%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU173+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 : n008.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 23.97s 3.44s
% Output : Proof 23.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 105 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 117 ( 43 ~; 41 |; 21 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 1 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
& ~ in(C,B) )
| ( ~ subset(C,A)
& in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,A,C] :
( ( ( subset(sk0(A,B),A)
& ~ in(sk0(A,B),B) )
| ( ~ subset(sk0(A,B),A)
& in(sk0(A,B),B) )
| B = powerset(A) )
& ( ( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( ~ subset(X2,X0)
| in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p68,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/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(sk1(A,B),B)
& in(sk1(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c13,plain,
( ~ in(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c12,plain,
( in(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f10,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f10_neg,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A,B] :
( ~ element(A,powerset(B))
& ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
! [C] :
( ~ element(sk3,powerset(sk4))
& ( in(C,sk4)
| ~ in(C,sk3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f10_nnf]) ).
cnf(c20,plain,
( in(X2,sk4)
| ~ in(X2,sk3) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p42,plain,
( in(sk1(sk3,X0),sk4)
| subset(sk3,X0) ),
inference(resolution,[status(thm)],[c12,c20]) ).
cnf(p48,plain,
( subset(sk3,sk4)
| subset(sk3,sk4) ),
inference(resolution,[status(thm)],[c13,p42]) ).
cnf(p49,plain,
subset(sk3,sk4),
inference(factoring,[status(thm)],[p48]) ).
cnf(p71,plain,
in(sk3,powerset(sk4)),
inference(resolution,[status(thm)],[p68,p49]) ).
fof(f2,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(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c8,plain,
( ~ in(X1,X0)
| element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p73,plain,
( element(sk3,powerset(sk4))
| empty(powerset(sk4)) ),
inference(resolution,[status(thm)],[p71,c8]) ).
cnf(c21,plain,
~ element(sk3,powerset(sk4)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p74,plain,
empty(powerset(sk4)),
inference(resolution,[status(thm)],[p73,c21]) ).
fof(f8,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f8_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c18,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p75,plain,
$false,
inference(resolution,[status(thm)],[p74,c18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU173+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:03:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.97/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.97/3.44 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------