%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU110+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 : n013.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 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 6 unt; 2 def)
% Number of atoms : 169 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 196 ( 76 ~; 81 |; 26 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 89 !; 6 ?)
% 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(f26,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f50,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f51,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)],[f50]) ).
fof(f52,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)],[f51]) ).
fof(f53,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))],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,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(f58,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)],[f57]) ).
fof(f59,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)],[f58]) ).
fof(f60,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))],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( finite(X2)
| ~ in(X2,X0)
| X0 != finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ finite(X2)
| ~ subset(X2,X1)
| in(X2,X0)
| X0 != finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f67,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f127,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f128,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
? [A,B] :
( ~ subset(finite_subsets(A),finite_subsets(B))
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f131,plain,
( ~ subset(finite_subsets(sK12_skl),finite_subsets(sK13_skl))
& subset(sK12_skl,sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(A,sK12_skl),skolemize(B,sK13_skl)],[f130]) ).
fof(f132,plain,
subset(sK12_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
~ subset(finite_subsets(sK12_skl),finite_subsets(sK13_skl)),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f154,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f61]) ).
fof(f155,plain,
! [X0,X1] :
( finite(X1)
| ~ in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f62]) ).
fof(f156,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X1,X0)
| in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f160,plain,
! [X0] :
( subset(X0,sK13_skl)
| ~ subset(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f129,f132]) ).
fof(f426,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f67]) ).
fof(f428,plain,
! [X0,X1] :
( subset(finite_subsets(X1),X0)
| subset(sK0_skl(X0,finite_subsets(X1)),X1) ),
inference(resolution,[status(thm)],[f426,f55]) ).
fof(f429,plain,
! [X0,X1] :
( finite(X0)
| ~ in(X0,finite_subsets(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f67]) ).
fof(f431,plain,
! [X0,X1] :
( subset(finite_subsets(X1),X0)
| finite(sK0_skl(X0,finite_subsets(X1))) ),
inference(resolution,[status(thm)],[f429,f55]) ).
fof(f432,plain,
! [X0,X1] :
( ~ finite(X0)
| ~ subset(X0,X1)
| in(X0,finite_subsets(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f67]) ).
fof(f433,plain,
! [X0,X1] :
( subset(X1,finite_subsets(X0))
| ~ finite(sK0_skl(finite_subsets(X0),X1))
| ~ subset(sK0_skl(finite_subsets(X0),X1),X0) ),
inference(resolution,[status(thm)],[f432,f56]) ).
fof(f1576,plain,
! [X0] :
( subset(sK0_skl(X0,finite_subsets(sK12_skl)),sK13_skl)
| subset(finite_subsets(sK12_skl),X0) ),
inference(resolution,[status(thm)],[f428,f160]) ).
fof(f1664,plain,
( subset(finite_subsets(sK12_skl),finite_subsets(sK13_skl))
| ~ finite(sK0_skl(finite_subsets(sK13_skl),finite_subsets(sK12_skl)))
| subset(finite_subsets(sK12_skl),finite_subsets(sK13_skl)) ),
inference(resolution,[status(thm)],[f1576,f433]) ).
fof(f1671,definition,
( sQ137_spl
<=> subset(finite_subsets(sK12_skl),finite_subsets(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1672,plain,
( ~ sQ137_spl
| subset(finite_subsets(sK12_skl),finite_subsets(sK13_skl)) ),
inference(component_clause,[status(thm)],[f1671]) ).
fof(f1674,definition,
( sQ138_spl
<=> finite(sK0_skl(finite_subsets(sK13_skl),finite_subsets(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1676,plain,
( sQ138_spl
| ~ finite(sK0_skl(finite_subsets(sK13_skl),finite_subsets(sK12_skl))) ),
inference(component_clause,[status(thm)],[f1674]) ).
fof(f1677,plain,
( ~ sQ138_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1664,f1671,f1674]) ).
fof(f1690,plain,
( ~ sQ137_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1672,f133]) ).
fof(f1691,plain,
~ sQ137_spl,
inference(contradiction_clause,[status(thm)],[f1690]) ).
fof(f2482,plain,
( sQ138_spl
| subset(finite_subsets(sK12_skl),finite_subsets(sK13_skl)) ),
inference(resolution,[status(thm)],[f1676,f431]) ).
fof(f2483,plain,
( sQ138_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f2482,f1671,f1674]) ).
fof(f2484,plain,
$false,
inference(sat_refutation,[status(thm)],[f1677,f1691,f2483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:50:06 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.51/0.50 % Elapsed time: 0.125559 seconds
% 0.51/0.50 % CPU time: 0.664056 seconds
% 0.51/0.50 % Total memory used: 89.540 MB
% 0.51/0.50 % Net memory used: 88.534 MB
%------------------------------------------------------------------------------