%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:50:56 PM UTC 2026
% Result : Theorem 65.88s 10.06s
% Output : Proof 65.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 51 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 14 ~; 10 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 6 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f14_nnf,plain,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c27,plain,
symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f12,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f12_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c25,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p237,plain,
set_union2(set_difference(X0,X1),set_difference(X1,X0)) = symmetric_difference(X1,X0),
inference(superposition,[status(thm)],[c27,c25]) ).
fof(f27,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(f27_nnf,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c50,plain,
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f16,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f16_nnf,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c29,plain,
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f59,conjecture,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(symmetric_difference(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).
fof(f59_neg,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(symmetric_difference(A,B)) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f59_nnf,plain,
? [A,B] :
( ~ finite(symmetric_difference(A,B))
& finite(B)
& finite(A) ),
inference(nnf_transformation,[status(thm)],[f59_neg]) ).
fof(f59_sk,plain,
( ~ finite(symmetric_difference(sk26,sk27))
& finite(sk27)
& finite(sk26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk26,sk27])],[f59_nnf]) ).
cnf(c142,plain,
finite(sk26),
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(p248,plain,
finite(set_difference(sk26,X0)),
inference(resolution,[status(thm)],[c29,c142]) ).
cnf(p344,plain,
( finite(set_union2(set_difference(sk26,X1),X0))
| ~ finite(X0) ),
inference(resolution,[status(thm)],[c50,p248]) ).
cnf(c143,plain,
finite(sk27),
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(p249,plain,
finite(set_difference(sk27,X0)),
inference(resolution,[status(thm)],[c29,c143]) ).
cnf(p2197,plain,
finite(set_union2(set_difference(sk26,X0),set_difference(sk27,X1))),
inference(resolution,[status(thm)],[p344,p249]) ).
cnf(p2461,plain,
finite(symmetric_difference(sk26,sk27)),
inference(superposition,[status(thm)],[p237,p2197]) ).
cnf(c144,plain,
~ finite(symmetric_difference(sk26,sk27)),
inference(cnf_transformation,[status(esa)],[f59_sk]) ).
cnf(p2464,plain,
$false,
inference(resolution,[status(thm)],[p2461,c144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:47:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 65.88/10.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.88/10.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------