%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU201+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:19:39 PM UTC 2026
% Result : Theorem 264.16s 38.92s
% Output : CNFRefutation 264.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 123 ( 19 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 144 ( 56 ~; 56 |; 25 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 76 ( 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,conjecture,
! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f118,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f204,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f333,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f334,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f333]) ).
fof(f335,plain,
( ! [A,B,C] :
( ( ( ( in(sK27_skl(C,B,A),B)
& in(sK27_skl(C,B,A),A) )
| in(sK27_skl(C,B,A),C) )
& ( ~ in(sK27_skl(C,B,A),B)
| ~ in(sK27_skl(C,B,A),A)
| ~ in(sK27_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl]),skolemize(D,sK27_skl(C,B,A))],[f334]) ).
fof(f339,plain,
! [X0,X1,X2] :
( ~ in(sK27_skl(X0,X2,X1),X2)
| ~ in(sK27_skl(X0,X2,X1),X1)
| ~ in(sK27_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f340,plain,
! [X0,X1,X2] :
( in(sK27_skl(X0,X2,X1),X1)
| in(sK27_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f341,plain,
! [X0,X1,X2] :
( in(sK27_skl(X0,X2,X1),X2)
| in(sK27_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f559,plain,
! [A,B,C] :
( ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f112]) ).
fof(f560,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f559]) ).
fof(f561,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ! [A,B] :
( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f560]) ).
fof(f562,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f561]) ).
fof(f563,plain,
! [X0,X1,X2] :
( in(X1,relation_rng(X0))
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f561]) ).
fof(f564,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_rng(X0))
| ~ in(X1,X2)
| in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f561]) ).
fof(f578,plain,
? [A,B] :
( relation_rng(relation_rng_restriction(A,B)) != set_intersection2(relation_rng(B),A)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f118]) ).
fof(f579,plain,
? [B] :
( ? [A] : relation_rng(relation_rng_restriction(A,B)) != set_intersection2(relation_rng(B),A)
& relation(B) ),
inference(miniscoping,[status(thm)],[f578]) ).
fof(f580,plain,
( relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)) != set_intersection2(relation_rng(sK53_skl),sK54_skl)
& relation(sK53_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl]),skolemize(B,sK53_skl),skolemize(A,sK54_skl)],[f579]) ).
fof(f581,plain,
relation(sK53_skl),
inference(cnf_transformation,[status(thm)],[f580]) ).
fof(f582,plain,
relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)) != set_intersection2(relation_rng(sK53_skl),sK54_skl),
inference(cnf_transformation,[status(thm)],[f580]) ).
fof(f882,plain,
relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)) != set_intersection2(sK54_skl,relation_rng(sK53_skl)),
inference(paramodulation,[status(thm)],[f204,f582]) ).
fof(f974,plain,
! [X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sK53_skl))) ),
inference(resolution,[status(thm)],[f562,f581]) ).
fof(f980,plain,
! [X0,X1] :
( in(X0,relation_rng(sK53_skl))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sK53_skl))) ),
inference(resolution,[status(thm)],[f563,f581]) ).
fof(f988,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(sK53_skl))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,sK53_skl))) ),
inference(resolution,[status(thm)],[f564,f581]) ).
fof(f3300,plain,
( ~ in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(sK53_skl))
| ~ in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),sK54_skl)
| ~ in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(relation_rng_restriction(sK54_skl,sK53_skl))) ),
inference(resolution,[status(thm)],[f339,f882]) ).
fof(f3314,plain,
( ~ in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(sK53_skl))
| ~ in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3300,f988]) ).
fof(f3320,plain,
( in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),sK54_skl)
| in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(relation_rng_restriction(sK54_skl,sK53_skl))) ),
inference(resolution,[status(thm)],[f340,f882]) ).
fof(f3365,plain,
~ in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(sK53_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f3314,f3366]) ).
fof(f3366,plain,
in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),sK54_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3320,f974]) ).
fof(f3376,plain,
( in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(sK53_skl))
| in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(relation_rng_restriction(sK54_skl,sK53_skl))) ),
inference(resolution,[status(thm)],[f341,f882]) ).
fof(f3425,plain,
in(sK27_skl(relation_rng(relation_rng_restriction(sK54_skl,sK53_skl)),relation_rng(sK53_skl),sK54_skl),relation_rng(sK53_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f3376,f980]) ).
fof(f3426,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f3365,f3425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU201+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n017.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Mon Sep 21 05:52:48 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.14/5.41 % Drodi V4.1.1
% 264.16/38.92 % Refutation found
% 264.16/38.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 264.16/38.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 73.76/39.02 % Elapsed time: 33.626119 seconds
% 73.76/39.02 % CPU time: 265.474170 seconds
% 73.76/39.02 % Total memory used: 636.623 MB
% 73.76/39.02 % Net memory used: 545.987 MB
%------------------------------------------------------------------------------