%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 03:13:30 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 37 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Y,Z,Xs] : aux(Y,Z,Xs,btrue) = union(Xs,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Y] : barbar(btrue,Y) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
eqNat(z,z) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Z,Xs] : elem(X,cons(Z,Xs)) = barbar(eqNat(X,Z),elem(X,Xs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Y] : union(nil,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Z,Xs,Y] : union(cons(Z,Xs),Y) = aux(Y,Z,Xs,elem(Z,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : prop_union_comm(X,Y) = eq(union(X,Y),union(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : eq2(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : eq3(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y,X2] :
( eq(cons(X,Y),cons(Z,X2)) = eq(Y,X2)
| eq2(X,Z) != btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Y] : eq(cons(X,Y),nil) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
! [X,Y] : eq3(prop_union_comm(X,Y),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X0,X1,X2] : aux(X0,X1,X2,btrue) = union(X2,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f29,plain,
! [X0] : barbar(btrue,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f34,plain,
eqNat(z,z) = btrue,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X0,X1,X2] : elem(X0,cons(X1,X2)) = barbar(eqNat(X0,X1),elem(X0,X2)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0] : union(nil,X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f38,plain,
! [X0,X1,X2] : union(cons(X0,X1),X2) = aux(X2,X0,X1,elem(X0,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
! [X0,X1] : prop_union_comm(X0,X1) = eq(union(X0,X1),union(X1,X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
! [X0] : eq2(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f47,plain,
! [X0] : eq3(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
! [X,Z] :
( ! [Y,X2] : eq(cons(X,Y),cons(Z,X2)) = eq(Y,X2)
| eq2(X,Z) != btrue ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3)
| eq2(X0,X1) != btrue ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0,X1] : eq(cons(X0,X1),nil) = bfalse,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f54,plain,
! [X0,X1] : eq3(prop_union_comm(X0,X1),bfalse) != btrue,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
! [X0] : elem(z,cons(z,X0)) = barbar(btrue,elem(z,X0)),
inference(paramodulation,[status(thm)],[f34,f36]) ).
fof(f85,plain,
! [X0] : elem(z,cons(z,X0)) = btrue,
inference(forward_demodulation,[status(thm)],[f29,f81]) ).
fof(f87,plain,
! [X0,X1] : union(cons(z,X0),cons(z,X1)) = aux(cons(z,X1),z,X0,btrue),
inference(paramodulation,[status(thm)],[f85,f38]) ).
fof(f88,plain,
! [X0,X1] : union(cons(z,X0),cons(z,X1)) = union(X0,cons(z,X1)),
inference(forward_demodulation,[status(thm)],[f27,f87]) ).
fof(f106,plain,
! [X0,X1,X2] : eq(cons(X0,X1),cons(X0,X2)) = eq(X1,X2),
inference(resolution,[status(thm)],[f51,f46]) ).
fof(f154,plain,
! [X0,X1] : prop_union_comm(cons(z,X0),cons(z,X1)) = eq(union(cons(z,X0),cons(z,X1)),union(X1,cons(z,X0))),
inference(paramodulation,[status(thm)],[f88,f39]) ).
fof(f156,plain,
! [X0,X1] : prop_union_comm(cons(z,X0),cons(z,X1)) = eq(union(X0,cons(z,X1)),union(X1,cons(z,X0))),
inference(forward_demodulation,[status(thm)],[f88,f154]) ).
fof(f160,plain,
! [X0] : prop_union_comm(cons(z,nil),cons(z,X0)) = eq(cons(z,X0),union(X0,cons(z,nil))),
inference(paramodulation,[status(thm)],[f37,f156]) ).
fof(f164,plain,
! [X0] : prop_union_comm(cons(z,nil),cons(z,cons(z,X0))) = eq(cons(z,cons(z,X0)),union(X0,cons(z,nil))),
inference(paramodulation,[status(thm)],[f88,f160]) ).
fof(f173,plain,
prop_union_comm(cons(z,nil),cons(z,cons(z,nil))) = eq(cons(z,cons(z,nil)),cons(z,nil)),
inference(paramodulation,[status(thm)],[f37,f164]) ).
fof(f174,plain,
prop_union_comm(cons(z,nil),cons(z,cons(z,nil))) = eq(cons(z,nil),nil),
inference(forward_demodulation,[status(thm)],[f106,f173]) ).
fof(f175,plain,
prop_union_comm(cons(z,nil),cons(z,cons(z,nil))) = bfalse,
inference(forward_demodulation,[status(thm)],[f53,f174]) ).
fof(f180,plain,
eq3(bfalse,bfalse) != btrue,
inference(paramodulation,[status(thm)],[f175,f54]) ).
fof(f181,plain,
btrue != btrue,
inference(forward_demodulation,[status(thm)],[f47,f180]) ).
fof(f182,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n020.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 10:37:18 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.47 % Refutation found
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.51 % Elapsed time: 0.069558 seconds
% 0.23/0.51 % CPU time: 0.209926 seconds
% 0.23/0.51 % Total memory used: 65.737 MB
% 0.23/0.51 % Net memory used: 65.495 MB
%------------------------------------------------------------------------------