%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET689+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:10:27 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 7 unt; 2 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 33 ~; 31 |; 24 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 46 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] :
( ( subset(C,A)
& subset(B,C)
& subset(A,B) )
=> equal_set(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] :
( ( subset(C,A)
& subset(B,C)
& subset(A,B) )
=> equal_set(A,C) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f68,plain,
? [A,B,C] :
( ~ equal_set(A,C)
& subset(C,A)
& subset(B,C)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,C] :
( ~ equal_set(A,C)
& subset(C,A)
& ? [B] :
( subset(B,C)
& subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
( ~ equal_set(sK3_skl,sK4_skl)
& subset(sK4_skl,sK3_skl)
& subset(sK5_skl,sK4_skl)
& subset(sK3_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(C,sK4_skl),skolemize(B,sK5_skl)],[f69]) ).
fof(f71,plain,
subset(sK3_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
subset(sK5_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
subset(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f74,plain,
~ equal_set(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f79,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f18,f72]) ).
fof(f80,plain,
! [X0] :
( member(X0,sK5_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f18,f71]) ).
fof(f81,plain,
( ~ subset(sK3_skl,sK4_skl)
| equal_set(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f25,f73]) ).
fof(f84,definition,
( sQ0_spl
<=> equal_set(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ0_spl
| equal_set(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ1_spl
<=> subset(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f84,f87]) ).
fof(f105,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f74]) ).
fof(f106,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f156,plain,
! [X0] :
( member(sK0_skl(X0,sK3_skl),sK5_skl)
| subset(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f19,f80]) ).
fof(f167,plain,
! [X0] :
( member(sK0_skl(X0,sK3_skl),sK4_skl)
| subset(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f156,f79]) ).
fof(f186,plain,
( subset(sK3_skl,sK4_skl)
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f167,f20]) ).
fof(f188,plain,
sQ1_spl,
inference(split_clause,[status(thm)],[f186,f87]) ).
fof(f189,plain,
$false,
inference(sat_refutation,[status(thm)],[f90,f106,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET689+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:32:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.049384 seconds
% 0.09/0.41 % CPU time: 0.144373 seconds
% 0.09/0.41 % Total memory used: 80.745 MB
% 0.09/0.41 % Net memory used: 80.515 MB
%------------------------------------------------------------------------------