%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU126+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 : n002.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 02:19:17 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 52 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 20 ~; 15 |; 8 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f32,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f97,plain,
? [A,B] :
( set_union2(A,B) != B
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f98,plain,
( set_union2(sK6_skl,sK7_skl) != sK7_skl
& subset(sK6_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl)],[f97]) ).
fof(f99,plain,
subset(sK6_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
set_union2(sK6_skl,sK7_skl) != sK7_skl,
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f124,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f128,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f129,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f41]) ).
fof(f143,plain,
set_union2(sK7_skl,sK6_skl) != sK7_skl,
inference(paramodulation,[status(thm)],[f37,f100]) ).
fof(f153,plain,
! [X0,X1] :
( ~ subset(set_union2(X0,X1),X0)
| set_union2(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f43,f124]) ).
fof(f217,plain,
! [X0] :
( subset(set_union2(X0,sK6_skl),sK7_skl)
| ~ subset(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f129,f99]) ).
fof(f311,plain,
subset(set_union2(sK7_skl,sK6_skl),sK7_skl),
inference(resolution,[status(thm)],[f217,f130]) ).
fof(f314,plain,
set_union2(sK7_skl,sK6_skl) = sK7_skl,
inference(resolution,[status(thm)],[f311,f153]) ).
fof(f318,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f314,f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU126+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:54:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.055026 seconds
% 0.09/0.44 % CPU time: 0.161065 seconds
% 0.09/0.44 % Total memory used: 103.145 MB
% 0.09/0.44 % Net memory used: 103.017 MB
%------------------------------------------------------------------------------