%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET997+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 02:44:26 PM UTC 2026
% Result : Theorem 25.90s 3.98s
% Output : Proof 25.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 5 unt; 0 def)
% Number of atoms : 123 ( 25 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 145 ( 52 ~; 52 |; 32 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 31 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c4,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f23,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ! [C] :
~ ( ! [D] :
~ ( C = apply(B,D)
& in(D,relation_dom(B)) )
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
fof(f23_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ! [C] :
~ ( ! [D] :
~ ( C = apply(B,D)
& in(D,relation_dom(B)) )
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f23_nnf,plain,
? [A,B] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( ? [D] :
( C = apply(B,D)
& in(D,relation_dom(B)) )
| ~ in(C,A) )
& function(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f23_neg]) ).
fof(f23_sk,plain,
! [C] :
( ~ subset(sk13,relation_rng(sk14))
& ( ( C = apply(sk14,sk15(C))
& in(sk15(C),relation_dom(sk14)) )
| ~ in(C,sk13) )
& function(sk14)
& relation(sk14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15])],[f23_nnf]) ).
cnf(c47,plain,
( X2 = apply(sk14,sk15(X2))
| ~ in(X2,sk13) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p65,plain,
( sk0(sk13,X0) = apply(sk14,sk15(sk0(sk13,X0)))
| subset(sk13,X0) ),
inference(resolution,[status(thm)],[c4,c47]) ).
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/sandbox2/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(c8,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]) ).
cnf(c44,plain,
relation(sk14),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p92,plain,
( X1 != apply(sk14,X2)
| ~ in(X2,relation_dom(sk14))
| in(X1,X0)
| X0 != relation_rng(sk14)
| ~ function(sk14) ),
inference(resolution,[status(thm)],[c8,c44]) ).
cnf(p132,plain,
( X0 != apply(sk14,X1)
| ~ in(X1,relation_dom(sk14))
| in(X0,relation_rng(sk14))
| ~ function(sk14) ),
inference(equality_resolution,[status(thm)],[p92]) ).
cnf(p144,plain,
( ~ in(X0,relation_dom(sk14))
| in(apply(sk14,X0),relation_rng(sk14))
| ~ function(sk14) ),
inference(equality_resolution,[status(thm)],[p132]) ).
cnf(c45,plain,
function(sk14),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p146,plain,
( ~ in(X0,relation_dom(sk14))
| in(apply(sk14,X0),relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p144,c45]) ).
cnf(c46,plain,
( in(sk15(X2),relation_dom(sk14))
| ~ in(X2,sk13) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p63,plain,
( in(sk15(sk0(sk13,X0)),relation_dom(sk14))
| subset(sk13,X0) ),
inference(resolution,[status(thm)],[c4,c46]) ).
cnf(p148,plain,
( subset(sk13,X0)
| in(apply(sk14,sk15(sk0(sk13,X0))),relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p146,p63]) ).
cnf(p154,plain,
( subset(sk13,X0)
| in(sk0(sk13,X0),relation_rng(sk14))
| subset(sk13,X0) ),
inference(superposition,[status(thm)],[p65,p148]) ).
cnf(p169,plain,
( in(sk0(sk13,X0),relation_rng(sk14))
| subset(sk13,X0) ),
inference(factoring,[status(thm)],[p154]) ).
cnf(c5,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p171,plain,
( subset(sk13,relation_rng(sk14))
| subset(sk13,relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p169,c5]) ).
cnf(p182,plain,
subset(sk13,relation_rng(sk14)),
inference(factoring,[status(thm)],[p171]) ).
cnf(c48,plain,
~ subset(sk13,relation_rng(sk14)),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p183,plain,
$false,
inference(resolution,[status(thm)],[p182,c48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET997+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:35:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.90/3.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.90/3.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------