%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 6.21s 1.33s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 81 ( 10 unt; 11 def)
% Number of atoms : 303 ( 78 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 361 ( 139 ~; 140 |; 54 &)
% ( 14 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f122,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f174,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,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/sandbox/benchmark/theBenchmark.p') ).
fof(f203,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)],[f202]) ).
fof(f487,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f488,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f487]) ).
fof(f489,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f490,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f489]) ).
fof(f491,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f489]) ).
fof(f572,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f99]) ).
fof(f573,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f572]) ).
fof(f638,plain,
( one_to_one(sK61_skl)
& function(sK61_skl)
& relation(sK61_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61_skl]),skolemize(A,sK61_skl)],[f122]) ).
fof(f641,plain,
one_to_one(sK61_skl),
inference(cnf_transformation,[status(thm)],[f638]) ).
fof(f800,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)],[f174]) ).
fof(f801,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f800]) ).
fof(f870,plain,
! [A] :
( ! [B] :
( ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f200]) ).
fof(f871,definition,
! [A,B,C,D] :
( sP1_prd(D,C,B,A)
<=> ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f872,plain,
! [A] :
( ! [B] :
( ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& sP1_prd(D,C,B,A) )
& relation_dom(B) = relation_rng(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(formula_renaming,[status(thm)],[f870,f871]) ).
fof(f873,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ sP1_prd(D,C,B,A) )
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& sP1_prd(D,C,B,A) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f872]) ).
fof(f874,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ? [C,D] : ~ sP1_prd(D,C,B,A)
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ! [C,D] : sP1_prd(D,C,B,A)
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f873]) ).
fof(f875,plain,
! [A] :
( ! [B] :
( ( ( ( ( sK73_skl(B,A) != apply(B,sK72_skl(B,A))
| ~ in(sK72_skl(B,A),relation_rng(A)) )
& sK72_skl(B,A) = apply(A,sK73_skl(B,A))
& in(sK73_skl(B,A),relation_dom(A)) )
| ~ sP1_prd(sK71_skl(B,A),sK70_skl(B,A),B,A)
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ! [C,D] : sP1_prd(D,C,B,A)
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70_skl,sK71_skl,sK72_skl,sK73_skl]),skolemize(C,sK70_skl(B,A)),skolemize(D,sK71_skl(B,A)),skolemize(C,sK72_skl(B,A)),skolemize(D,sK73_skl(B,A))],[f874]) ).
fof(f876,plain,
! [X0,X1] :
( relation_dom(X1) = relation_rng(X0)
| X1 != function_inverse(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f875]) ).
fof(f886,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)],[f203]) ).
fof(f887,plain,
( ( relation_dom(sK74_skl) != relation_rng(function_inverse(sK74_skl))
| relation_rng(sK74_skl) != relation_dom(function_inverse(sK74_skl)) )
& one_to_one(sK74_skl)
& function(sK74_skl)
& relation(sK74_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74_skl]),skolemize(A,sK74_skl)],[f886]) ).
fof(f888,plain,
relation(sK74_skl),
inference(cnf_transformation,[status(thm)],[f887]) ).
fof(f889,plain,
function(sK74_skl),
inference(cnf_transformation,[status(thm)],[f887]) ).
fof(f890,plain,
one_to_one(sK74_skl),
inference(cnf_transformation,[status(thm)],[f887]) ).
fof(f891,plain,
( relation_dom(sK74_skl) != relation_rng(function_inverse(sK74_skl))
| relation_rng(sK74_skl) != relation_dom(function_inverse(sK74_skl)) ),
inference(cnf_transformation,[status(thm)],[f887]) ).
fof(f997,definition,
( sQ0_spl
<=> relation_rng(sK74_skl) = relation_dom(function_inverse(sK74_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1000,definition,
( sQ1_spl
<=> relation_dom(sK74_skl) = relation_rng(function_inverse(sK74_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1002,plain,
( sQ1_spl
| relation_dom(sK74_skl) != relation_rng(function_inverse(sK74_skl)) ),
inference(component_clause,[status(thm)],[f1000]) ).
fof(f1003,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f891,f997,f1000]) ).
fof(f1095,plain,
! [X0] :
( relation_dom(function_inverse(X0)) = relation_rng(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f876]) ).
fof(f1096,plain,
! [X0] :
( relation_dom(function_inverse(X0)) = relation_rng(X0)
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1095,f490]) ).
fof(f1109,plain,
( relation(function_inverse(sK74_skl))
| ~ function(sK74_skl) ),
inference(resolution,[status(thm)],[f490,f888]) ).
fof(f1110,definition,
( sQ2_spl
<=> function(sK74_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
( sQ2_spl
| ~ function(sK74_skl) ),
inference(component_clause,[status(thm)],[f1110]) ).
fof(f1113,definition,
( sQ3_spl
<=> relation(function_inverse(sK74_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1114,plain,
( ~ sQ3_spl
| relation(function_inverse(sK74_skl)) ),
inference(component_clause,[status(thm)],[f1113]) ).
fof(f1116,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1109,f1110,f1113]) ).
fof(f1117,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1112,f889]) ).
fof(f1118,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1117]) ).
fof(f1120,definition,
( sQ4_spl
<=> function(function_inverse(sK74_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1121,plain,
( ~ sQ4_spl
| function(function_inverse(sK74_skl)) ),
inference(component_clause,[status(thm)],[f1120]) ).
fof(f1128,plain,
( function(function_inverse(sK74_skl))
| ~ function(sK74_skl) ),
inference(resolution,[status(thm)],[f491,f888]) ).
fof(f1133,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1128,f1110,f1120]) ).
fof(f1164,definition,
( sQ14_spl
<=> one_to_one(sK74_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1166,plain,
( sQ14_spl
| ~ one_to_one(sK74_skl) ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1335,plain,
( function_inverse(sK74_skl) = relation_inverse(sK74_skl)
| ~ function(sK74_skl)
| ~ relation(sK74_skl) ),
inference(resolution,[status(thm)],[f488,f890]) ).
fof(f1361,definition,
( sQ50_spl
<=> relation(sK74_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1363,plain,
( sQ50_spl
| ~ relation(sK74_skl) ),
inference(component_clause,[status(thm)],[f1361]) ).
fof(f1364,definition,
( sQ51_spl
<=> function_inverse(sK74_skl) = relation_inverse(sK74_skl) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1365,plain,
( ~ sQ51_spl
| function_inverse(sK74_skl) = relation_inverse(sK74_skl) ),
inference(component_clause,[status(thm)],[f1364]) ).
fof(f1367,plain,
( sQ51_spl
| ~ sQ2_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1335,f1361,f1110,f1364]) ).
fof(f1374,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1363,f888]) ).
fof(f1375,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f1374]) ).
fof(f1381,plain,
( ~ sQ4_spl
| ~ sQ51_spl
| function(relation_inverse(sK74_skl)) ),
inference(backward_demodulation,[status(thm)],[f1365,f1121]) ).
fof(f1382,plain,
( ~ sQ3_spl
| ~ sQ51_spl
| relation(relation_inverse(sK74_skl)) ),
inference(backward_demodulation,[status(thm)],[f1365,f1114]) ).
fof(f1440,definition,
( sQ59_spl
<=> one_to_one(sK61_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1442,plain,
( sQ59_spl
| ~ one_to_one(sK61_skl) ),
inference(component_clause,[status(thm)],[f1440]) ).
fof(f1708,definition,
( sQ69_spl
<=> function(relation_inverse(sK74_skl)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1710,plain,
( sQ69_spl
| ~ function(relation_inverse(sK74_skl)) ),
inference(component_clause,[status(thm)],[f1708]) ).
fof(f1719,plain,
( sQ69_spl
| ~ sQ4_spl
| ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1710,f1381]) ).
fof(f1720,plain,
( sQ69_spl
| ~ sQ4_spl
| ~ sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f1719]) ).
fof(f2232,plain,
relation_inverse(relation_inverse(sK74_skl)) = sK74_skl,
inference(resolution,[status(thm)],[f573,f888]) ).
fof(f2624,plain,
( ~ sQ51_spl
| relation_dom(function_inverse(sK74_skl)) = relation_rng(sK74_skl)
| ~ function(relation_inverse(sK74_skl))
| ~ one_to_one(sK74_skl)
| ~ function(sK74_skl)
| ~ relation(sK74_skl) ),
inference(paramodulation,[status(thm)],[f1365,f1096]) ).
fof(f2669,plain,
( ~ sQ51_spl
| sQ0_spl
| ~ sQ69_spl
| ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2624,f1361,f1110,f1164,f1708,f997,f1364]) ).
fof(f2675,plain,
( sQ1_spl
| ~ sQ51_spl
| relation_dom(sK74_skl) != relation_rng(relation_inverse(sK74_skl)) ),
inference(forward_demodulation,[status(thm)],[f1365,f1002]) ).
fof(f2686,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1166,f890]) ).
fof(f2687,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f2686]) ).
fof(f2736,plain,
( sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1442,f641]) ).
fof(f2737,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f2736]) ).
fof(f3158,plain,
( ~ sQ3_spl
| ~ sQ51_spl
| relation_rng(relation_inverse(sK74_skl)) = relation_dom(relation_inverse(relation_inverse(sK74_skl))) ),
inference(resolution,[status(thm)],[f801,f1382]) ).
fof(f3194,plain,
( ~ sQ3_spl
| ~ sQ51_spl
| relation_rng(relation_inverse(sK74_skl)) = relation_dom(sK74_skl) ),
inference(forward_demodulation,[status(thm)],[f2232,f3158]) ).
fof(f3195,plain,
( ~ sQ3_spl
| ~ sQ51_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3194,f2675]) ).
fof(f3196,plain,
( ~ sQ3_spl
| ~ sQ51_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f3195]) ).
fof(f3197,plain,
$false,
inference(sat_refutation,[status(thm)],[f1003,f1116,f1118,f1133,f1367,f1375,f1720,f2669,f2687,f2737,f3196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:59:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 6.21/1.33 % Refutation found
% 6.21/1.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.21/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.21/1.36 % Elapsed time: 0.973155 seconds
% 6.21/1.36 % CPU time: 7.293124 seconds
% 6.21/1.36 % Total memory used: 190.248 MB
% 6.21/1.36 % Net memory used: 181.240 MB
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