%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU183+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 : 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 02:19:34 PM UTC 2026
% Result : Theorem 0.13s 0.64s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 8 unt; 5 def)
% Number of atoms : 243 ( 19 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 300 ( 119 ~; 119 |; 37 &)
% ( 15 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-5 aty)
% Number of variables : 149 ( 127 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
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(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] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f48,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)],[f47]) ).
fof(f49,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)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK3_skl(B,A),sK2_skl(B,A)),A)
| in(sK2_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK2_skl(B,A)),A)
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK1_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(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(sK1_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,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)],[f50]) ).
fof(f56,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ! [D,E] :
( ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ( ( in(ordered_pair(sK7_skl(C,B,A),sK6_skl(C,B,A)),B)
& in(ordered_pair(sK5_skl(C,B,A),sK7_skl(C,B,A)),A) )
| in(ordered_pair(sK5_skl(C,B,A),sK6_skl(C,B,A)),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,sK6_skl(C,B,A)),B)
| ~ in(ordered_pair(sK5_skl(C,B,A),F),A) )
| ~ in(ordered_pair(sK5_skl(C,B,A),sK6_skl(C,B,A)),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(sK4_skl(E,D,C,B,A),E),B)
& in(ordered_pair(D,sK4_skl(E,D,C,B,A)),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(F,sK4_skl(E,D,C,B,A)),skolemize(D,sK5_skl(C,B,A)),skolemize(E,sK6_skl(C,B,A)),skolemize(F,sK7_skl(C,B,A))],[f58]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK4_skl(X4,X3,X2,X1,X0),X4),X1)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f66,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f67,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f99,plain,
? [A] :
( ? [B] :
( ~ subset(relation_rng(relation_composition(A,B)),relation_rng(B))
& relation(B) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f100,plain,
( ~ subset(relation_rng(relation_composition(sK14_skl,sK15_skl)),relation_rng(sK15_skl))
& relation(sK15_skl)
& relation(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(A,sK14_skl),skolemize(B,sK15_skl)],[f99]) ).
fof(f101,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
~ subset(relation_rng(relation_composition(sK14_skl,sK15_skl)),relation_rng(sK15_skl)),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f118,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK4_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f61]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK4_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f122,f67]) ).
fof(f134,plain,
~ in(sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl))),relation_rng(sK15_skl)),
inference(resolution,[status(thm)],[f46,f103]) ).
fof(f151,plain,
! [X0] :
( ~ in(ordered_pair(X0,sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl)))),sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f134,f119]) ).
fof(f153,definition,
( sQ0_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ0_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
! [X0] :
( sQ1_spl
<=> ~ in(ordered_pair(X0,sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl)))),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f157,plain,
! [X0] :
( ~ sQ1_spl
| ~ in(ordered_pair(X0,sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl)))),sK15_skl) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f151,f153,f156]) ).
fof(f160,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f102]) ).
fof(f161,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f434,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK4_skl(X2,X1,relation_composition(X0,sK15_skl),sK15_skl,X0),X2),sK15_skl)
| ~ in(ordered_pair(X1,X2),relation_composition(X0,sK15_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f125,f102]) ).
fof(f474,plain,
! [X0,X1] :
( in(ordered_pair(sK4_skl(X1,X0,relation_composition(sK14_skl,sK15_skl),sK15_skl,sK14_skl),X1),sK15_skl)
| ~ in(ordered_pair(X0,X1),relation_composition(sK14_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f434,f101]) ).
fof(f499,definition,
( sQ35_spl
<=> relation(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( sQ35_spl
| ~ relation(sK14_skl) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f507,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f101]) ).
fof(f508,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f601,plain,
! [X0] :
( ~ sQ1_spl
| ~ in(ordered_pair(X0,sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl)))),relation_composition(sK14_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f474,f157]) ).
fof(f737,plain,
( ~ sQ1_spl
| ~ in(sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl))),relation_rng(relation_composition(sK14_skl,sK15_skl)))
| ~ relation(relation_composition(sK14_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f601,f118]) ).
fof(f740,definition,
( sQ62_spl
<=> relation(relation_composition(sK14_skl,sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f742,plain,
( sQ62_spl
| ~ relation(relation_composition(sK14_skl,sK15_skl)) ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f743,definition,
( sQ63_spl
<=> in(sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl))),relation_rng(relation_composition(sK14_skl,sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f745,plain,
( sQ63_spl
| ~ in(sK0_skl(relation_rng(sK15_skl),relation_rng(relation_composition(sK14_skl,sK15_skl))),relation_rng(relation_composition(sK14_skl,sK15_skl))) ),
inference(component_clause,[status(thm)],[f743]) ).
fof(f746,plain,
( ~ sQ1_spl
| ~ sQ63_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f737,f740,f743,f156]) ).
fof(f751,plain,
( sQ62_spl
| ~ relation(sK15_skl)
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f742,f67]) ).
fof(f752,plain,
( sQ62_spl
| ~ sQ0_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f751,f499,f153,f740]) ).
fof(f762,plain,
( sQ63_spl
| subset(relation_rng(relation_composition(sK14_skl,sK15_skl)),relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f745,f45]) ).
fof(f765,plain,
( sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f103]) ).
fof(f766,plain,
sQ63_spl,
inference(contradiction_clause,[status(thm)],[f765]) ).
fof(f767,plain,
$false,
inference(sat_refutation,[status(thm)],[f159,f161,f508,f746,f752,f766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU183+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:56:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.64 % Refutation found
% 0.13/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.77/0.67 % Elapsed time: 0.289698 seconds
% 1.77/0.67 % CPU time: 2.021369 seconds
% 1.77/0.67 % Total memory used: 128.443 MB
% 1.77/0.67 % Net memory used: 125.167 MB
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