%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:42:39 PM UTC 2026
% Result : Theorem 9.82s 1.80s
% Output : Proof 9.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 90 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 33 ~; 33 |; 13 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 5 sgn 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f4_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c9,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/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(p29,plain,
( member(sk0(union(X0,X1),X2),X1)
| member(sk0(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c9,c0]) ).
fof(f1,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f1_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p118,plain,
( member(sk0(union(empty_set,X0),X1),X0)
| subset(union(empty_set,X0),X1) ),
inference(resolution,[status(thm)],[p29,c3]) ).
cnf(c10,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p263,plain,
( subset(union(empty_set,X0),X0)
| subset(union(empty_set,X0),X0) ),
inference(resolution,[status(thm)],[p118,c10]) ).
cnf(p265,plain,
subset(union(empty_set,X0),X0),
inference(factoring,[status(thm)],[p263]) ).
fof(f3,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/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(c1,plain,
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p30,plain,
( member(sk0(X0,X1),union(X0,X2))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(p42,plain,
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[p30,c10]) ).
cnf(p92,plain,
subset(X0,union(X0,X1)),
inference(factoring,[status(thm)],[p42]) ).
cnf(p93,plain,
subset(X0,union(X1,X0)),
inference(superposition,[status(thm)],[c7,p92]) ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f2_nnf,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p95,plain,
( ~ subset(union(X1,X0),X0)
| X0 = union(X1,X0) ),
inference(resolution,[status(thm)],[p93,c6]) ).
cnf(p269,plain,
X0 = union(empty_set,X0),
inference(resolution,[status(thm)],[p265,p95]) ).
cnf(p278,plain,
union(X0,empty_set) = X0,
inference(superposition,[status(thm)],[p269,c7]) ).
fof(f8,conjecture,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(f8_neg,negated_conjecture,
~ ! [B] : union(B,empty_set) = B,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B] : union(B,empty_set) != B,
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
union(sk3,empty_set) != sk3,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f8_nnf]) ).
cnf(c20,plain,
union(sk3,empty_set) != sk3,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p279,plain,
sk3 != sk3,
inference(demodulation,[status(thm)],[p278,c20]) ).
cnf(p298,plain,
$false,
inference(equality_resolution,[status(thm)],[p279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 10:08:08 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.82/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.82/1.80 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------