%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 258.80s 37.75s
% Output : Proof 258.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 6 unt; 0 def)
% Number of atoms : 170 ( 80 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 202 ( 77 ~; 86 |; 30 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn 25 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c4,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p71,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
cnf(p741,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[p71]) ).
fof(f4,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(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ( ( sk2(A,B) = apply(A,sk3(A,B))
& in(sk3(A,B),relation_dom(A))
& ~ in(sk2(A,B),B) )
| ( ( sk2(A,B) != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(sk2(A,B),B) )
| B = relation_rng(A) )
& ( ( ( C != apply(A,D)
| ~ in(D,relation_dom(A))
| in(C,B) )
& ( ( C = apply(A,sk1(A,B,C))
& in(sk1(A,B,C),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f4_nnf]) ).
cnf(c11,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)],[f4_sk]) ).
fof(f24,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(B) = singleton(A)
=> relation_rng(B) = singleton(apply(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
fof(f24_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(B) = singleton(A)
=> relation_rng(B) = singleton(apply(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
? [A,B] :
( relation_rng(B) != singleton(apply(B,A))
& relation_dom(B) = singleton(A)
& function(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
( relation_rng(sk14) != singleton(apply(sk14,sk13))
& relation_dom(sk14) = singleton(sk13)
& function(sk14)
& relation(sk14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f24_nnf]) ).
cnf(c48,plain,
relation(sk14),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p124,plain,
( X1 != apply(sk14,X2)
| ~ in(X2,singleton(sk13))
| in(X1,X0)
| X0 != relation_rng(sk14)
| ~ function(sk14) ),
inference(resolution,[status(thm)],[c11,c48]) ).
cnf(p133,plain,
( X0 != apply(sk14,X1)
| ~ in(X1,singleton(sk13))
| in(X0,relation_rng(sk14))
| ~ function(sk14) ),
inference(equality_resolution,[status(thm)],[p124]) ).
cnf(c49,plain,
function(sk14),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p137,plain,
( X0 != apply(sk14,X1)
| ~ in(X1,singleton(sk13))
| in(X0,relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p133,c49]) ).
cnf(p14451,plain,
( X0 != apply(sk14,sk13)
| in(X0,relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p741,p137]) ).
cnf(c6,plain,
( sk0(X0,X1) = X0
| in(sk0(X0,X1),X1)
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p14523,plain,
( in(sk0(apply(sk14,sk13),X0),X0)
| X0 = singleton(apply(sk14,sk13))
| in(sk0(apply(sk14,sk13),X0),relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p14451,c6]) ).
cnf(p18616,plain,
( relation_rng(sk14) = singleton(apply(sk14,sk13))
| in(sk0(apply(sk14,sk13),relation_rng(sk14)),relation_rng(sk14)) ),
inference(factoring,[status(thm)],[p14523]) ).
cnf(c9,plain,
( in(sk1(X0,X1,X2),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p93,plain,
( in(sk1(sk14,X0,X1),singleton(sk13))
| ~ in(X1,X0)
| X0 != relation_rng(sk14)
| ~ function(sk14) ),
inference(resolution,[status(thm)],[c9,c48]) ).
cnf(p102,plain,
( in(sk1(sk14,relation_rng(sk14),X0),singleton(sk13))
| ~ in(X0,relation_rng(sk14))
| ~ function(sk14) ),
inference(equality_resolution,[status(thm)],[p93]) ).
cnf(p104,plain,
( in(sk1(sk14,relation_rng(sk14),X0),singleton(sk13))
| ~ in(X0,relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p102,c49]) ).
cnf(p18653,plain,
( in(sk1(sk14,relation_rng(sk14),sk0(apply(sk14,sk13),relation_rng(sk14))),singleton(sk13))
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(resolution,[status(thm)],[p18616,p104]) ).
cnf(c3,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p70,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p19270,plain,
( sk1(sk14,relation_rng(sk14),sk0(apply(sk14,sk13),relation_rng(sk14))) = sk13
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(resolution,[status(thm)],[p18653,p70]) ).
cnf(c10,plain,
( X2 = apply(X0,sk1(X0,X1,X2))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p108,plain,
( X1 = apply(sk14,sk1(sk14,X0,X1))
| ~ in(X1,X0)
| X0 != relation_rng(sk14)
| ~ function(sk14) ),
inference(resolution,[status(thm)],[c10,c48]) ).
cnf(p117,plain,
( X0 = apply(sk14,sk1(sk14,relation_rng(sk14),X0))
| ~ in(X0,relation_rng(sk14))
| ~ function(sk14) ),
inference(equality_resolution,[status(thm)],[p108]) ).
cnf(p119,plain,
( X0 = apply(sk14,sk1(sk14,relation_rng(sk14),X0))
| ~ in(X0,relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p117,c49]) ).
cnf(p18654,plain,
( sk0(apply(sk14,sk13),relation_rng(sk14)) = apply(sk14,sk1(sk14,relation_rng(sk14),sk0(apply(sk14,sk13),relation_rng(sk14))))
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(resolution,[status(thm)],[p18616,p119]) ).
cnf(p52719,plain,
( sk0(apply(sk14,sk13),relation_rng(sk14)) = apply(sk14,sk13)
| relation_rng(sk14) = singleton(apply(sk14,sk13))
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(superposition,[status(thm)],[p19270,p18654]) ).
cnf(p52726,plain,
( sk0(apply(sk14,sk13),relation_rng(sk14)) = apply(sk14,sk13)
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(factoring,[status(thm)],[p52719]) ).
cnf(c7,plain,
( ~ in(sk0(X0,X1),X1)
| sk0(X0,X1) != X0
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p52832,plain,
( ~ in(sk0(apply(sk14,sk13),relation_rng(sk14)),relation_rng(sk14))
| relation_rng(sk14) = singleton(apply(sk14,sk13))
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(resolution,[status(thm)],[p52726,c7]) ).
cnf(p52954,plain,
( ~ in(sk0(apply(sk14,sk13),relation_rng(sk14)),relation_rng(sk14))
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(factoring,[status(thm)],[p52832]) ).
cnf(p52955,plain,
( relation_rng(sk14) = singleton(apply(sk14,sk13))
| relation_rng(sk14) = singleton(apply(sk14,sk13)) ),
inference(resolution,[status(thm)],[p52954,p18616]) ).
cnf(p52957,plain,
relation_rng(sk14) = singleton(apply(sk14,sk13)),
inference(factoring,[status(thm)],[p52955]) ).
cnf(c51,plain,
relation_rng(sk14) != singleton(apply(sk14,sk13)),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p53066,plain,
$false,
inference(resolution,[status(thm)],[p52957,c51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 12:34:49 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 258.80/37.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 258.80/37.75 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------