%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:19:07 PM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 73 ( 14 unt; 10 def)
% Number of atoms : 241 ( 59 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 275 ( 107 ~; 107 |; 36 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 33 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ! [D] :
( ( function(D)
& relation(D) )
=> ( ( relation_composition(C,D) = identity_relation(A)
& relation_composition(B,C) = identity_relation(relation_dom(D))
& relation_rng(B) = A )
=> D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [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(f39,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A))
& relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(B,A) = identity_relation(relation_rng(A))
& relation_rng(B) = relation_dom(A)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(B,A) = identity_relation(relation_rng(A))
& relation_rng(B) = relation_dom(A)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f55,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f92,plain,
! [A,B] :
( ! [C] :
( ! [D] :
( D = B
| relation_composition(C,D) != identity_relation(A)
| relation_composition(B,C) != identity_relation(relation_dom(D))
| relation_rng(B) != A
| ~ function(D)
| ~ relation(D) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f93,plain,
! [B] :
( ! [C] :
( ! [D] :
( D = B
| ! [A] :
( relation_composition(C,D) != identity_relation(A)
| relation_composition(B,C) != identity_relation(relation_dom(D))
| relation_rng(B) != A )
| ~ function(D)
| ~ relation(D) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( X2 = X0
| relation_composition(X1,X2) != identity_relation(X3)
| relation_composition(X0,X1) != identity_relation(relation_dom(X2))
| relation_rng(X0) != X3
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f139,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)],[f37]) ).
fof(f140,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f145,plain,
! [A] :
( ( relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A))
& relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f146,plain,
! [X0] :
( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f148,plain,
? [A] :
( ? [B] :
( B != function_inverse(A)
& relation_composition(B,A) = identity_relation(relation_rng(A))
& relation_rng(B) = relation_dom(A)
& one_to_one(A)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f149,plain,
( sK12_skl != function_inverse(sK11_skl)
& relation_composition(sK12_skl,sK11_skl) = identity_relation(relation_rng(sK11_skl))
& relation_rng(sK12_skl) = relation_dom(sK11_skl)
& one_to_one(sK11_skl)
& function(sK12_skl)
& relation(sK12_skl)
& function(sK11_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f148]) ).
fof(f150,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f151,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f152,plain,
relation(sK12_skl),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f153,plain,
function(sK12_skl),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f154,plain,
one_to_one(sK11_skl),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f155,plain,
relation_rng(sK12_skl) = relation_dom(sK11_skl),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f156,plain,
relation_composition(sK12_skl,sK11_skl) = identity_relation(relation_rng(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f157,plain,
sK12_skl != function_inverse(sK11_skl),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f166,plain,
! [X0,X1,X2] :
( X2 = X0
| relation_composition(X1,X2) != identity_relation(relation_rng(X0))
| relation_composition(X0,X1) != identity_relation(relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f211,definition,
( sQ8_spl
<=> relation(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ8_spl
| ~ relation(sK12_skl) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
( sQ9_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( sQ9_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f238,definition,
( sQ11_spl
<=> function(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ11_spl
| ~ function(sK12_skl) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
( sQ12_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ12_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f248,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f152]) ).
fof(f249,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f150]) ).
fof(f251,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f412,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f153]) ).
fof(f413,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f151]) ).
fof(f415,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f414]) ).
fof(f419,plain,
( relation_rng(sK11_skl) = relation_dom(function_inverse(sK11_skl))
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f140,f154]) ).
fof(f423,definition,
( sQ27_spl
<=> relation_rng(sK11_skl) = relation_dom(function_inverse(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( ~ sQ27_spl
| relation_rng(sK11_skl) = relation_dom(function_inverse(sK11_skl)) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( sQ27_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f419,f214,f241,f423]) ).
fof(f495,definition,
( sQ36_spl
<=> relation(function_inverse(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ36_spl
| ~ relation(function_inverse(sK11_skl)) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f544,plain,
( relation_composition(sK11_skl,function_inverse(sK11_skl)) = identity_relation(relation_dom(sK11_skl))
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f146,f154]) ).
fof(f548,definition,
( sQ42_spl
<=> relation_composition(sK11_skl,function_inverse(sK11_skl)) = identity_relation(relation_dom(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( ~ sQ42_spl
| relation_composition(sK11_skl,function_inverse(sK11_skl)) = identity_relation(relation_dom(sK11_skl)) ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f551,plain,
( sQ42_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f544,f214,f241,f548]) ).
fof(f562,plain,
( ~ sQ42_spl
| relation_composition(sK11_skl,function_inverse(sK11_skl)) = identity_relation(relation_rng(sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f155,f549]) ).
fof(f616,definition,
( sQ48_spl
<=> function(function_inverse(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( sQ48_spl
| ~ function(function_inverse(sK11_skl)) ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f625,plain,
( sQ36_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f497,f56]) ).
fof(f627,plain,
( sQ36_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f625,f214,f241,f495]) ).
fof(f628,plain,
( sQ48_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f618,f57]) ).
fof(f629,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f628,f214,f241,f616]) ).
fof(f712,plain,
( ~ sQ42_spl
| function_inverse(sK11_skl) = sK12_skl
| relation_composition(sK12_skl,sK11_skl) != identity_relation(relation_dom(function_inverse(sK11_skl)))
| ~ function(function_inverse(sK11_skl))
| ~ relation(function_inverse(sK11_skl))
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(sK12_skl)
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f562,f166]) ).
fof(f718,definition,
( sQ56_spl
<=> relation_composition(sK12_skl,sK11_skl) = identity_relation(relation_dom(function_inverse(sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f720,plain,
( sQ56_spl
| relation_composition(sK12_skl,sK11_skl) != identity_relation(relation_dom(function_inverse(sK11_skl))) ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f721,definition,
( sQ57_spl
<=> function_inverse(sK11_skl) = sK12_skl ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f722,plain,
( ~ sQ57_spl
| function_inverse(sK11_skl) = sK12_skl ),
inference(component_clause,[status(thm)],[f721]) ).
fof(f724,plain,
( ~ sQ42_spl
| sQ57_spl
| ~ sQ56_spl
| ~ sQ48_spl
| ~ sQ36_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f712,f211,f238,f214,f241,f495,f616,f718,f721,f548]) ).
fof(f740,plain,
( sQ56_spl
| identity_relation(relation_rng(sK11_skl)) != identity_relation(relation_dom(function_inverse(sK11_skl))) ),
inference(forward_demodulation,[status(thm)],[f156,f720]) ).
fof(f741,plain,
( sQ56_spl
| ~ sQ27_spl
| identity_relation(relation_rng(sK11_skl)) != identity_relation(relation_rng(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f424,f740]) ).
fof(f742,plain,
( sQ56_spl
| ~ sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f741]) ).
fof(f743,plain,
( sQ56_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f742]) ).
fof(f744,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f722,f157]) ).
fof(f745,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f746,plain,
$false,
inference(sat_refutation,[status(thm)],[f249,f251,f413,f415,f426,f551,f627,f629,f724,f743,f745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n009.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 05:47:28 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 % Drodi V4.1.1
% 0.16/0.44 % Refutation found
% 0.16/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.48 % Elapsed time: 0.083506 seconds
% 0.16/0.48 % CPU time: 0.291367 seconds
% 0.16/0.48 % Total memory used: 105.583 MB
% 0.16/0.48 % Net memory used: 105.417 MB
%------------------------------------------------------------------------------