%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET693+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 02:10:28 PM UTC 2026
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 4 unt; 0 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 58 ~; 64 |; 17 &)
% ( 6 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 75 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] :
( equal_set(A,union(A,B))
<=> subset(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] :
( equal_set(A,union(A,B))
<=> subset(B,A) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ! [X,A,B] :
( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f68,plain,
? [A,B] :
( equal_set(A,union(A,B))
<~> subset(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,B] :
( ( ~ subset(B,A)
| ~ equal_set(A,union(A,B)) )
& ( subset(B,A)
| equal_set(A,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( ~ subset(sK4_skl,sK3_skl)
| ~ equal_set(sK3_skl,union(sK3_skl,sK4_skl)) )
& ( subset(sK4_skl,sK3_skl)
| equal_set(sK3_skl,union(sK3_skl,sK4_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f69]) ).
fof(f71,plain,
( subset(sK4_skl,sK3_skl)
| equal_set(sK3_skl,union(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
( ~ subset(sK4_skl,sK3_skl)
| ~ equal_set(sK3_skl,union(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f77,plain,
( subset(sK4_skl,sK3_skl)
| subset(sK3_skl,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f23,f71]) ).
fof(f78,plain,
( subset(sK4_skl,sK3_skl)
| subset(union(sK3_skl,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f24,f71]) ).
fof(f79,plain,
( ~ subset(sK4_skl,sK3_skl)
| ~ subset(union(sK3_skl,sK4_skl),sK3_skl)
| ~ subset(sK3_skl,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f25,f72]) ).
fof(f84,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,union(X0,X1)),X1)
| member(sK0_skl(X2,union(X0,X1)),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f37]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(union(X1,X2),X0),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f20,f38]) ).
fof(f91,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,union(sK3_skl,sK4_skl))
| subset(sK4_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f78,f18]) ).
fof(f96,plain,
( ~ subset(sK4_skl,sK3_skl)
| ~ subset(union(sK3_skl,sK4_skl),sK3_skl)
| ~ member(sK0_skl(union(sK3_skl,sK4_skl),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f87,f79]) ).
fof(f99,plain,
( subset(sK3_skl,union(sK3_skl,sK4_skl))
| ~ subset(sK4_skl,sK3_skl)
| ~ subset(union(sK3_skl,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f96,f19]) ).
fof(f100,plain,
( ~ subset(sK4_skl,sK3_skl)
| ~ subset(union(sK3_skl,sK4_skl),sK3_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f79,f101]) ).
fof(f101,plain,
( subset(sK3_skl,union(sK3_skl,sK4_skl))
| ~ subset(union(sK3_skl,sK4_skl),sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f77]) ).
fof(f108,plain,
( member(sK0_skl(sK3_skl,union(sK3_skl,sK4_skl)),sK4_skl)
| member(sK0_skl(sK3_skl,union(sK3_skl,sK4_skl)),sK3_skl)
| ~ subset(sK4_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f100,f84]) ).
fof(f109,plain,
( member(sK0_skl(sK3_skl,union(sK3_skl,sK4_skl)),sK3_skl)
| ~ subset(sK4_skl,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f18]) ).
fof(f110,plain,
( subset(union(sK3_skl,sK4_skl),sK3_skl)
| ~ subset(sK4_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f109,f20]) ).
fof(f112,plain,
~ subset(sK4_skl,sK3_skl),
inference(backward_subsumption_resolution,[status(thm)],[f100,f113]) ).
fof(f113,plain,
subset(union(sK3_skl,sK4_skl),sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f110,f78]) ).
fof(f115,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,union(sK3_skl,sK4_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f91,f112]) ).
fof(f121,plain,
! [X0] :
( ~ member(X0,sK4_skl)
| member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f115,f39]) ).
fof(f123,plain,
! [X0] :
( subset(sK4_skl,X0)
| member(sK0_skl(X0,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f121,f19]) ).
fof(f131,plain,
( subset(sK4_skl,sK3_skl)
| subset(sK4_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f123,f20]) ).
fof(f132,plain,
subset(sK4_skl,sK3_skl),
inference(duplicate_literals_removal,[status(thm)],[f131]) ).
fof(f133,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f132,f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET693+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n013.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Mon Sep 21 05:32:21 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.53 % Drodi V4.1.1
% 0.21/0.58 % Refutation found
% 0.21/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.61 % Elapsed time: 0.078762 seconds
% 0.21/0.61 % CPU time: 0.327704 seconds
% 0.21/0.61 % Total memory used: 85.090 MB
% 0.21/0.61 % Net memory used: 84.166 MB
%------------------------------------------------------------------------------