%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:19:44 PM UTC 2026
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 64 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 19 |; 13 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 10 ( 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
? [A] :
( ( relation_dom(A) != relation_rng(function_inverse(A))
| relation_rng(A) != relation_dom(function_inverse(A)) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f36,plain,
( ( relation_dom(sK2_skl) != relation_rng(function_inverse(sK2_skl))
| relation_rng(sK2_skl) != relation_dom(function_inverse(sK2_skl)) )
& one_to_one(sK2_skl)
& function(sK2_skl)
& relation(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(A,sK2_skl)],[f35]) ).
fof(f37,plain,
relation(sK2_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
function(sK2_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
one_to_one(sK2_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
( relation_dom(sK2_skl) != relation_rng(function_inverse(sK2_skl))
| relation_rng(sK2_skl) != relation_dom(function_inverse(sK2_skl)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
( function_inverse(sK2_skl) = relation_inverse(sK2_skl)
| ~ one_to_one(sK2_skl)
| ~ function(sK2_skl) ),
inference(resolution,[status(thm)],[f14,f37]) ).
fof(f42,plain,
( function_inverse(sK2_skl) = relation_inverse(sK2_skl)
| ~ one_to_one(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f38]) ).
fof(f43,plain,
( relation_dom(sK2_skl) != relation_rng(relation_inverse(sK2_skl))
| relation_rng(sK2_skl) != relation_dom(function_inverse(sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f44,f40]) ).
fof(f44,plain,
function_inverse(sK2_skl) = relation_inverse(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f42,f39]) ).
fof(f45,plain,
( relation_dom(sK2_skl) != relation_rng(relation_inverse(sK2_skl))
| relation_rng(sK2_skl) != relation_dom(relation_inverse(sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f44,f43]) ).
fof(f53,plain,
relation_rng(sK2_skl) = relation_dom(relation_inverse(sK2_skl)),
inference(resolution,[status(thm)],[f33,f37]) ).
fof(f54,plain,
relation_dom(sK2_skl) = relation_rng(relation_inverse(sK2_skl)),
inference(resolution,[status(thm)],[f34,f37]) ).
fof(f55,plain,
( relation_dom(sK2_skl) != relation_rng(relation_inverse(sK2_skl))
| relation_rng(sK2_skl) != relation_rng(sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f53,f45]) ).
fof(f56,plain,
( relation_dom(sK2_skl) != relation_dom(sK2_skl)
| relation_rng(sK2_skl) != relation_rng(sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f54,f55]) ).
fof(f57,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n002.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 06:02:17 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 0.20/0.50 % Refutation found
% 0.20/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58 % Elapsed time: 0.115346 seconds
% 0.20/0.58 % CPU time: 0.097848 seconds
% 0.20/0.58 % Total memory used: 2.799 MB
% 0.20/0.58 % Net memory used: 2.798 MB
%------------------------------------------------------------------------------