%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:19:41 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 8 unt; 10 def)
% Number of atoms : 289 ( 68 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 325 ( 119 ~; 128 |; 44 &)
% ( 22 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 94 ( 77 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f207,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f206]) ).
fof(f221,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f222,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f385,plain,
! [A] :
( ! [B,C] :
( ( ( C = apply(A,B)
<=> C = empty_set )
| in(B,relation_dom(A)) )
& ( ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f386,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f385]) ).
fof(f387,plain,
! [A] :
( ( ! [B] :
( ( ! [C] :
( C != empty_set
| C = apply(A,B) )
& ! [C] :
( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ! [B] :
( ( ! [C] :
( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ! [C] :
( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f386]) ).
fof(f388,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
| X2 != apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f389,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f392,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f393,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f392]) ).
fof(f394,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f393]) ).
fof(f395,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK35_skl(B,A),sK36_skl(B,A)),A)
| in(sK35_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK35_skl(B,A),D),A)
| ~ in(sK35_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK34_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl]),skolemize(D,sK34_skl(C,B,A)),skolemize(C,sK35_skl(B,A)),skolemize(D,sK36_skl(B,A))],[f394]) ).
fof(f397,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f395]) ).
fof(f494,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f520,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f521,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f520]) ).
fof(f522,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f520]) ).
fof(f812,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f819,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f192]) ).
fof(f820,plain,
! [X0] :
( X0 = empty_set
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f819]) ).
fof(f822,plain,
! [A] :
( ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f193]) ).
fof(f823,plain,
! [A] :
( ( ( relation_rng(A) != empty_set
| relation_dom(A) = empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) != empty_set ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f822]) ).
fof(f824,plain,
! [X0] :
( relation_rng(X0) = empty_set
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f823]) ).
fof(f864,plain,
? [A,B,C] :
( ( in(ordered_pair(A,B),C)
<~> ( B = apply(C,A)
& in(A,relation_dom(C)) ) )
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f207]) ).
fof(f865,plain,
? [A,B,C] :
( ( B != apply(C,A)
| ~ in(A,relation_dom(C))
| ~ in(ordered_pair(A,B),C) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| in(ordered_pair(A,B),C) )
& function(C)
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f864]) ).
fof(f866,plain,
? [C] :
( ? [A,B] :
( ( B != apply(C,A)
| ~ in(A,relation_dom(C))
| ~ in(ordered_pair(A,B),C) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| in(ordered_pair(A,B),C) ) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f865]) ).
fof(f867,plain,
( ( sK71_skl != apply(sK69_skl,sK70_skl)
| ~ in(sK70_skl,relation_dom(sK69_skl))
| ~ in(ordered_pair(sK70_skl,sK71_skl),sK69_skl) )
& ( ( sK71_skl = apply(sK69_skl,sK70_skl)
& in(sK70_skl,relation_dom(sK69_skl)) )
| in(ordered_pair(sK70_skl,sK71_skl),sK69_skl) )
& function(sK69_skl)
& relation(sK69_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69_skl,sK70_skl,sK71_skl]),skolemize(C,sK69_skl),skolemize(A,sK70_skl),skolemize(B,sK71_skl)],[f866]) ).
fof(f868,plain,
relation(sK69_skl),
inference(cnf_transformation,[status(thm)],[f867]) ).
fof(f869,plain,
function(sK69_skl),
inference(cnf_transformation,[status(thm)],[f867]) ).
fof(f870,plain,
( in(sK70_skl,relation_dom(sK69_skl))
| in(ordered_pair(sK70_skl,sK71_skl),sK69_skl) ),
inference(cnf_transformation,[status(thm)],[f867]) ).
fof(f871,plain,
( sK71_skl = apply(sK69_skl,sK70_skl)
| in(ordered_pair(sK70_skl,sK71_skl),sK69_skl) ),
inference(cnf_transformation,[status(thm)],[f867]) ).
fof(f872,plain,
( sK71_skl != apply(sK69_skl,sK70_skl)
| ~ in(sK70_skl,relation_dom(sK69_skl))
| ~ in(ordered_pair(sK70_skl,sK71_skl),sK69_skl) ),
inference(cnf_transformation,[status(thm)],[f867]) ).
fof(f907,definition,
( sQ0_spl
<=> in(ordered_pair(sK70_skl,sK71_skl),sK69_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f908,plain,
( ~ sQ0_spl
| in(ordered_pair(sK70_skl,sK71_skl),sK69_skl) ),
inference(component_clause,[status(thm)],[f907]) ).
fof(f910,definition,
( sQ1_spl
<=> in(sK70_skl,relation_dom(sK69_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f870,f907,f910]) ).
fof(f914,definition,
( sQ2_spl
<=> sK71_skl = apply(sK69_skl,sK70_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f915,plain,
( ~ sQ2_spl
| sK71_skl = apply(sK69_skl,sK70_skl) ),
inference(component_clause,[status(thm)],[f914]) ).
fof(f917,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f871,f907,f914]) ).
fof(f918,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f872,f907,f910,f914]) ).
fof(f957,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f388]) ).
fof(f961,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f397]) ).
fof(f984,plain,
! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f521,f222]) ).
fof(f986,definition,
( sQ3_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f988,plain,
( sQ3_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f986]) ).
fof(f990,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f812,f522]) ).
fof(f991,definition,
( sQ4_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f994,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f990,f986,f991]) ).
fof(f995,plain,
( function(empty_set)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f812,f984]) ).
fof(f996,definition,
( sQ5_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f999,plain,
( sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f995,f986,f996]) ).
fof(f1005,plain,
( empty_set = empty_set
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f820,f812]) ).
fof(f1007,definition,
( sQ6_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1010,plain,
( sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1005,f991,f1007]) ).
fof(f1013,plain,
( ~ sQ0_spl
| sK71_skl = apply(sK69_skl,sK70_skl)
| ~ in(sK70_skl,relation_dom(sK69_skl))
| ~ function(sK69_skl)
| ~ relation(sK69_skl) ),
inference(resolution,[status(thm)],[f389,f908]) ).
fof(f1015,definition,
( sQ7_spl
<=> relation(sK69_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1017,plain,
( sQ7_spl
| ~ relation(sK69_skl) ),
inference(component_clause,[status(thm)],[f1015]) ).
fof(f1018,definition,
( sQ8_spl
<=> function(sK69_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1020,plain,
( sQ8_spl
| ~ function(sK69_skl) ),
inference(component_clause,[status(thm)],[f1018]) ).
fof(f1021,plain,
( ~ sQ0_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1013,f1015,f1018,f910,f914,f907]) ).
fof(f1022,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1017,f868]) ).
fof(f1023,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1022]) ).
fof(f1024,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1020,f869]) ).
fof(f1025,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1024]) ).
fof(f1026,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f988]) ).
fof(f1027,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1026]) ).
fof(f1038,plain,
( ~ sQ2_spl
| in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)
| ~ in(sK70_skl,relation_dom(sK69_skl))
| ~ function(sK69_skl)
| ~ relation(sK69_skl) ),
inference(paramodulation,[status(thm)],[f915,f957]) ).
fof(f1039,plain,
( ~ sQ2_spl
| sQ0_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1038,f1015,f1018,f910,f907,f914]) ).
fof(f1043,plain,
( relation_rng(empty_set) = empty_set
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f824,f812]) ).
fof(f1045,definition,
( sQ9_spl
<=> relation_rng(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1048,plain,
( sQ9_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1043,f991,f1045]) ).
fof(f1060,plain,
( ~ sQ0_spl
| in(sK70_skl,relation_dom(sK69_skl))
| ~ relation(sK69_skl) ),
inference(resolution,[status(thm)],[f961,f908]) ).
fof(f1062,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1060,f1015,f910,f907]) ).
fof(f1063,plain,
$false,
inference(sat_refutation,[status(thm)],[f913,f917,f918,f994,f999,f1010,f1021,f1023,f1025,f1027,f1039,f1048,f1062]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n020.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 05:59:17 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.19/0.49 % Refutation found
% 0.19/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.54 % Elapsed time: 0.076846 seconds
% 0.26/0.54 % CPU time: 0.238471 seconds
% 0.26/0.54 % Total memory used: 115.548 MB
% 0.26/0.54 % Net memory used: 115.295 MB
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