%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU139+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:19:21 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 7 unt; 2 def)
% Number of atoms : 59 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 27 ~; 18 |; 9 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 25 ( 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f15,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
( ! [A,B] :
( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ! [A,B] :
( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f24,plain,
? [A,B] :
( proper_subset(B,A)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
( proper_subset(sK1_skl,sK0_skl)
& subset(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f24]) ).
fof(f26,plain,
subset(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
proper_subset(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f31,plain,
~ proper_subset(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f9,f27]) ).
fof(f35,definition,
( sQ0_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ0_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f42,plain,
( sK0_skl = sK1_skl
| ~ subset(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f19,f31]) ).
fof(f45,definition,
( sQ2_spl
<=> subset(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( sQ2_spl
| ~ subset(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f42,f45,f35]) ).
fof(f50,plain,
( ~ sQ0_spl
| proper_subset(sK0_skl,sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f36,f27]) ).
fof(f52,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f30]) ).
fof(f53,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f59,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f47]) ).
fof(f60,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f53,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU139+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n010.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 05:52:39 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.50 % Refutation found
% 0.18/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.55 % Elapsed time: 0.073755 seconds
% 0.24/0.55 % CPU time: 0.096093 seconds
% 0.24/0.55 % Total memory used: 2.499 MB
% 0.24/0.55 % Net memory used: 2.499 MB
%------------------------------------------------------------------------------