%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET031-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:08:59 PM UTC 2026
% Result : Unsatisfiable 4.67s 1.09s
% Output : CNFRefutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 8 unt; 4 def)
% Number of atoms : 75 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 32 ~; 33 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X,Y,Z] :
( X != ordered_pair(Y,Z)
| ~ little_set(Z)
| ~ little_set(Y)
| ordered_pair_predicate(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [Z] :
( member(f18(Z),Z)
| relation(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [Z] :
( ~ ordered_pair_predicate(f18(Z))
| relation(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f128,axiom,
! [Z,Xf,Xg] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [Z,Xf,Xg] :
( little_set(f30(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,axiom,
! [Z,Xf,Xg] :
( Z = ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f142,negated_conjecture,
~ relation(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,plain,
! [X0,X1,X2] :
( X0 != ordered_pair(X1,X2)
| ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f239,plain,
! [X0] :
( member(f18(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f240,plain,
! [X0] :
( ~ ordered_pair_predicate(f18(X0))
| relation(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f301,plain,
! [X0,X1,X2] :
( little_set(f29(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f302,plain,
! [X0,X1,X2] :
( little_set(f30(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f304,plain,
! [X0,X1,X2] :
( X0 = ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f320,plain,
~ relation(compose(a,b)),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f323,plain,
! [X0,X1] :
( ~ little_set(X1)
| ~ little_set(X0)
| ordered_pair_predicate(ordered_pair(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f160]) ).
fof(f894,plain,
member(f18(compose(a,b)),compose(a,b)),
inference(resolution,[status(thm)],[f239,f320]) ).
fof(f1284,definition,
( sQ79_spl
<=> ordered_pair_predicate(f18(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1285,plain,
( ~ sQ79_spl
| ordered_pair_predicate(f18(compose(a,b))) ),
inference(component_clause,[status(thm)],[f1284]) ).
fof(f1346,definition,
( sQ80_spl
<=> relation(compose(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1347,plain,
( ~ sQ80_spl
| relation(compose(a,b)) ),
inference(component_clause,[status(thm)],[f1346]) ).
fof(f1350,plain,
( ~ sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1347,f320]) ).
fof(f1351,plain,
~ sQ80_spl,
inference(contradiction_clause,[status(thm)],[f1350]) ).
fof(f1452,plain,
f18(compose(a,b)) = ordered_pair(f29(f18(compose(a,b)),a,b),f30(f18(compose(a,b)),a,b)),
inference(resolution,[status(thm)],[f304,f894]) ).
fof(f1471,definition,
( sQ82_spl
<=> little_set(f29(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1473,plain,
( sQ82_spl
| ~ little_set(f29(f18(compose(a,b)),a,b)) ),
inference(component_clause,[status(thm)],[f1471]) ).
fof(f1474,definition,
( sQ83_spl
<=> little_set(f30(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1476,plain,
( sQ83_spl
| ~ little_set(f30(f18(compose(a,b)),a,b)) ),
inference(component_clause,[status(thm)],[f1474]) ).
fof(f1551,plain,
( sQ83_spl
| ~ member(f18(compose(a,b)),compose(a,b)) ),
inference(resolution,[status(thm)],[f1476,f302]) ).
fof(f1553,plain,
( sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1551,f894]) ).
fof(f1554,plain,
sQ83_spl,
inference(contradiction_clause,[status(thm)],[f1553]) ).
fof(f1724,plain,
( sQ82_spl
| ~ member(f18(compose(a,b)),compose(a,b)) ),
inference(resolution,[status(thm)],[f1473,f301]) ).
fof(f1726,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1724,f894]) ).
fof(f1727,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f1726]) ).
fof(f1831,plain,
( ~ little_set(f30(f18(compose(a,b)),a,b))
| ~ little_set(f29(f18(compose(a,b)),a,b))
| ordered_pair_predicate(f18(compose(a,b))) ),
inference(paramodulation,[status(thm)],[f1452,f323]) ).
fof(f1832,plain,
( ~ sQ83_spl
| ~ sQ82_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f1831,f1284,f1471,f1474]) ).
fof(f1882,plain,
( ~ sQ79_spl
| relation(compose(a,b)) ),
inference(resolution,[status(thm)],[f1285,f240]) ).
fof(f1883,plain,
( ~ sQ79_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1882,f1346,f1284]) ).
fof(f1884,plain,
$false,
inference(sat_refutation,[status(thm)],[f1351,f1554,f1727,f1832,f1883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET031-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.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
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:45:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 4.67/1.09 % Refutation found
% 4.67/1.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.67/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.83/1.13 % Elapsed time: 0.745241 seconds
% 1.83/1.13 % CPU time: 5.538869 seconds
% 1.83/1.13 % Total memory used: 171.838 MB
% 1.83/1.13 % Net memory used: 166.862 MB
%------------------------------------------------------------------------------