%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 02:43:07 PM UTC 2026
% Result : Theorem 31.31s 25.03s
% Output : Proof 31.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 4 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 55 ( 20 ~; 19 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 21 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
fof(f9_nnf,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,A,Y] :
( ( ~ member(X,Y)
| ~ member(Y,A)
| member(X,sum(A)) )
& ( ( member(X,sk1(X,A))
& member(sk1(X,A),A) )
| ~ member(X,sum(A)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f9_nnf]) ).
cnf(c25,plain,
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f11,conjecture,
! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI43) ).
fof(f11_neg,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,X] :
( ~ subset(X,sum(A))
& member(X,A) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ~ subset(sk4,sum(sk3))
& member(sk4,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f11_nnf]) ).
cnf(c29,plain,
member(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p317,plain,
( ~ member(X0,sk4)
| member(X0,sum(sk3)) ),
inference(resolution,[status(thm)],[c25,c29]) ).
fof(f0,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f0_nnf,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,X] :
( ( ( ~ member(sk0(A,B),B)
& member(sk0(A,B),A) )
| subset(A,B) )
& ( member(X,B)
| ~ member(X,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p368,plain,
( subset(sk4,X0)
| member(sk0(sk4,X0),sum(sk3)) ),
inference(resolution,[status(thm)],[p317,c1]) ).
cnf(c2,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p514,plain,
( subset(sk4,sum(sk3))
| subset(sk4,sum(sk3)) ),
inference(resolution,[status(thm)],[p368,c2]) ).
cnf(p544,plain,
subset(sk4,sum(sk3)),
inference(factoring,[status(thm)],[p514]) ).
cnf(c30,plain,
~ subset(sk4,sum(sk3)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p545,plain,
$false,
inference(resolution,[status(thm)],[p544,c30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/20.47 % Computer : n016.cluster.edu
% 0.20/20.47 % Model : x86_64 x86_64
% 0.20/20.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/20.47 % Memory : 8046.5625MB
% 0.20/20.47 % OS : Linux 6.8.0-71-generic
% 0.20/20.47 % CPULimit : 300
% 0.20/20.47 % WCLimit : 300
% 0.20/20.47 % DateTime : Thu Sep 24 10:46:35 UTC 2026
% 0.20/20.48 % CPUTime :
% 0.20/20.48 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 31.31/25.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.31/25.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------