%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU019+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 : n017.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 02:19:05 PM UTC 2026
% Result : Theorem 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 76 ( 14 unt; 9 def)
% Number of atoms : 237 ( 61 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 277 ( 116 ~; 117 |; 27 &)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A] : one_to_one(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A] : one_to_one(identity_relation(A)),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f40,plain,
! [A] :
( ( one_to_one(A)
<=> ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [A] :
( ( ( ( sK0_skl(A) != sK1_skl(A)
& apply(A,sK0_skl(A)) = apply(A,sK1_skl(A))
& in(sK1_skl(A),relation_dom(A))
& in(sK0_skl(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl(A)),skolemize(C,sK1_skl(A))],[f41]) ).
fof(f44,plain,
! [X0] :
( in(sK0_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0] :
( in(sK1_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [X0] :
( apply(X0,sK0_skl(X0)) = apply(X0,sK1_skl(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [X0] :
( sK0_skl(X0) != sK1_skl(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f48,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f58,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f69,plain,
( relation(sK4_skl)
& empty(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f15]) ).
fof(f70,plain,
empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f95,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A ) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f96,plain,
! [A,B] :
( ( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [B] :
( ( ! [A] :
( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [B] :
( ( ! [A] :
( ( apply(B,sK11_skl(A,B)) != sK11_skl(A,B)
& in(sK11_skl(A,B),A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(C,sK11_skl(A,B))],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| X0 != identity_relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( apply(X0,X2) = X2
| ~ in(X2,X1)
| X0 != identity_relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f110,plain,
? [A] : ~ one_to_one(identity_relation(A)),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f111,plain,
~ one_to_one(identity_relation(sK12_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f110]) ).
fof(f112,plain,
~ one_to_one(identity_relation(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f124,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f99]) ).
fof(f125,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f100]) ).
fof(f129,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f48]) ).
fof(f130,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(resolution,[status(thm)],[f129,f58]) ).
fof(f132,plain,
( in(sK0_skl(identity_relation(sK12_skl)),relation_dom(identity_relation(sK12_skl)))
| ~ function(identity_relation(sK12_skl))
| ~ relation(identity_relation(sK12_skl)) ),
inference(resolution,[status(thm)],[f44,f112]) ).
fof(f133,definition,
( sQ0_spl
<=> relation(identity_relation(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ0_spl
| ~ relation(identity_relation(sK12_skl)) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ1_spl
<=> function(identity_relation(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ1_spl
| ~ function(identity_relation(sK12_skl)) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
( sQ2_spl
<=> in(sK0_skl(identity_relation(sK12_skl)),relation_dom(identity_relation(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ2_spl
| in(sK0_skl(identity_relation(sK12_skl)),relation_dom(identity_relation(sK12_skl))) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f132,f133,f136,f139]) ).
fof(f143,plain,
( ~ sQ2_spl
| in(sK0_skl(identity_relation(sK12_skl)),sK12_skl) ),
inference(forward_demodulation,[status(thm)],[f130,f140]) ).
fof(f144,plain,
( in(sK1_skl(identity_relation(sK12_skl)),relation_dom(identity_relation(sK12_skl)))
| ~ function(identity_relation(sK12_skl))
| ~ relation(identity_relation(sK12_skl)) ),
inference(resolution,[status(thm)],[f45,f112]) ).
fof(f145,definition,
( sQ3_spl
<=> in(sK1_skl(identity_relation(sK12_skl)),relation_dom(identity_relation(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ3_spl
| in(sK1_skl(identity_relation(sK12_skl)),relation_dom(identity_relation(sK12_skl))) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f144,f133,f136,f145]) ).
fof(f149,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f58]) ).
fof(f150,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f48]) ).
fof(f152,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f153,plain,
( ~ sQ3_spl
| in(sK1_skl(identity_relation(sK12_skl)),sK12_skl) ),
inference(forward_demodulation,[status(thm)],[f130,f146]) ).
fof(f156,plain,
( apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl))) = apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl)))
| ~ function(identity_relation(sK12_skl))
| ~ relation(identity_relation(sK12_skl)) ),
inference(resolution,[status(thm)],[f46,f112]) ).
fof(f157,definition,
( sQ4_spl
<=> apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl))) = apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ4_spl
| apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl))) = apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl))) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ4_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f156,f133,f136,f157]) ).
fof(f168,definition,
( sQ6_spl
<=> sK0_skl(identity_relation(sK12_skl)) = sK1_skl(identity_relation(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ6_spl
| sK0_skl(identity_relation(sK12_skl)) != sK1_skl(identity_relation(sK12_skl)) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f193,plain,
( sK0_skl(identity_relation(sK12_skl)) != sK1_skl(identity_relation(sK12_skl))
| ~ function(identity_relation(sK12_skl))
| ~ relation(identity_relation(sK12_skl)) ),
inference(resolution,[status(thm)],[f47,f112]) ).
fof(f194,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f193,f133,f136,f168]) ).
fof(f208,definition,
( sQ8_spl
<=> empty(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ8_spl
| ~ empty(sK4_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f248,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f70]) ).
fof(f249,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f259,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f48]) ).
fof(f260,plain,
( ~ sQ3_spl
| apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl))) = sK1_skl(identity_relation(sK12_skl))
| ~ function(identity_relation(sK12_skl)) ),
inference(resolution,[status(thm)],[f259,f153]) ).
fof(f261,plain,
( ~ sQ2_spl
| apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl))) = sK0_skl(identity_relation(sK12_skl))
| ~ function(identity_relation(sK12_skl)) ),
inference(resolution,[status(thm)],[f259,f143]) ).
fof(f262,definition,
( sQ10_spl
<=> apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl))) = sK1_skl(identity_relation(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( ~ sQ10_spl
| apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl))) = sK1_skl(identity_relation(sK12_skl)) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( ~ sQ3_spl
| sQ10_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f260,f136,f262,f145]) ).
fof(f266,definition,
( sQ11_spl
<=> apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl))) = sK0_skl(identity_relation(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ11_spl
| apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl))) = sK0_skl(identity_relation(sK12_skl)) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( ~ sQ2_spl
| sQ11_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f261,f136,f266,f139]) ).
fof(f270,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl))) = sK1_skl(identity_relation(sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f158,f263]) ).
fof(f279,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sK0_skl(identity_relation(sK12_skl)) = sK1_skl(identity_relation(sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f267,f270]) ).
fof(f280,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f170]) ).
fof(f281,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f282,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f148,f150,f152,f160,f194,f249,f265,f269,f281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU019+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:42:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.41 % Refutation found
% 0.08/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.067877 seconds
% 0.14/0.44 % CPU time: 0.190955 seconds
% 0.14/0.44 % Total memory used: 64.128 MB
% 0.14/0.44 % Net memory used: 64.083 MB
%------------------------------------------------------------------------------