%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:18:31 PM UTC 2026
% Result : Unsatisfiable 8.80s 1.53s
% Output : Proof 8.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 28 unt; 0 def)
% Number of atoms : 100 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 106 ( 66 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 6 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f170,axiom,
( ~ member(Z,f44(Z))
| member(Z,natural_numbers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers6) ).
fof(f170_nnf,plain,
! [Z] :
( ~ member(Z,f44(Z))
| member(Z,natural_numbers) ),
inference(nnf_transformation,[status(thm)],[f170]) ).
fof(f170_sk,plain,
! [Z] :
( ~ member(Z,f44(Z))
| member(Z,natural_numbers) ),
inference(skolemisation,[status(esa)],[f170_nnf]) ).
cnf(c170,plain,
( ~ member(X0,f44(X0))
| member(X0,natural_numbers) ),
inference(cnf_transformation,[status(esa)],[f170_sk]) ).
cnf(t72,plain,
ifeq(member(X1,f44(X1)),true,member(X1,natural_numbers),true) = true,
inference(equality_encoding,[status(esa)],[c170]) ).
cnf(t521,plain,
ifeq(member(X1,f44(X1)),true,member(X1,natural_numbers),true) = true,
inference(orient,[status(thm)],[t72]) ).
cnf(f168,axiom,
( member(empty_set,f44(Z))
| ~ little_set(Z)
| member(Z,natural_numbers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',natural_numbers4) ).
fof(f168_nnf,plain,
! [Z] :
( member(empty_set,f44(Z))
| ~ little_set(Z)
| member(Z,natural_numbers) ),
inference(nnf_transformation,[status(thm)],[f168]) ).
fof(f168_sk,plain,
! [Z] :
( member(empty_set,f44(Z))
| ~ little_set(Z)
| member(Z,natural_numbers) ),
inference(skolemisation,[status(esa)],[f168_nnf]) ).
cnf(c168,plain,
( member(empty_set,f44(X0))
| ~ little_set(X0)
| member(X0,natural_numbers) ),
inference(cnf_transformation,[status(esa)],[f168_sk]) ).
cnf(t126,plain,
ifeq(little_set(X1),true,or(member(X1,natural_numbers),member(empty_set,f44(X1))),true) = true,
inference(equality_encoding,[status(esa)],[c168]) ).
cnf(t442,plain,
ifeq(little_set(X1),true,or(member(X1,natural_numbers),member(empty_set,f44(X1))),true) = true,
inference(orient,[status(thm)],[t126]) ).
cnf(f0,axiom,
( little_set(X)
| ~ member(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f0_nnf,plain,
! [X,Y] :
( little_set(X)
| ~ member(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( little_set(X)
| ~ member(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t38,plain,
ifeq(member(X1,X2),true,little_set(X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t469,plain,
ifeq(member(X1,X2),true,little_set(X1),true) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(f60,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity2) ).
fof(f60_nnf,plain,
member(empty_set,infinity),
inference(nnf_transformation,[status(thm)],[f60]) ).
cnf(c60,plain,
member(empty_set,infinity),
inference(cnf_transformation,[status(esa)],[f60_nnf]) ).
cnf(t6,plain,
member(empty_set,infinity) = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(t981,plain,
member(empty_set,infinity) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t982,plain,
true = ifeq(true,true,little_set(empty_set),true),
inference(cp,[status(thm)],[t469,t981]) ).
cnf(t1097,plain,
little_set(empty_set) = true,
inference(orient,[status(thm)],[t982]) ).
cnf(t1106,plain,
true = ifeq(true,true,or(member(empty_set,natural_numbers),member(empty_set,f44(empty_set))),true),
inference(cp,[status(thm)],[t442,t1097]) ).
cnf(t2083,plain,
member(empty_set,f44(empty_set)) = true,
inference(orient,[status(thm)],[t1106]) ).
cnf(t2090,plain,
true = ifeq(true,true,member(empty_set,natural_numbers),true),
inference(cp,[status(thm)],[t521,t2083]) ).
cnf(t2145,plain,
false = true,
inference(orient,[status(thm)],[t2090]) ).
cnf(f30,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f30_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f57,axiom,
~ member(Z,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f57_nnf,plain,
! [Z] : ~ member(Z,empty_set),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [Z] : ~ member(Z,empty_set),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(f70,axiom,
( X != Y
| ~ proper_subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset2) ).
fof(f70_nnf,plain,
! [X,Y] :
( X != Y
| ~ proper_subset(X,Y) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [X,Y] :
( X != Y
| ~ proper_subset(X,Y) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f94,axiom,
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint1) ).
fof(f94_nnf,plain,
! [X,Y,U] :
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
inference(nnf_transformation,[status(thm)],[f94]) ).
fof(f94_sk,plain,
! [X,Y,U] :
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
inference(skolemisation,[status(esa)],[f94_nnf]) ).
cnf(c94,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(f200,axiom,
( Z != empty_set
| ~ member(Z,prime_numbers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers2) ).
fof(f200_nnf,plain,
! [Z] :
( Z != empty_set
| ~ member(Z,prime_numbers) ),
inference(nnf_transformation,[status(thm)],[f200]) ).
fof(f200_sk,plain,
! [Z] :
( Z != empty_set
| ~ member(Z,prime_numbers) ),
inference(skolemisation,[status(esa)],[f200_nnf]) ).
cnf(c200,plain,
( X0 != empty_set
| ~ member(X0,prime_numbers) ),
inference(cnf_transformation,[status(esa)],[f200_sk]) ).
cnf(f201,axiom,
( Z != successor(empty_set)
| ~ member(Z,prime_numbers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_numbers3) ).
fof(f201_nnf,plain,
! [Z] :
( Z != successor(empty_set)
| ~ member(Z,prime_numbers) ),
inference(nnf_transformation,[status(thm)],[f201]) ).
fof(f201_sk,plain,
! [Z] :
( Z != successor(empty_set)
| ~ member(Z,prime_numbers) ),
inference(skolemisation,[status(esa)],[f201_nnf]) ).
cnf(c201,plain,
( X0 != successor(empty_set)
| ~ member(X0,prime_numbers) ),
inference(cnf_transformation,[status(esa)],[f201_sk]) ).
cnf(f219,negated_conjecture,
~ member(empty_set,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_a_natural) ).
fof(f219_nnf,plain,
~ member(empty_set,natural_numbers),
inference(nnf_transformation,[status(thm)],[f219]) ).
fof(f219_sk,plain,
~ member(empty_set,natural_numbers),
inference(skolemisation,[status(esa)],[f219_nnf]) ).
cnf(c219,plain,
~ member(empty_set,natural_numbers),
inference(cnf_transformation,[status(esa)],[f219_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c30,c57,c70,c94,c200,c201,c219]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2145]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 02:44:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.80/1.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.80/1.53 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------