%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM383+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 : n010.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 02:19:55 PM UTC 2026
% Result : Theorem 3.32s 0.88s
% Output : Proof 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 98 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 43 ~; 33 |; 15 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 61 ( 1 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f22_nnf,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c40,plain,
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f26,conjecture,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(f26_neg,negated_conjecture,
~ ! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [A,B] :
( subset(B,A)
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
( subset(sk12,sk11)
& in(sk11,sk12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12])],[f26_nnf]) ).
cnf(c44,plain,
in(sk11,sk12),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p72,plain,
( element(sk11,X0)
| ~ element(sk12,powerset(X0)) ),
inference(resolution,[status(thm)],[c40,c44]) ).
fof(f21,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f21_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c39,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(c45,plain,
subset(sk12,sk11),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p70,plain,
element(sk12,powerset(sk11)),
inference(resolution,[status(thm)],[c39,c45]) ).
cnf(p83,plain,
element(sk11,sk11),
inference(resolution,[status(thm)],[p72,p70]) ).
fof(f20,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f20_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c37,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p84,plain,
( in(sk11,sk11)
| empty(sk11) ),
inference(resolution,[status(thm)],[p83,c37]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p47,plain,
~ in(X0,X0),
inference(factoring,[status(thm)],[c0]) ).
cnf(p85,plain,
empty(sk11),
inference(resolution,[status(thm)],[p84,p47]) ).
fof(f24,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f24_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c42,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p88,plain,
sk11 = empty_set,
inference(resolution,[status(thm)],[p85,c42]) ).
fof(f23,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f23_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c41,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p77,plain,
( ~ empty(X0)
| ~ element(sk12,powerset(X0)) ),
inference(resolution,[status(thm)],[c41,c44]) ).
cnf(p79,plain,
~ empty(sk11),
inference(resolution,[status(thm)],[p77,p70]) ).
cnf(p96,plain,
~ empty(empty_set),
inference(demodulation,[status(thm)],[p88,p79]) ).
fof(f5,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f5_nnf,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p98,plain,
$false,
inference(resolution,[status(thm)],[p96,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM383+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 : n010.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 03:49:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.32/0.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.32/0.88 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------