%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET002+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 02:08:46 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 33 ~; 39 |; 15 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 72 !; 3 ?)
% 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] : equal_set(union(A,A),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : equal_set(union(A,A),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(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(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(f39,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f68,plain,
? [A] : ~ equal_set(union(A,A),A),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ equal_set(union(sK3_skl,sK3_skl),sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f68]) ).
fof(f70,plain,
~ equal_set(union(sK3_skl,sK3_skl),sK3_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f81,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(f111,plain,
! [X0,X1] :
( member(sK0_skl(X1,union(X0,X1)),X0)
| subset(union(X0,X1),X1)
| subset(union(X0,X1),X1) ),
inference(resolution,[status(thm)],[f20,f81]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(union(X1,X2),X0),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f20,f39]) ).
fof(f118,plain,
! [X0,X1] :
( member(sK0_skl(X1,union(X0,X1)),X0)
| subset(union(X0,X1),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f111]) ).
fof(f206,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[f114,f19]) ).
fof(f215,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f206]) ).
fof(f218,plain,
! [X0,X1] :
( ~ subset(union(X0,X1),X1)
| equal_set(union(X0,X1),X1) ),
inference(resolution,[status(thm)],[f215,f25]) ).
fof(f240,plain,
! [X0] :
( subset(union(X0,X0),X0)
| subset(union(X0,X0),X0) ),
inference(resolution,[status(thm)],[f118,f20]) ).
fof(f256,plain,
! [X0] : subset(union(X0,X0),X0),
inference(duplicate_literals_removal,[status(thm)],[f240]) ).
fof(f257,plain,
! [X0] : equal_set(union(X0,X0),X0),
inference(resolution,[status(thm)],[f256,f218]) ).
fof(f264,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f70,f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:40:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.060149 seconds
% 0.14/0.45 % CPU time: 0.186237 seconds
% 0.14/0.45 % Total memory used: 81.746 MB
% 0.14/0.45 % Net memory used: 81.310 MB
%------------------------------------------------------------------------------