%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU284+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 : n026.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 02:20:01 PM UTC 2026
% Result : Theorem 0.17s 5.44s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 3 unt; 7 def)
% Number of atoms : 228 ( 76 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 258 ( 92 ~; 100 |; 53 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 120 ( 91 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [A] :
( ( ! [B] :
~ ( ! [C] : C != singleton(B)
& in(B,A) )
& ! [B,C,D] :
( ( D = singleton(B)
& C = singleton(B)
& in(B,A) )
=> C = D ) )
=> ? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,plain,
? [A] :
! [B] :
( ? [C] :
( apply(B,C) != singleton(C)
& in(C,A) )
| relation_dom(B) != A
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f30,plain,
! [B] :
( ( apply(B,sK1_skl(B)) != singleton(sK1_skl(B))
& in(sK1_skl(B),sK0_skl) )
| relation_dom(B) != sK0_skl
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(C,sK1_skl(B))],[f29]) ).
fof(f31,plain,
! [X0] :
( in(sK1_skl(X0),sK0_skl)
| relation_dom(X0) != sK0_skl
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0] :
( apply(X0,sK1_skl(X0)) != singleton(sK1_skl(X0))
| relation_dom(X0) != sK0_skl
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f38,plain,
! [A] :
( ? [B] :
( ! [C] :
( apply(B,C) = singleton(C)
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) )
| ? [B] :
( ! [C] : C != singleton(B)
& in(B,A) )
| ? [B,C,D] :
( C != D
& D = singleton(B)
& C = singleton(B)
& in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f39,definition,
! [A] :
( sP0_prd(A)
<=> ( ? [B] :
( ! [C] : C != singleton(B)
& in(B,A) )
| ? [B,C,D] :
( C != D
& D = singleton(B)
& C = singleton(B)
& in(B,A) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f40,plain,
! [A] :
( ? [B] :
( ! [C] :
( apply(B,C) = singleton(C)
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) )
| sP0_prd(A) ),
inference(formula_renaming,[status(thm)],[f38,f39]) ).
fof(f41,plain,
! [A] :
( ( ! [C] :
( apply(sK3_skl(A),C) = singleton(C)
| ~ in(C,A) )
& relation_dom(sK3_skl(A)) = A
& function(sK3_skl(A))
& relation(sK3_skl(A)) )
| sP0_prd(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl(A))],[f40]) ).
fof(f42,plain,
! [X0] :
( relation(sK3_skl(X0))
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( function(sK3_skl(X0))
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0] :
( relation_dom(sK3_skl(X0)) = X0
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( apply(sK3_skl(X0),X1) = singleton(X1)
| ~ in(X1,X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,definition,
! [A,B,C,D] :
( sP1_prd(D,C,B,A)
<=> ( C != D
& D = singleton(B)
& C = singleton(B)
& in(B,A) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f89,plain,
! [A] :
( sP0_prd(A)
<=> ( ? [B] :
( ! [C] : C != singleton(B)
& in(B,A) )
| ? [B,C,D] : sP1_prd(D,C,B,A) ) ),
inference(formula_renaming,[status(thm)],[f39,f88]) ).
fof(f90,plain,
! [A] :
( ( ( ! [B] :
( ? [C] : C = singleton(B)
| ~ in(B,A) )
& ! [B,C,D] : ~ sP1_prd(D,C,B,A) )
| sP0_prd(A) )
& ( ? [B] :
( ! [C] : C != singleton(B)
& in(B,A) )
| ? [B,C,D] : sP1_prd(D,C,B,A)
| ~ sP0_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( ! [A] :
( ( ! [B] :
( ? [C] : C = singleton(B)
| ~ in(B,A) )
& ! [B,C,D] : ~ sP1_prd(D,C,B,A) )
| sP0_prd(A) )
& ! [A] :
( ? [B] :
( ! [C] : C != singleton(B)
& in(B,A) )
| ? [B,C,D] : sP1_prd(D,C,B,A)
| ~ sP0_prd(A) ) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f92,plain,
( ! [A] :
( ( ! [B] :
( sK14_skl(B,A) = singleton(B)
| ~ in(B,A) )
& ! [B,C,D] : ~ sP1_prd(D,C,B,A) )
| sP0_prd(A) )
& ! [A] :
( ( ! [C] : C != singleton(sK13_skl(A))
& in(sK13_skl(A),A) )
| sP1_prd(sK12_skl(A),sK11_skl(A),sK10_skl(A),A)
| ~ sP0_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK10_skl(A)),skolemize(C,sK11_skl(A)),skolemize(D,sK12_skl(A)),skolemize(B,sK13_skl(A)),skolemize(C,sK14_skl(B,A))],[f91]) ).
fof(f94,plain,
! [X0,X1] :
( X1 != singleton(sK13_skl(X0))
| sP1_prd(sK12_skl(X0),sK11_skl(X0),sK10_skl(X0),X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f97,plain,
! [A,B,C,D] :
( ( C = D
| D != singleton(B)
| C != singleton(B)
| ~ in(B,A)
| sP1_prd(D,C,B,A) )
& ( ( C != D
& D = singleton(B)
& C = singleton(B)
& in(B,A) )
| ~ sP1_prd(D,C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f88]) ).
fof(f98,plain,
( ! [A,B,C,D] :
( C = D
| D != singleton(B)
| C != singleton(B)
| ~ in(B,A)
| sP1_prd(D,C,B,A) )
& ! [A,B,C,D] :
( ( C != D
& D = singleton(B)
& C = singleton(B)
& in(B,A) )
| ~ sP1_prd(D,C,B,A) ) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( X1 = singleton(X2)
| ~ sP1_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( X0 = singleton(X2)
| ~ sP1_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( X1 != X0
| ~ sP1_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f104,plain,
! [X0] :
( sP1_prd(sK12_skl(X0),sK11_skl(X0),sK10_skl(X0),X0)
| ~ sP0_prd(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f105,plain,
! [X0,X1,X2] : ~ sP1_prd(X0,X0,X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f102]) ).
fof(f238,plain,
! [X0] :
( relation_dom(sK3_skl(X0)) = X0
| sP1_prd(sK12_skl(X0),sK11_skl(X0),sK10_skl(X0),X0) ),
inference(resolution,[status(thm)],[f104,f44]) ).
fof(f239,plain,
! [X0,X1] :
( apply(sK3_skl(X0),X1) = singleton(X1)
| ~ in(X1,X0)
| sP1_prd(sK12_skl(X0),sK11_skl(X0),sK10_skl(X0),X0) ),
inference(resolution,[status(thm)],[f104,f45]) ).
fof(f249,definition,
( sQ16_spl
<=> sP1_prd(sK12_skl(sK0_skl),sK11_skl(sK0_skl),sK10_skl(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( ~ sQ16_spl
| sP1_prd(sK12_skl(sK0_skl),sK11_skl(sK0_skl),sK10_skl(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f251,plain,
( sQ16_spl
| ~ sP1_prd(sK12_skl(sK0_skl),sK11_skl(sK0_skl),sK10_skl(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f255,definition,
! [X0] :
( sQ18_spl
<=> ( relation_dom(X0) != sK0_skl
| ~ function(X0)
| ~ relation(X0)
| apply(sK3_skl(sK0_skl),sK1_skl(X0)) = singleton(sK1_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f256,plain,
! [X0] :
( ~ sQ18_spl
| relation_dom(X0) != sK0_skl
| ~ function(X0)
| ~ relation(X0)
| apply(sK3_skl(sK0_skl),sK1_skl(X0)) = singleton(sK1_skl(X0)) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f287,plain,
! [X0] :
( relation_dom(X0) != sK0_skl
| ~ function(X0)
| ~ relation(X0)
| apply(sK3_skl(sK0_skl),sK1_skl(X0)) = singleton(sK1_skl(X0))
| sP1_prd(sK12_skl(sK0_skl),sK11_skl(sK0_skl),sK10_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f239,f31]) ).
fof(f288,plain,
( sQ18_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f287,f249,f255]) ).
fof(f289,plain,
( ~ sQ16_spl
| sK12_skl(sK0_skl) = singleton(sK10_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f250,f101]) ).
fof(f290,plain,
( ~ sQ16_spl
| sK11_skl(sK0_skl) = singleton(sK10_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f250,f100]) ).
fof(f302,plain,
( ~ sQ16_spl
| sP1_prd(sK12_skl(sK0_skl),sK12_skl(sK0_skl),sK10_skl(sK0_skl),sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f303,f250]) ).
fof(f303,plain,
( ~ sQ16_spl
| sK11_skl(sK0_skl) = sK12_skl(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f289,f290]) ).
fof(f304,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f302,f105]) ).
fof(f305,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( sQ16_spl
| relation_dom(sK3_skl(sK0_skl)) = sK0_skl ),
inference(resolution,[status(thm)],[f238,f251]) ).
fof(f315,definition,
( sQ21_spl
<=> relation(sK3_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ21_spl
| ~ relation(sK3_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f327,plain,
( ~ sQ18_spl
| relation_dom(sK3_skl(sK0_skl)) != sK0_skl
| ~ function(sK3_skl(sK0_skl))
| ~ relation(sK3_skl(sK0_skl))
| relation_dom(sK3_skl(sK0_skl)) != sK0_skl
| ~ function(sK3_skl(sK0_skl))
| ~ relation(sK3_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f256,f32]) ).
fof(f328,definition,
( sQ24_spl
<=> function(sK3_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ24_spl
| ~ function(sK3_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
( sQ25_spl
<=> relation_dom(sK3_skl(sK0_skl)) = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( sQ25_spl
| relation_dom(sK3_skl(sK0_skl)) != sK0_skl ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( ~ sQ18_spl
| ~ sQ25_spl
| ~ sQ24_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f327,f315,f328,f331,f255]) ).
fof(f335,plain,
( sQ21_spl
| sP0_prd(sK0_skl) ),
inference(resolution,[status(thm)],[f317,f42]) ).
fof(f337,plain,
( sQ21_spl
| sP1_prd(sK12_skl(sK0_skl),sK11_skl(sK0_skl),sK10_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f335,f104]) ).
fof(f338,plain,
( sQ21_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f337,f249,f315]) ).
fof(f339,plain,
( sQ24_spl
| sP0_prd(sK0_skl) ),
inference(resolution,[status(thm)],[f330,f43]) ).
fof(f341,plain,
( sQ24_spl
| sP1_prd(sK12_skl(sK0_skl),sK11_skl(sK0_skl),sK10_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f339,f104]) ).
fof(f342,plain,
( sQ24_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f341,f249,f328]) ).
fof(f343,plain,
( sQ25_spl
| sQ16_spl
| sK0_skl != sK0_skl ),
inference(forward_demodulation,[status(thm)],[f306,f333]) ).
fof(f344,plain,
( sQ25_spl
| sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f343]) ).
fof(f345,plain,
( sQ25_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f346,plain,
$false,
inference(sat_refutation,[status(thm)],[f288,f305,f334,f338,f342,f345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU284+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.39 % Computer : n026.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Mon Sep 21 06:10:27 UTC 2026
% 0.17/5.40 % CPUTime :
% 0.17/5.41 % Drodi V4.1.1
% 0.17/5.44 % Refutation found
% 0.17/5.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/5.47 % Elapsed time: 0.061432 seconds
% 0.17/5.47 % CPU time: 0.193138 seconds
% 0.17/5.47 % Total memory used: 61.532 MB
% 0.17/5.47 % Net memory used: 61.397 MB
%------------------------------------------------------------------------------