%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 : Thu Sep 24 02:19:14 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 142 ( 9 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 162 ( 59 ~; 62 |; 31 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 90 ( 85 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ ! [A] : subset(finite_subsets(A),powerset(A)),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f50,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)],[f49]) ).
fof(f51,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f51]) ).
fof(f54,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [A,B] :
( ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) )
| ~ preboolean(B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f57,plain,
! [A,B] :
( ( ( ? [C] :
( ( ( finite(C)
& subset(C,A) )
| in(C,B) )
& ( ~ finite(C)
| ~ subset(C,A)
| ~ in(C,B) ) )
| B = finite_subsets(A) )
& ( ! [C] :
( ( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [B] :
( ( ! [A] :
( ? [C] :
( ( ( finite(C)
& subset(C,A) )
| in(C,B) )
& ( ~ finite(C)
| ~ subset(C,A)
| ~ in(C,B) ) )
| B = finite_subsets(A) )
& ! [A] :
( ( ! [C] :
( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ! [C] :
( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [B] :
( ( ! [A] :
( ( ( ( finite(sK1_skl(A,B))
& subset(sK1_skl(A,B),A) )
| in(sK1_skl(A,B),B) )
& ( ~ finite(sK1_skl(A,B))
| ~ subset(sK1_skl(A,B),A)
| ~ in(sK1_skl(A,B),B) ) )
| B = finite_subsets(A) )
& ! [A] :
( ( ! [C] :
( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ! [C] :
( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(A,B))],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f66,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f69,plain,
( ! [A] : preboolean(powerset(A))
& ! [A] : diff_closed(powerset(A))
& ! [A] : cup_closed(powerset(A))
& ! [A] : ~ empty(powerset(A)) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f70,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f126,plain,
? [A] : ~ subset(finite_subsets(A),powerset(A)),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f127,plain,
~ subset(finite_subsets(sK12_skl),powerset(sK12_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f126]) ).
fof(f128,plain,
~ subset(finite_subsets(sK12_skl),powerset(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f130,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f132,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f134,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f149,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f60]) ).
fof(f153,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f66]) ).
fof(f179,plain,
! [X0,X1] :
( subset(sK0_skl(X1,finite_subsets(X0)),X0)
| subset(finite_subsets(X0),X1) ),
inference(resolution,[status(thm)],[f54,f153]) ).
fof(f481,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| in(X1,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f130,f134]) ).
fof(f486,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f70]) ).
fof(f491,plain,
! [X0,X1] :
( subset(X1,powerset(X0))
| ~ subset(sK0_skl(powerset(X0),X1),X0) ),
inference(resolution,[status(thm)],[f486,f55]) ).
fof(f959,plain,
! [X0] :
( subset(finite_subsets(X0),powerset(X0))
| subset(finite_subsets(X0),powerset(X0)) ),
inference(resolution,[status(thm)],[f491,f179]) ).
fof(f963,plain,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(duplicate_literals_removal,[status(thm)],[f959]) ).
fof(f965,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f128,f963]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:50:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.071767 seconds
% 0.13/0.44 % CPU time: 0.348261 seconds
% 0.13/0.44 % Total memory used: 59.635 MB
% 0.13/0.44 % Net memory used: 58.714 MB
%------------------------------------------------------------------------------