%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:19:09 PM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 16 unt; 0 def)
% Number of atoms : 84 ( 27 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 30 ~; 21 |; 19 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( one_to_one(C)
=> relation_image(C,set_intersection2(A,B)) = set_intersection2(relation_image(C,A),relation_image(C,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( one_to_one(C)
& disjoint(A,B) )
=> disjoint(relation_image(C,A),relation_image(C,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( one_to_one(C)
& disjoint(A,B) )
=> disjoint(relation_image(C,A),relation_image(C,B)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [A] :
( relation(A)
=> relation_image(A,empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f51,plain,
( ! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ! [A,B] :
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f102,plain,
! [A,B,C] :
( relation_image(C,set_intersection2(A,B)) = set_intersection2(relation_image(C,A),relation_image(C,B))
| ~ one_to_one(C)
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f103,plain,
! [C] :
( ! [A,B] : relation_image(C,set_intersection2(A,B)) = set_intersection2(relation_image(C,A),relation_image(C,B))
| ~ one_to_one(C)
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
? [A,B,C] :
( ~ disjoint(relation_image(C,A),relation_image(C,B))
& one_to_one(C)
& disjoint(A,B)
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f106,plain,
? [C] :
( ? [A,B] :
( ~ disjoint(relation_image(C,A),relation_image(C,B))
& one_to_one(C)
& disjoint(A,B) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
( ~ disjoint(relation_image(sK11_skl,sK12_skl),relation_image(sK11_skl,sK13_skl))
& one_to_one(sK11_skl)
& disjoint(sK12_skl,sK13_skl)
& function(sK11_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(C,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl)],[f106]) ).
fof(f108,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
disjoint(sK12_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f111,plain,
one_to_one(sK11_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
~ disjoint(relation_image(sK11_skl,sK12_skl),relation_image(sK11_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f113,plain,
! [A] :
( relation_image(A,empty_set) = empty_set
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f114,plain,
! [X0] :
( relation_image(X0,empty_set) = empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f146,plain,
! [X0,X1] :
( set_intersection2(X1,X0) = empty_set
| ~ disjoint(X0,X1) ),
inference(paramodulation,[status(thm)],[f49,f52]) ).
fof(f148,plain,
set_intersection2(relation_image(sK11_skl,sK12_skl),relation_image(sK11_skl,sK13_skl)) != empty_set,
inference(resolution,[status(thm)],[f112,f53]) ).
fof(f156,plain,
relation_image(sK11_skl,empty_set) = empty_set,
inference(resolution,[status(thm)],[f114,f108]) ).
fof(f158,plain,
! [X0,X1] :
( relation_image(sK11_skl,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK11_skl,X0),relation_image(sK11_skl,X1))
| ~ one_to_one(sK11_skl)
| ~ function(sK11_skl) ),
inference(resolution,[status(thm)],[f104,f108]) ).
fof(f160,plain,
! [X0,X1] :
( relation_image(sK11_skl,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK11_skl,X0),relation_image(sK11_skl,X1))
| ~ one_to_one(sK11_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f109]) ).
fof(f161,plain,
set_intersection2(sK13_skl,sK12_skl) = empty_set,
inference(resolution,[status(thm)],[f146,f110]) ).
fof(f164,plain,
set_intersection2(sK12_skl,sK13_skl) = empty_set,
inference(forward_demodulation,[status(thm)],[f49,f161]) ).
fof(f183,plain,
relation_image(sK11_skl,set_intersection2(sK12_skl,sK13_skl)) != empty_set,
inference(backward_demodulation,[status(thm)],[f184,f148]) ).
fof(f184,plain,
! [X0,X1] : relation_image(sK11_skl,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK11_skl,X0),relation_image(sK11_skl,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f160,f111]) ).
fof(f193,plain,
relation_image(sK11_skl,empty_set) != empty_set,
inference(forward_demodulation,[status(thm)],[f164,f183]) ).
fof(f194,plain,
empty_set != empty_set,
inference(forward_demodulation,[status(thm)],[f156,f193]) ).
fof(f195,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:50:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.039779 seconds
% 0.12/0.40 % CPU time: 0.124824 seconds
% 0.12/0.40 % Total memory used: 70.786 MB
% 0.12/0.40 % Net memory used: 70.766 MB
%------------------------------------------------------------------------------