%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:51:13 PM UTC 2026
% Result : Theorem 30.38s 4.47s
% Output : Proof 30.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 122 ( 22 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 139 ( 52 ~; 43 |; 28 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk0(A,B,C),B)
& in(sk0(A,B,C),A)
& ~ in(sk0(A,B,C),C) )
| ( ( in(sk0(A,B,C),B)
| ~ in(sk0(A,B,C),A) )
& in(sk0(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c7,plain,
( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p70,plain,
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c7]) ).
fof(f1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f19,conjecture,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f19_neg,negated_conjecture,
~ ! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(C,subset_complement(A,B))
& ~ in(C,B)
& element(C,A) )
& element(B,powerset(A)) )
& A != empty_set ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ~ in(sk8,subset_complement(sk6,sk7))
& ~ in(sk8,sk7)
& element(sk8,sk6)
& element(sk7,powerset(sk6))
& sk6 != empty_set ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7,sk8])],[f19_nnf]) ).
cnf(c34,plain,
element(sk8,sk6),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p41,plain,
( in(sk8,sk6)
| empty(sk6) ),
inference(resolution,[status(thm)],[c1,c34]) ).
cnf(p182,plain,
( empty(sk6)
| in(sk8,X0)
| in(sk8,set_difference(sk6,X0)) ),
inference(resolution,[status(thm)],[p70,p41]) ).
fof(f3,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f3_nnf,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,A] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c14,plain,
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c33,plain,
element(sk7,powerset(sk6)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p116,plain,
subset_complement(sk6,sk7) = set_difference(sk6,sk7),
inference(resolution,[status(thm)],[c14,c33]) ).
cnf(c36,plain,
~ in(sk8,subset_complement(sk6,sk7)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p117,plain,
~ in(sk8,set_difference(sk6,sk7)),
inference(demodulation,[status(thm)],[p116,c36]) ).
cnf(p219,plain,
( empty(sk6)
| in(sk8,sk7) ),
inference(resolution,[status(thm)],[p182,p117]) ).
cnf(c35,plain,
~ in(sk8,sk7),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p221,plain,
empty(sk6),
inference(resolution,[status(thm)],[p219,c35]) ).
fof(f20,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f20_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c37,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p224,plain,
sk6 = empty_set,
inference(resolution,[status(thm)],[p221,c37]) ).
cnf(c32,plain,
sk6 != empty_set,
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p225,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p224,c32]) ).
cnf(p282,plain,
$false,
inference(equality_resolution,[status(thm)],[p225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n011.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 13:02:45 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 30.38/4.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.38/4.47 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------