%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU180+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 : n003.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 0.53s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 16 unt; 0 def)
% Number of atoms : 175 ( 24 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 202 ( 76 ~; 76 |; 32 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 111 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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(f22,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(f25,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f143,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f157,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f236,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f237,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)],[f236]) ).
fof(f238,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)],[f237]) ).
fof(f239,plain,
( ! [A,B] :
( ( ~ in(sK16_skl(B,A),B)
& in(sK16_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,[sK16_skl]),skolemize(C,sK16_skl(B,A))],[f238]) ).
fof(f240,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f252,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)],[f18]) ).
fof(f253,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)],[f252]) ).
fof(f254,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)],[f253]) ).
fof(f255,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK19_skl(B,A),sK20_skl(B,A)),A)
| in(sK19_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK19_skl(B,A),D),A)
| ~ in(sK19_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,sK18_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl]),skolemize(D,sK18_skl(C,B,A)),skolemize(C,sK19_skl(B,A)),skolemize(D,sK20_skl(B,A))],[f254]) ).
fof(f257,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)],[f255]) ).
fof(f279,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)],[f22]) ).
fof(f280,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)],[f279]) ).
fof(f281,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)],[f280]) ).
fof(f282,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK27_skl(B,A),sK26_skl(B,A)),A)
| in(sK26_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK26_skl(B,A)),A)
| ~ in(sK26_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK25_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl,sK27_skl]),skolemize(D,sK25_skl(C,B,A)),skolemize(C,sK26_skl(B,A)),skolemize(D,sK27_skl(B,A))],[f281]) ).
fof(f284,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)],[f282]) ).
fof(f290,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f291,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f463,plain,
? [A,B,C] :
( ( ~ in(B,relation_field(C))
| ~ in(A,relation_field(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f109]) ).
fof(f464,plain,
? [C] :
( ? [A,B] :
( ( ~ in(B,relation_field(C))
| ~ in(A,relation_field(C)) )
& in(ordered_pair(A,B),C) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f463]) ).
fof(f465,plain,
( ( ~ in(sK40_skl,relation_field(sK38_skl))
| ~ in(sK39_skl,relation_field(sK38_skl)) )
& in(ordered_pair(sK39_skl,sK40_skl),sK38_skl)
& relation(sK38_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl,sK40_skl]),skolemize(C,sK38_skl),skolemize(A,sK39_skl),skolemize(B,sK40_skl)],[f464]) ).
fof(f466,plain,
relation(sK38_skl),
inference(cnf_transformation,[status(thm)],[f465]) ).
fof(f467,plain,
in(ordered_pair(sK39_skl,sK40_skl),sK38_skl),
inference(cnf_transformation,[status(thm)],[f465]) ).
fof(f468,plain,
( ~ in(sK40_skl,relation_field(sK38_skl))
| ~ in(sK39_skl,relation_field(sK38_skl)) ),
inference(cnf_transformation,[status(thm)],[f465]) ).
fof(f558,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f615,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f257]) ).
fof(f623,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f284]) ).
fof(f635,plain,
relation_field(sK38_skl) = set_union2(relation_dom(sK38_skl),relation_rng(sK38_skl)),
inference(resolution,[status(thm)],[f291,f466]) ).
fof(f1126,plain,
subset(relation_dom(sK38_skl),relation_field(sK38_skl)),
inference(paramodulation,[status(thm)],[f635,f558]) ).
fof(f1129,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(paramodulation,[status(thm)],[f157,f558]) ).
fof(f1450,plain,
subset(relation_rng(sK38_skl),relation_field(sK38_skl)),
inference(paramodulation,[status(thm)],[f635,f1129]) ).
fof(f1540,plain,
! [X0] :
( in(X0,relation_field(sK38_skl))
| ~ in(X0,relation_rng(sK38_skl)) ),
inference(resolution,[status(thm)],[f240,f1450]) ).
fof(f1542,plain,
! [X0] :
( in(X0,relation_field(sK38_skl))
| ~ in(X0,relation_dom(sK38_skl)) ),
inference(resolution,[status(thm)],[f240,f1126]) ).
fof(f2009,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK38_skl)
| in(X0,relation_dom(sK38_skl)) ),
inference(resolution,[status(thm)],[f615,f466]) ).
fof(f2068,plain,
in(sK39_skl,relation_dom(sK38_skl)),
inference(resolution,[status(thm)],[f2009,f467]) ).
fof(f2121,plain,
in(sK39_skl,relation_field(sK38_skl)),
inference(resolution,[status(thm)],[f2068,f1542]) ).
fof(f2126,plain,
~ in(sK40_skl,relation_field(sK38_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f468,f2121]) ).
fof(f2811,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,X0),sK38_skl)
| in(X0,relation_rng(sK38_skl)) ),
inference(resolution,[status(thm)],[f623,f466]) ).
fof(f2824,plain,
in(sK40_skl,relation_rng(sK38_skl)),
inference(resolution,[status(thm)],[f2811,f467]) ).
fof(f2841,plain,
in(sK40_skl,relation_field(sK38_skl)),
inference(resolution,[status(thm)],[f2824,f1540]) ).
fof(f2846,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2841,f2126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+2 : 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 : n003.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 05:56:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.53 % Refutation found
% 0.14/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.55 % Elapsed time: 0.179196 seconds
% 0.14/0.55 % CPU time: 1.079877 seconds
% 0.14/0.55 % Total memory used: 128.685 MB
% 0.14/0.55 % Net memory used: 126.400 MB
%------------------------------------------------------------------------------