%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET031-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 6.74s 21.51s
% Output : CNFRefutation 7.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 8 unt; 3 def)
% Number of atoms : 69 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 30 ~; 31 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 4 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [Z] :
( member(f18(Z),Z)
| relation(Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [Z] :
( ~ ordered_pair_predicate(f18(Z))
| relation(Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f128,axiom,
! [Z,Xf,Xg] :
( little_set(f29(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [Z,Xf,Xg] :
( little_set(f30(Z,Xf,Xg))
| ~ member(Z,compose(Xf,Xg)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f157,negated_conjecture,
~ relation(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f175,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(f254,plain,
! [X0] :
( member(f18(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f255,plain,
! [X0] :
( ~ ordered_pair_predicate(f18(X0))
| relation(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f316,plain,
! [X0,X1,X2] :
( little_set(f29(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f317,plain,
! [X0,X1,X2] :
( little_set(f30(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f319,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(f355,plain,
~ relation(compose(a,b)),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f358,plain,
! [X0,X1] :
( ~ little_set(X1)
| ~ little_set(X0)
| ordered_pair_predicate(ordered_pair(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f175]) ).
fof(f987,plain,
member(f18(compose(a,b)),compose(a,b)),
inference(resolution,[status(thm)],[f254,f355]) ).
fof(f1561,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)],[f319,f987]) ).
fof(f1585,definition,
( sQ84_spl
<=> little_set(f29(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1587,plain,
( sQ84_spl
| ~ little_set(f29(f18(compose(a,b)),a,b)) ),
inference(component_clause,[status(thm)],[f1585]) ).
fof(f1588,definition,
( sQ85_spl
<=> little_set(f30(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1590,plain,
( sQ85_spl
| ~ little_set(f30(f18(compose(a,b)),a,b)) ),
inference(component_clause,[status(thm)],[f1588]) ).
fof(f1707,plain,
( sQ85_spl
| ~ member(f18(compose(a,b)),compose(a,b)) ),
inference(resolution,[status(thm)],[f1590,f317]) ).
fof(f1710,plain,
( sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1707,f987]) ).
fof(f1711,plain,
sQ85_spl,
inference(contradiction_clause,[status(thm)],[f1710]) ).
fof(f2078,plain,
( sQ84_spl
| ~ member(f18(compose(a,b)),compose(a,b)) ),
inference(resolution,[status(thm)],[f1587,f316]) ).
fof(f2081,plain,
( sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2078,f987]) ).
fof(f2082,plain,
sQ84_spl,
inference(contradiction_clause,[status(thm)],[f2081]) ).
fof(f2743,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)],[f1561,f358]) ).
fof(f2746,definition,
( sQ183_spl
<=> ordered_pair_predicate(f18(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2747,plain,
( ~ sQ183_spl
| ordered_pair_predicate(f18(compose(a,b))) ),
inference(component_clause,[status(thm)],[f2746]) ).
fof(f2749,plain,
( ~ sQ85_spl
| ~ sQ84_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f2743,f2746,f1585,f1588]) ).
fof(f2861,plain,
( ~ sQ183_spl
| relation(compose(a,b)) ),
inference(resolution,[status(thm)],[f2747,f255]) ).
fof(f2863,plain,
( ~ sQ183_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2861,f355]) ).
fof(f2864,plain,
~ sQ183_spl,
inference(contradiction_clause,[status(thm)],[f2863]) ).
fof(f2865,plain,
$false,
inference(sat_refutation,[status(thm)],[f1711,f2082,f2749,f2864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET031-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/20.51 % CPULimit : 300
% 0.07/20.51 % WCLimit : 300
% 0.07/20.51 % DateTime : Mon Sep 21 04:44:58 UTC 2026
% 0.07/20.51 % CPUTime :
% 0.07/20.54 % Drodi V4.1.1
% 6.74/21.51 % Refutation found
% 6.74/21.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.74/21.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.57/21.58 % Elapsed time: 1.048123 seconds
% 7.57/21.58 % CPU time: 7.745739 seconds
% 7.57/21.58 % Total memory used: 182.021 MB
% 7.57/21.58 % Net memory used: 175.177 MB
%------------------------------------------------------------------------------