%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU354+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 : 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 02:20:16 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 16 unt; 0 def)
% Number of atoms : 77 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 23 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 32 ( 27 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> B != union(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A] :
? [B] :
( ~ proper_element(B,powerset(A))
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] : k1_pcomps_1(A) = powerset(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f44,axiom,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,plain,
! [A,B] :
( ( proper_element(B,A)
<=> B != union(A) )
| ~ element(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f102,plain,
! [A,B] :
( ( ( B = union(A)
| proper_element(B,A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(NNF_transformation,[status(thm)],[f101]) ).
fof(f104,plain,
! [X0,X1] :
( X0 = union(X1)
| proper_element(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f131,plain,
! [A] :
( ~ proper_element(sK4_skl(A),powerset(A))
& element(sK4_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(B,sK4_skl(A))],[f30]) ).
fof(f132,plain,
! [X0] : element(sK4_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0] : ~ proper_element(sK4_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
! [X0] : k1_pcomps_1(X0) = powerset(X0),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f153,plain,
? [A,B] :
( ( proper_element(B,powerset(A))
<~> B != A )
& element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f154,plain,
? [A,B] :
( ( B = A
| ~ proper_element(B,powerset(A)) )
& ( B != A
| proper_element(B,powerset(A)) )
& element(B,powerset(A)) ),
inference(NNF_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
( ( sK6_skl = sK5_skl
| ~ proper_element(sK6_skl,powerset(sK5_skl)) )
& ( sK6_skl != sK5_skl
| proper_element(sK6_skl,powerset(sK5_skl)) )
& element(sK6_skl,powerset(sK5_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f154]) ).
fof(f156,plain,
element(sK6_skl,powerset(sK5_skl)),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
( sK6_skl != sK5_skl
| proper_element(sK6_skl,powerset(sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f158,plain,
( sK6_skl = sK5_skl
| ~ proper_element(sK6_skl,powerset(sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f167,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f170,plain,
( sK6_skl = sK5_skl
| ~ proper_element(sK6_skl,k1_pcomps_1(sK5_skl)) ),
inference(backward_demodulation,[status(thm)],[f134,f158]) ).
fof(f171,plain,
( sK6_skl != sK5_skl
| proper_element(sK6_skl,k1_pcomps_1(sK5_skl)) ),
inference(backward_demodulation,[status(thm)],[f134,f157]) ).
fof(f172,plain,
element(sK6_skl,k1_pcomps_1(sK5_skl)),
inference(backward_demodulation,[status(thm)],[f134,f156]) ).
fof(f178,plain,
! [X0] : union(k1_pcomps_1(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f134,f167]) ).
fof(f181,plain,
! [X0] : element(sK4_skl(X0),k1_pcomps_1(X0)),
inference(forward_demodulation,[status(thm)],[f134,f132]) ).
fof(f183,plain,
! [X0] : ~ proper_element(sK4_skl(X0),k1_pcomps_1(X0)),
inference(forward_demodulation,[status(thm)],[f134,f133]) ).
fof(f210,plain,
! [X0] :
( sK4_skl(X0) = union(k1_pcomps_1(X0))
| ~ element(sK4_skl(X0),k1_pcomps_1(X0)) ),
inference(resolution,[status(thm)],[f104,f183]) ).
fof(f211,plain,
( sK6_skl = sK5_skl
| sK6_skl = union(k1_pcomps_1(sK5_skl))
| ~ element(sK6_skl,k1_pcomps_1(sK5_skl)) ),
inference(resolution,[status(thm)],[f104,f170]) ).
fof(f212,plain,
! [X0] :
( sK4_skl(X0) = X0
| ~ element(sK4_skl(X0),k1_pcomps_1(X0)) ),
inference(forward_demodulation,[status(thm)],[f178,f210]) ).
fof(f213,plain,
! [X0] : sK4_skl(X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f212,f181]) ).
fof(f214,plain,
( sK6_skl = sK5_skl
| sK6_skl = sK5_skl
| ~ element(sK6_skl,k1_pcomps_1(sK5_skl)) ),
inference(forward_demodulation,[status(thm)],[f178,f211]) ).
fof(f215,plain,
( sK6_skl = sK5_skl
| ~ element(sK6_skl,k1_pcomps_1(sK5_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f214]) ).
fof(f216,plain,
sK6_skl = sK5_skl,
inference(forward_subsumption_resolution,[status(thm)],[f215,f172]) ).
fof(f217,plain,
! [X0] : ~ proper_element(X0,k1_pcomps_1(X0)),
inference(backward_demodulation,[status(thm)],[f213,f183]) ).
fof(f219,plain,
( sK5_skl != sK5_skl
| proper_element(sK6_skl,k1_pcomps_1(sK5_skl)) ),
inference(backward_demodulation,[status(thm)],[f216,f171]) ).
fof(f222,plain,
( sK5_skl != sK5_skl
| proper_element(sK5_skl,k1_pcomps_1(sK5_skl)) ),
inference(forward_demodulation,[status(thm)],[f216,f219]) ).
fof(f223,plain,
proper_element(sK5_skl,k1_pcomps_1(sK5_skl)),
inference(trivial_equality_resolution,[status(thm)],[f222]) ).
fof(f225,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f223,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 : Mon Sep 21 06:14:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.051335 seconds
% 0.14/0.43 % CPU time: 0.142841 seconds
% 0.14/0.43 % Total memory used: 100.607 MB
% 0.14/0.43 % Net memory used: 100.563 MB
%------------------------------------------------------------------------------