%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 02:08:52 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 14 unt; 2 def)
% Number of atoms : 57 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 19 ~; 22 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : member(X,singleton_set(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( X = Y
| ~ member(X,singleton_set(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : member(X,unordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
m1 != m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : member(X0,singleton_set(X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( X = Y
| ~ member(X,unordered_pair(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
m1 != m2,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,X2)
| X0 = singleton_set(X1)
| ~ member(X0,ordered_pair(X1,X2)) ),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f24,plain,
! [X0,X1] : member(singleton_set(X0),ordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f35,plain,
! [X0] :
( X0 = unordered_pair(m1,r1)
| X0 = singleton_set(m1)
| ~ member(X0,ordered_pair(m2,r2)) ),
inference(paramodulation,[status(thm)],[f16,f22]) ).
fof(f36,definition,
( sQ0_spl
<=> unordered_pair(m1,r1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ0_spl
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f43,definition,
( sQ2_spl
<=> singleton_set(m1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ2_spl
| singleton_set(m1) = singleton_set(m2) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f55,plain,
( ~ sQ2_spl
| member(m1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[f44,f9]) ).
fof(f56,plain,
( ~ sQ2_spl
| m1 = m2 ),
inference(resolution,[status(thm)],[f55,f10]) ).
fof(f57,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f17]) ).
fof(f58,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f69,plain,
( singleton_set(m2) = unordered_pair(m1,r1)
| singleton_set(m2) = singleton_set(m1) ),
inference(resolution,[status(thm)],[f35,f24]) ).
fof(f78,plain,
( sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f69,f43,f36]) ).
fof(f86,plain,
( ~ sQ0_spl
| member(m1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[f37,f11]) ).
fof(f94,plain,
( ~ sQ0_spl
| m1 = m2 ),
inference(resolution,[status(thm)],[f86,f10]) ).
fof(f95,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f17]) ).
fof(f96,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f97,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f78,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n001.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 04:48:13 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.54 % Elapsed time: 0.077670 seconds
% 0.17/0.54 % CPU time: 0.103601 seconds
% 0.17/0.54 % Total memory used: 6.403 MB
% 0.17/0.54 % Net memory used: 6.400 MB
%------------------------------------------------------------------------------