf(c_339,plain,
( member(sK0,union(A,difference(sK2,sK1)))
| member(sK0,sK1) ),
inference(resolve,[status(thm)],[c_278,c_10]) ).
cnf(c_1916,plain,
( member(sK0,sK1)
| member(sK0,sK1) ),
inference(resolve,[status(thm)],[c_271,c_339]) ).
cnf(c_884,plain,
member(sK0,sK1),
inference(copy,[status(thm)],[c_1916]) ).
cnf(c_885,negated_conjecture,
( member(sK0,sK2)
| ~ member(sK0,union(difference(sK1,sK2),difference(sK2,sK1))) ),
inference(resolve,[status(thm)],[c_884,c_26]) ).
cnf(c_886,negated_conjecture,
( ~ member(sK0,sK2)
| member(sK0,union(difference(sK1,sK2),difference(sK2,sK1))) ),
inference(resolve,[status(thm)],[c_884,c_24]) ).
cnf(c_888,plain,
( member(sK0,A)
| member(sK0,difference(sK1,A)) ),
inference(resolve,[status(thm)],[c_884,c_13]) ).
cnf(c_889,plain,
~ member(sK0,difference(A,sK1)),
inference(resolve,[status(thm)],[c_884,c_12]) ).
cnf(c_936,plain,
( member(sK0,union(difference(sK1,A),B))
| member(sK0,A) ),
inference(resolve,[status(thm)],[c_888,c_9]) ).
cnf(c_1917,negated_conjecture,
( member(sK0,sK2)
| member(sK0,sK2) ),
inference(resolve,[status(thm)],[c_885,c_936]) ).
cnf(c_1604,negated_conjecture,
member(sK0,sK2),
inference(copy,[status(thm)],[c_1917]) ).
cnf(c_1605,negated_conjecture,
member(sK0,union(difference(sK1,sK2),difference(sK2,sK1))),
inference(resolve,[status(thm)],[c_1604,c_886]) ).
cnf(c_1804,plain,
~ member(sK0,difference(A,sK2)),
inference(resolve,[status(thm)],[c_1604,c_12]) ).
cnf(c_1918,plain,
( member(sK0,B)
| ~ member(sK0,union(difference(A,sK2),B)) ),
inference(resolve,[status(thm)],[c_8,c_1804]) ).
cnf(c_1911,plain,
~ member(sK0,union(difference(A,sK2),difference(B,sK1))),
inference(resolve,[status(thm)],[c_1918,c_889]) ).
cnf(c_1912,plain,
$false,
inference(resolve,[status(thm)],[c_1911,c_1605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.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 07:58:06 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 1022651 was started by sandbox on n020,
% 0.08/0.36 % Sat Sep 26 07:58:06 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 3.39/0.84
% 3.39/0.84 % SZS status Theorem for theBenchmark
% 3.39/0.84
% 3.39/0.84 % Proof 1 at 0.32 (+ 0.08) seconds.
% 3.39/0.84 % Length of proof is 37.
% 3.39/0.84 % Level of proof is 15.
% 3.39/0.84 % Maximum clause weight is 30.000.
% 3.39/0.84 % Given clauses 232.
% 3.39/0.84
% 3.39/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------