%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET994+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 : n004.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 02:11:07 PM UTC 2026
% Result : Theorem 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 153 ( 65 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 149 ( 54 ~; 57 |; 26 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 58 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = n0 )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = n1 )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
empty(n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ empty(n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [A] :
( ! [B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_dom(C) = A
& relation_dom(B) = A )
=> B = C ) ) )
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [A] :
( ! [B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_dom(C) = A
& relation_dom(B) = A )
=> B = C ) ) )
=> A = empty_set ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [A] : element(sK0_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f4]) ).
fof(f41,plain,
! [X0] : element(sK0_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f64,plain,
empty(sK4_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f14]) ).
fof(f65,plain,
empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f79,plain,
! [A] :
? [B] :
( ! [C] :
( apply(B,C) = n0
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f80,plain,
! [A] :
( ! [C] :
( apply(sK9_skl(A),C) = n0
| ~ in(C,A) )
& relation_dom(sK9_skl(A)) = A
& function(sK9_skl(A))
& relation(sK9_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(B,sK9_skl(A))],[f79]) ).
fof(f81,plain,
! [X0] : relation(sK9_skl(X0)),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0] : function(sK9_skl(X0)),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
! [X0] : relation_dom(sK9_skl(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,plain,
! [X0,X1] :
( apply(sK9_skl(X1),X0) = n0
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f85,plain,
! [A] :
? [B] :
( ! [C] :
( apply(B,C) = n1
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
! [A] :
( ! [C] :
( apply(sK10_skl(A),C) = n1
| ~ in(C,A) )
& relation_dom(sK10_skl(A)) = A
& function(sK10_skl(A))
& relation(sK10_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(B,sK10_skl(A))],[f85]) ).
fof(f87,plain,
! [X0] : relation(sK10_skl(X0)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [X0] : function(sK10_skl(X0)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
! [X0] : relation_dom(sK10_skl(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f90,plain,
! [X0,X1] :
( apply(sK10_skl(X1),X0) = n1
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f91,plain,
empty(n0),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f92,plain,
~ empty(n1),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f93,plain,
? [A] :
( A != empty_set
& ! [B] :
( ! [C] :
( B = C
| relation_dom(C) != A
| relation_dom(B) != A
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f94,plain,
( sK11_skl != empty_set
& ! [B] :
( ! [C] :
( B = C
| relation_dom(C) != sK11_skl
| relation_dom(B) != sK11_skl
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( X0 = X1
| relation_dom(X1) != sK11_skl
| relation_dom(X0) != sK11_skl
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
sK11_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f99,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f100,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f111,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f112,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f122,plain,
sK4_skl = empty_set,
inference(resolution,[status(thm)],[f112,f65]) ).
fof(f125,plain,
! [X0] :
( X0 = sK4_skl
| ~ empty(X0) ),
inference(backward_demodulation,[status(thm)],[f122,f112]) ).
fof(f130,plain,
sK11_skl != sK4_skl,
inference(backward_demodulation,[status(thm)],[f122,f96]) ).
fof(f148,plain,
n0 = sK4_skl,
inference(resolution,[status(thm)],[f91,f125]) ).
fof(f156,plain,
! [X0] :
( X0 = sK9_skl(sK11_skl)
| relation_dom(X0) != sK11_skl
| ~ function(sK9_skl(sK11_skl))
| ~ relation(sK9_skl(sK11_skl))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f83,f95]) ).
fof(f160,plain,
! [X0] :
( X0 = sK9_skl(sK11_skl)
| relation_dom(X0) != sK11_skl
| ~ function(sK9_skl(sK11_skl))
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f81]) ).
fof(f164,plain,
! [X0,X1] :
( apply(sK9_skl(X1),X0) = sK4_skl
| ~ in(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f148,f84]) ).
fof(f165,plain,
! [X0] :
( X0 = sK9_skl(sK11_skl)
| relation_dom(X0) != sK11_skl
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f160,f82]) ).
fof(f178,plain,
! [X0] :
( sK10_skl(X0) = sK9_skl(sK11_skl)
| relation_dom(sK10_skl(X0)) != sK11_skl
| ~ relation(sK10_skl(X0)) ),
inference(resolution,[status(thm)],[f88,f165]) ).
fof(f179,plain,
! [X0] :
( sK10_skl(X0) = sK9_skl(sK11_skl)
| relation_dom(sK10_skl(X0)) != sK11_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f87]) ).
fof(f191,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f100,f41]) ).
fof(f195,plain,
! [X0] :
( sK10_skl(X0) = sK9_skl(sK11_skl)
| X0 != sK11_skl ),
inference(forward_demodulation,[status(thm)],[f89,f179]) ).
fof(f196,plain,
sK10_skl(sK11_skl) = sK9_skl(sK11_skl),
inference(destructive_equality_resolution,[status(thm)],[f195]) ).
fof(f248,plain,
! [X0] :
( apply(sK10_skl(X0),sK0_skl(X0)) = n1
| empty(X0) ),
inference(resolution,[status(thm)],[f191,f90]) ).
fof(f250,plain,
! [X0] :
( apply(sK9_skl(X0),sK0_skl(X0)) = sK4_skl
| empty(X0) ),
inference(resolution,[status(thm)],[f191,f164]) ).
fof(f277,plain,
( apply(sK9_skl(sK11_skl),sK0_skl(sK11_skl)) = n1
| empty(sK11_skl) ),
inference(paramodulation,[status(thm)],[f196,f248]) ).
fof(f278,plain,
( empty(sK11_skl)
| sK4_skl = n1
| empty(sK11_skl) ),
inference(paramodulation,[status(thm)],[f250,f277]) ).
fof(f280,plain,
( sK4_skl = n1
| empty(sK11_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f278]) ).
fof(f286,plain,
( sK11_skl = sK4_skl
| sK4_skl = n1 ),
inference(resolution,[status(thm)],[f280,f125]) ).
fof(f290,plain,
sK4_skl = n1,
inference(forward_subsumption_resolution,[status(thm)],[f286,f130]) ).
fof(f297,plain,
~ empty(sK4_skl),
inference(backward_demodulation,[status(thm)],[f290,f92]) ).
fof(f298,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f297,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 05:46:27 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.44 % Elapsed time: 0.053230 seconds
% 0.13/5.44 % CPU time: 0.193410 seconds
% 0.13/5.44 % Total memory used: 104.200 MB
% 0.13/5.44 % Net memory used: 104.051 MB
%------------------------------------------------------------------------------