%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU179+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:19:33 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 6 unt; 2 def)
% Number of atoms : 201 ( 20 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 239 ( 91 ~; 95 |; 32 &)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 139 ( 119 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f40,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
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(f44,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
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_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f48,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)],[f47]) ).
fof(f49,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)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),A)
| in(sK2_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK2_skl(B,A),D),A)
| ~ in(sK2_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,sK1_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(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(f51,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK1_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,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)],[f50]) ).
fof(f55,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK6_skl(B,A),sK5_skl(B,A)),A)
| in(sK5_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK5_skl(B,A)),A)
| ~ in(sK5_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK4_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(C,sK5_skl(B,A)),skolemize(D,sK6_skl(B,A))],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK4_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f89,plain,
? [A] :
( ? [B] :
( ( ~ subset(relation_rng(A),relation_rng(B))
| ~ subset(relation_dom(A),relation_dom(B)) )
& subset(A,B)
& relation(B) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f90,plain,
( ( ~ subset(relation_rng(sK13_skl),relation_rng(sK14_skl))
| ~ subset(relation_dom(sK13_skl),relation_dom(sK14_skl)) )
& subset(sK13_skl,sK14_skl)
& relation(sK14_skl)
& relation(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f89]) ).
fof(f91,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f93,plain,
subset(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f94,plain,
( ~ subset(relation_rng(sK13_skl),relation_rng(sK14_skl))
| ~ subset(relation_dom(sK13_skl),relation_dom(sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f115,definition,
( sQ0_spl
<=> subset(relation_dom(sK13_skl),relation_dom(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f118,definition,
( sQ1_spl
<=> subset(relation_rng(sK13_skl),relation_rng(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f94,f115,f118]) ).
fof(f122,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK1_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f124,plain,
! [X0,X1] :
( in(ordered_pair(sK4_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f59]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f60]) ).
fof(f126,plain,
! [X0] :
( in(X0,sK14_skl)
| ~ in(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f44,f93]) ).
fof(f128,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK14_skl)
| in(X0,relation_dom(sK14_skl)) ),
inference(resolution,[status(thm)],[f123,f92]) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,X0),sK14_skl)
| in(X0,relation_rng(sK14_skl)) ),
inference(resolution,[status(thm)],[f125,f92]) ).
fof(f145,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK13_skl)
| in(X0,relation_dom(sK14_skl)) ),
inference(resolution,[status(thm)],[f128,f126]) ).
fof(f146,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,X0),sK13_skl)
| in(X0,relation_rng(sK14_skl)) ),
inference(resolution,[status(thm)],[f130,f126]) ).
fof(f158,plain,
! [X0] :
( in(ordered_pair(X0,sK1_skl(X0,relation_dom(sK13_skl),sK13_skl)),sK13_skl)
| ~ in(X0,relation_dom(sK13_skl)) ),
inference(resolution,[status(thm)],[f122,f91]) ).
fof(f172,plain,
! [X0] :
( in(X0,relation_dom(sK14_skl))
| ~ in(X0,relation_dom(sK13_skl)) ),
inference(resolution,[status(thm)],[f158,f145]) ).
fof(f176,plain,
! [X0] :
( subset(X0,relation_dom(sK14_skl))
| ~ in(sK0_skl(relation_dom(sK14_skl),X0),relation_dom(sK13_skl)) ),
inference(resolution,[status(thm)],[f172,f46]) ).
fof(f209,plain,
! [X0] :
( in(ordered_pair(sK4_skl(X0,relation_rng(sK13_skl),sK13_skl),X0),sK13_skl)
| ~ in(X0,relation_rng(sK13_skl)) ),
inference(resolution,[status(thm)],[f124,f91]) ).
fof(f247,plain,
( subset(relation_dom(sK13_skl),relation_dom(sK14_skl))
| subset(relation_dom(sK13_skl),relation_dom(sK14_skl)) ),
inference(resolution,[status(thm)],[f176,f45]) ).
fof(f248,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f247,f115]) ).
fof(f255,plain,
! [X0] :
( in(X0,relation_rng(sK14_skl))
| ~ in(X0,relation_rng(sK13_skl)) ),
inference(resolution,[status(thm)],[f209,f146]) ).
fof(f286,plain,
! [X0] :
( subset(X0,relation_rng(sK14_skl))
| ~ in(sK0_skl(relation_rng(sK14_skl),X0),relation_rng(sK13_skl)) ),
inference(resolution,[status(thm)],[f255,f46]) ).
fof(f420,plain,
( subset(relation_rng(sK13_skl),relation_rng(sK14_skl))
| subset(relation_rng(sK13_skl),relation_rng(sK14_skl)) ),
inference(resolution,[status(thm)],[f286,f45]) ).
fof(f421,plain,
sQ1_spl,
inference(split_clause,[status(thm)],[f420,f118]) ).
fof(f422,plain,
$false,
inference(sat_refutation,[status(thm)],[f121,f248,f421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU179+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:55:02 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.065762 seconds
% 0.14/0.43 % CPU time: 0.288089 seconds
% 0.14/0.43 % Total memory used: 106.389 MB
% 0.14/0.43 % Net memory used: 105.884 MB
%------------------------------------------------------------------------------