%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET997+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 02:11:07 PM UTC 2026
% Result : Theorem 0.16s 5.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 9 unt; 4 def)
% Number of atoms : 181 ( 32 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 209 ( 76 ~; 75 |; 42 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 84 ( 68 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ! [C] :
~ ( ! [D] :
~ ( C = apply(B,D)
& in(D,relation_dom(B)) )
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ! [C] :
~ ( ! [D] :
~ ( C = apply(B,D)
& in(D,relation_dom(B)) )
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f40,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f47,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f48,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK2_skl(B,A) = apply(A,sK3_skl(B,A))
& in(sK3_skl(B,A),relation_dom(A)) )
| in(sK2_skl(B,A),B) )
& ( ! [D] :
( sK2_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK1_skl(C,B,A))
& in(sK1_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f49]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f101,plain,
? [A,B] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( ? [D] :
( C = apply(B,D)
& in(D,relation_dom(B)) )
| ~ in(C,A) )
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f102,plain,
? [B] :
( ? [A] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( ? [D] :
( C = apply(B,D)
& in(D,relation_dom(B)) )
| ~ in(C,A) ) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
( ~ subset(sK14_skl,relation_rng(sK13_skl))
& ! [C] :
( ( C = apply(sK13_skl,sK15_skl(C))
& in(sK15_skl(C),relation_dom(sK13_skl)) )
| ~ in(C,sK14_skl) )
& function(sK13_skl)
& relation(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(B,sK13_skl),skolemize(A,sK14_skl),skolemize(D,sK15_skl(C))],[f102]) ).
fof(f104,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
function(sK13_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,plain,
! [X0] :
( in(sK15_skl(X0),relation_dom(sK13_skl))
| ~ in(X0,sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f107,plain,
! [X0] :
( X0 = apply(sK13_skl,sK15_skl(X0))
| ~ in(X0,sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f108,plain,
~ subset(sK14_skl,relation_rng(sK13_skl)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f145,plain,
! [X0] :
( subset(sK14_skl,X0)
| sK0_skl(X0,sK14_skl) = apply(sK13_skl,sK15_skl(sK0_skl(X0,sK14_skl))) ),
inference(resolution,[status(thm)],[f107,f45]) ).
fof(f146,plain,
sK0_skl(relation_rng(sK13_skl),sK14_skl) = apply(sK13_skl,sK15_skl(sK0_skl(relation_rng(sK13_skl),sK14_skl))),
inference(resolution,[status(thm)],[f145,f108]) ).
fof(f148,plain,
( ~ in(sK15_skl(sK0_skl(relation_rng(sK13_skl),sK14_skl)),relation_dom(sK13_skl))
| in(sK0_skl(relation_rng(sK13_skl),sK14_skl),relation_rng(sK13_skl))
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f146,f133]) ).
fof(f149,definition,
( sQ0_spl
<=> relation(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( sQ0_spl
| ~ relation(sK13_skl) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
( sQ1_spl
<=> function(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( sQ1_spl
| ~ function(sK13_skl) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ2_spl
<=> in(sK0_skl(relation_rng(sK13_skl),sK14_skl),relation_rng(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ2_spl
| in(sK0_skl(relation_rng(sK13_skl),sK14_skl),relation_rng(sK13_skl)) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,definition,
( sQ3_spl
<=> in(sK15_skl(sK0_skl(relation_rng(sK13_skl),sK14_skl)),relation_dom(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ3_spl
| ~ in(sK15_skl(sK0_skl(relation_rng(sK13_skl),sK14_skl)),relation_dom(sK13_skl)) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f148,f149,f152,f155,f158]) ).
fof(f196,plain,
( sQ3_spl
| ~ in(sK0_skl(relation_rng(sK13_skl),sK14_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f160,f106]) ).
fof(f197,plain,
( sQ3_spl
| subset(sK14_skl,relation_rng(sK13_skl)) ),
inference(resolution,[status(thm)],[f196,f45]) ).
fof(f198,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f108]) ).
fof(f199,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f200,plain,
( ~ sQ2_spl
| subset(sK14_skl,relation_rng(sK13_skl)) ),
inference(resolution,[status(thm)],[f156,f46]) ).
fof(f203,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f108]) ).
fof(f204,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f203]) ).
fof(f205,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f104]) ).
fof(f206,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f207,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f105]) ).
fof(f208,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f209,plain,
$false,
inference(sat_refutation,[status(thm)],[f161,f199,f204,f206,f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET997+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n010.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Mon Sep 21 05:46:47 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.46 % Drodi V4.1.1
% 0.16/5.48 % Refutation found
% 0.16/5.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/5.51 % Elapsed time: 0.055224 seconds
% 0.22/5.51 % CPU time: 0.152160 seconds
% 0.22/5.51 % Total memory used: 41.132 MB
% 0.22/5.51 % Net memory used: 41.098 MB
%------------------------------------------------------------------------------