%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 02:44:25 PM UTC 2026
% Result : Theorem 12.13s 2.06s
% Output : Proof 12.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 80 ( 19 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 99 ( 37 ~; 33 |; 22 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f30_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
& ~ in(C,B) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B,C,D] :
( ( ( ( sk12(A,B) = apply(A,sk13(A,B))
& in(sk13(A,B),relation_dom(A))
& ~ in(sk12(A,B),B) )
| ( ( sk12(A,B) != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(sk12(A,B),B) )
| B = relation_rng(A) )
& ( ( ( C != apply(A,D)
| ~ in(D,relation_dom(A))
| in(C,B) )
& ( ( C = apply(A,sk11(A,B,C))
& in(sk11(A,B,C),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13])],[f30_nnf]) ).
cnf(c47,plain,
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f29,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
fof(f29_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A,B] :
( ~ in(apply(B,A),relation_rng(B))
& in(A,relation_dom(B))
& function(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
( ~ in(apply(sk10,sk9),relation_rng(sk10))
& in(sk9,relation_dom(sk10))
& function(sk10)
& relation(sk10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f29_nnf]) ).
cnf(c41,plain,
relation(sk10),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p214,plain,
( X1 != apply(sk10,X2)
| ~ in(X2,relation_dom(sk10))
| in(X1,X0)
| X0 != relation_rng(sk10)
| ~ function(sk10) ),
inference(resolution,[status(thm)],[c47,c41]) ).
cnf(p218,plain,
( X0 != apply(sk10,X1)
| ~ in(X1,relation_dom(sk10))
| in(X0,relation_rng(sk10))
| ~ function(sk10) ),
inference(equality_resolution,[status(thm)],[p214]) ).
cnf(p221,plain,
( ~ in(X0,relation_dom(sk10))
| in(apply(sk10,X0),relation_rng(sk10))
| ~ function(sk10) ),
inference(equality_resolution,[status(thm)],[p218]) ).
cnf(c42,plain,
function(sk10),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p223,plain,
( ~ in(X0,relation_dom(sk10))
| in(apply(sk10,X0),relation_rng(sk10)) ),
inference(resolution,[status(thm)],[p221,c42]) ).
cnf(c43,plain,
in(sk9,relation_dom(sk10)),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p224,plain,
in(apply(sk10,sk9),relation_rng(sk10)),
inference(resolution,[status(thm)],[p223,c43]) ).
cnf(c44,plain,
~ in(apply(sk10,sk9),relation_rng(sk10)),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p225,plain,
$false,
inference(resolution,[status(thm)],[p224,c44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:32:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.13/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.13/2.06 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------