%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET095+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:42:12 PM UTC 2026
% Result : Theorem 55.15s 7.65s
% Output : Proof 55.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 34 unt; 0 def)
% Number of atoms : 90 ( 33 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 70 ( 31 ~; 20 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 64 ( 4 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/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(c2,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t170,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t807,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t170]) ).
fof(f7,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f7_nnf,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c18,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t36,plain,
ifeq(member(X1,singleton(X2)),true,X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t259,plain,
ifeq(member(X1,singleton(X2)),true,X1,X2) = X2,
inference(orient,[status(thm)],[t36]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t116,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t391,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t116]) ).
fof(f11,conjecture,
! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI44) ).
fof(f11_neg,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,X] :
( ~ subset(singleton(X),A)
& member(X,A) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ~ subset(singleton(sk4),sk3)
& member(sk4,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f11_nnf]) ).
cnf(c30,plain,
~ subset(singleton(sk4),sk3),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
subset(singleton(sk4),sk3) = false,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t912,plain,
subset(singleton(sk4),sk3) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t921,plain,
true = or(false,member(sk0(singleton(sk4),sk3),singleton(sk4))),
inference(cp,[status(thm)],[t391,t912]) ).
cnf(t7,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t1404,plain,
true = member(sk0(singleton(sk4),sk3),singleton(sk4)),
inference(step,[status(thm)],[t921,t257]) ).
cnf(t1288,plain,
member(sk0(singleton(sk4),sk3),singleton(sk4)) = true,
inference(orient,[status(thm)],[t1404]) ).
cnf(t1289,plain,
sk4 = ifeq(true,true,sk0(singleton(sk4),sk3),sk4),
inference(cp,[status(thm)],[t259,t1288]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t1405,plain,
sk4 = sk0(singleton(sk4),sk3),
inference(step,[status(thm)],[t1289,t258]) ).
cnf(t1301,plain,
sk0(singleton(sk4),sk3) = sk4,
inference(orient,[status(thm)],[t1405]) ).
cnf(t1302,plain,
true = ifeq(member(sk4,sk3),true,subset(singleton(sk4),sk3),true),
inference(cp,[status(thm)],[t807,t1301]) ).
cnf(c29,plain,
member(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t4,plain,
member(sk4,sk3) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t293,plain,
member(sk4,sk3) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t1406,plain,
true = ifeq(true,true,subset(singleton(sk4),sk3),true),
inference(step,[status(thm)],[t1302,t293]) ).
cnf(t1407,plain,
true = subset(singleton(sk4),sk3),
inference(step,[status(thm)],[t1406,t258]) ).
cnf(t1408,plain,
true = false,
inference(step,[status(thm)],[t1407,t912]) ).
cnf(t1303,plain,
false = true,
inference(orient,[status(thm)],[t1408]) ).
fof(f5,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f5_nnf,plain,
! [X] : ~ member(X,empty_set),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : ~ member(X,empty_set),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c14,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f6,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f6_nnf,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,E,A] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c16,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c16,c30]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1303]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET095+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:46:18 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 55.15/7.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.15/7.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------