%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:09:01 PM UTC 2026
% Result : Unsatisfiable 11.29s 2.03s
% Output : CNFRefutation 12.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 9 unt; 3 def)
% Number of atoms : 61 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 30 ~; 27 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f145,axiom,
! [X,Y] :
( X = Y
| ~ subset(Y,X)
| ~ subset(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f165,axiom,
! [Xf,X,Xg] :
( subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X))
| ~ member(X,domain_of(Xf))
| ~ function(Xf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f166,axiom,
! [Xf,Xg,X] :
( subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X)))
| ~ function(Xf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f167,hypothesis,
function(a_function),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f168,hypothesis,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f169,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f353,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f377,plain,
! [Xf,X] :
( ! [Xg] : subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X))
| ~ member(X,domain_of(Xf))
| ~ function(Xf) ),
inference(miniscoping,[status(thm)],[f165]) ).
fof(f378,plain,
! [X0,X1,X2] :
( subset(apply(X2,apply(X0,X1)),apply(compose(X2,X0),X1))
| ~ member(X1,domain_of(X0))
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f379,plain,
! [Xf] :
( ! [Xg,X] : subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X)))
| ~ function(Xf) ),
inference(miniscoping,[status(thm)],[f166]) ).
fof(f380,plain,
! [X0,X1,X2] :
( subset(apply(compose(X1,X0),X2),apply(X1,apply(X0,X2)))
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f381,plain,
function(a_function),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f382,plain,
member(a,domain_of(a_function)),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f383,plain,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f1533,plain,
! [X0,X1,X2] :
( ~ function(X1)
| apply(X0,apply(X1,X2)) = apply(compose(X0,X1),X2)
| ~ subset(apply(X0,apply(X1,X2)),apply(compose(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f353,f380]) ).
fof(f2881,definition,
( sQ130_spl
<=> function(a_function) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f2883,plain,
( sQ130_spl
| ~ function(a_function) ),
inference(component_clause,[status(thm)],[f2881]) ).
fof(f2888,plain,
( sQ130_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2883,f381]) ).
fof(f2889,plain,
sQ130_spl,
inference(contradiction_clause,[status(thm)],[f2888]) ).
fof(f2890,plain,
! [X0] :
( subset(apply(X0,apply(a_function,a)),apply(compose(X0,a_function),a))
| ~ function(a_function) ),
inference(resolution,[status(thm)],[f378,f382]) ).
fof(f2895,definition,
! [X0] :
( sQ132_spl
<=> subset(apply(X0,apply(a_function,a)),apply(compose(X0,a_function),a)) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f2896,plain,
! [X0] :
( ~ sQ132_spl
| subset(apply(X0,apply(a_function,a)),apply(compose(X0,a_function),a)) ),
inference(component_clause,[status(thm)],[f2895]) ).
fof(f2898,plain,
( sQ132_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f2890,f2881,f2895]) ).
fof(f3144,plain,
! [X0] :
( ~ sQ132_spl
| ~ function(a_function)
| apply(X0,apply(a_function,a)) = apply(compose(X0,a_function),a) ),
inference(resolution,[status(thm)],[f2896,f1533]) ).
fof(f3150,definition,
! [X0] :
( sQ161_spl
<=> apply(X0,apply(a_function,a)) = apply(compose(X0,a_function),a) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f3151,plain,
! [X0] :
( ~ sQ161_spl
| apply(X0,apply(a_function,a)) = apply(compose(X0,a_function),a) ),
inference(component_clause,[status(thm)],[f3150]) ).
fof(f3153,plain,
( ~ sQ132_spl
| ~ sQ130_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f3144,f3150,f2881,f2895]) ).
fof(f3248,plain,
( ~ sQ161_spl
| apply(another_function,apply(a_function,a)) != apply(another_function,apply(a_function,a)) ),
inference(backward_demodulation,[status(thm)],[f3151,f383]) ).
fof(f3274,plain,
( ~ sQ161_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3248]) ).
fof(f3275,plain,
~ sQ161_spl,
inference(contradiction_clause,[status(thm)],[f3274]) ).
fof(f3276,plain,
$false,
inference(sat_refutation,[status(thm)],[f2889,f2898,f3153,f3275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 04:50:06 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 11.29/2.03 % Refutation found
% 11.29/2.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 11.29/2.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.09/2.08 % Elapsed time: 1.622551 seconds
% 12.09/2.08 % CPU time: 12.412164 seconds
% 12.09/2.08 % Total memory used: 215.611 MB
% 12.09/2.08 % Net memory used: 204.696 MB
%------------------------------------------------------------------------------