%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 : Fri Sep 25 02:43:29 PM UTC 2026
% Result : Theorem 5.41s 16.65s
% Output : Proof 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 19 unt; 0 def)
% Number of atoms : 152 ( 13 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 137 ( 45 ~; 67 |; 19 &)
% ( 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 : 78 ( 5 sgn 42 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(f4_nnf,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c8,plain,
symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f2,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2_nnf,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f3,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f3_nnf,plain,
! [B,C] : union(B,C) = union(C,B),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] : union(B,C) = union(C,B),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c7,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p75,plain,
union(difference(X0,X1),difference(X1,X0)) = symmetric_difference(X1,X0),
inference(superposition,[status(thm)],[c6,c7]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p73,plain,
( member(X0,difference(X2,X1))
| member(X0,difference(X1,X2))
| ~ member(X0,symmetric_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c6,c0]) ).
fof(f6,conjecture,
! [B,C,D] :
( member(B,symmetric_difference(C,D))
<=> ~ ( member(B,C)
<=> member(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th23) ).
fof(f6_neg,negated_conjecture,
~ ! [B,C,D] :
( member(B,symmetric_difference(C,D))
<=> ~ ( member(B,C)
<=> member(B,D) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,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(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ( ( ( member(sk1,sk3)
& ~ member(sk1,sk2) )
| ( ~ member(sk1,sk3)
& member(sk1,sk2) ) )
& ~ member(sk1,symmetric_difference(sk2,sk3)) )
| ( ( ~ member(sk1,sk3)
| member(sk1,sk2) )
& ( member(sk1,sk3)
| ~ member(sk1,sk2) )
& member(sk1,symmetric_difference(sk2,sk3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f6_nnf]) ).
cnf(c17,plain,
( member(sk1,sk3)
| member(sk1,sk2)
| member(sk1,symmetric_difference(sk2,sk3)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p490,plain,
( member(sk1,sk3)
| member(sk1,sk2)
| member(sk1,difference(sk3,sk2))
| member(sk1,difference(sk2,sk3)) ),
inference(resolution,[status(thm)],[p73,c17]) ).
fof(f1,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f1_nnf,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [D,B,C] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p501,plain,
( member(sk1,sk3)
| member(sk1,sk3)
| member(sk1,sk2)
| member(sk1,difference(sk2,sk3)) ),
inference(resolution,[status(thm)],[p490,c3]) ).
cnf(p503,plain,
( member(sk1,sk3)
| member(sk1,sk2)
| member(sk1,difference(sk2,sk3)) ),
inference(factoring,[status(thm)],[p501]) ).
cnf(p539,plain,
( member(sk1,sk2)
| member(sk1,sk3)
| member(sk1,sk2) ),
inference(resolution,[status(thm)],[p503,c3]) ).
cnf(p541,plain,
( member(sk1,sk3)
| member(sk1,sk2) ),
inference(factoring,[status(thm)],[p539]) ).
cnf(c5,plain,
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p545,plain,
( member(sk1,X0)
| member(sk1,difference(sk3,X0))
| member(sk1,sk2) ),
inference(resolution,[status(thm)],[p541,c5]) ).
cnf(p662,plain,
( member(sk1,difference(sk3,sk2))
| member(sk1,sk2) ),
inference(factoring,[status(thm)],[p545]) ).
cnf(c1,plain,
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p680,plain,
( member(sk1,union(difference(sk3,sk2),X0))
| member(sk1,sk2) ),
inference(resolution,[status(thm)],[p662,c1]) ).
cnf(p686,plain,
( member(sk1,symmetric_difference(sk2,sk3))
| member(sk1,sk2) ),
inference(superposition,[status(thm)],[p75,p680]) ).
cnf(c25,plain,
( ~ member(sk1,symmetric_difference(sk2,sk3))
| ~ member(sk1,sk3)
| member(sk1,sk2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p543,plain,
( ~ member(sk1,symmetric_difference(sk2,sk3))
| member(sk1,sk2)
| member(sk1,sk2) ),
inference(resolution,[status(thm)],[p541,c25]) ).
cnf(p661,plain,
( ~ member(sk1,symmetric_difference(sk2,sk3))
| member(sk1,sk2) ),
inference(factoring,[status(thm)],[p543]) ).
cnf(p690,plain,
( member(sk1,sk2)
| member(sk1,sk2) ),
inference(resolution,[status(thm)],[p686,p661]) ).
cnf(p691,plain,
member(sk1,sk2),
inference(factoring,[status(thm)],[p690]) ).
cnf(p708,plain,
( member(sk1,X0)
| member(sk1,difference(sk2,X0)) ),
inference(resolution,[status(thm)],[p691,c5]) ).
cnf(p752,plain,
( member(sk1,union(difference(sk2,X0),X1))
| member(sk1,X0) ),
inference(resolution,[status(thm)],[p708,c1]) ).
cnf(p823,plain,
( member(sk1,symmetric_difference(X0,sk2))
| member(sk1,X0) ),
inference(superposition,[status(thm)],[p75,p752]) ).
cnf(p828,plain,
( member(sk1,symmetric_difference(sk2,X0))
| member(sk1,X0) ),
inference(superposition,[status(thm)],[c8,p823]) ).
cnf(c20,plain,
( ~ member(sk1,symmetric_difference(sk2,sk3))
| member(sk1,sk3)
| ~ member(sk1,sk2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p707,plain,
( ~ member(sk1,symmetric_difference(sk2,sk3))
| member(sk1,sk3) ),
inference(resolution,[status(thm)],[p691,c20]) ).
cnf(p832,plain,
( member(sk1,sk3)
| member(sk1,sk3) ),
inference(resolution,[status(thm)],[p828,p707]) ).
cnf(p833,plain,
member(sk1,sk3),
inference(factoring,[status(thm)],[p832]) ).
cnf(c18,plain,
( ~ member(sk1,sk2)
| ~ member(sk1,sk3)
| member(sk1,symmetric_difference(sk2,sk3)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p834,plain,
( ~ member(sk1,sk2)
| member(sk1,symmetric_difference(sk2,sk3)) ),
inference(resolution,[status(thm)],[p833,c18]) ).
cnf(p868,plain,
member(sk1,symmetric_difference(sk2,sk3)),
inference(resolution,[status(thm)],[p834,p691]) ).
cnf(p872,plain,
( member(sk1,difference(sk3,sk2))
| member(sk1,difference(sk2,sk3)) ),
inference(resolution,[status(thm)],[p868,p73]) ).
cnf(c4,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p1126,plain,
( ~ member(sk1,sk2)
| member(sk1,difference(sk2,sk3)) ),
inference(resolution,[status(thm)],[p872,c4]) ).
cnf(p1153,plain,
member(sk1,difference(sk2,sk3)),
inference(resolution,[status(thm)],[p1126,p691]) ).
cnf(p1156,plain,
~ member(sk1,sk3),
inference(resolution,[status(thm)],[p1153,c4]) ).
cnf(p1158,plain,
$false,
inference(resolution,[status(thm)],[p1156,p833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/15.59 % Computer : n006.cluster.edu
% 0.10/15.59 % Model : x86_64 x86_64
% 0.10/15.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.59 % Memory : 8046.5625MB
% 0.10/15.59 % OS : Linux 6.8.0-71-generic
% 0.10/15.59 % CPULimit : 300
% 0.10/15.59 % WCLimit : 300
% 0.10/15.59 % DateTime : Thu Sep 24 11:20:28 UTC 2026
% 0.10/15.59 % CPUTime :
% 0.10/15.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.41/16.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.41/16.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------