%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX186-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 03:13:23 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.52s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Q] : impl(btrue,Q) = Q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Z] : drop(s(Z),nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : prop_drop_inj2(X,Y,Z) = impl(eq(drop(X,Y),drop(X,Z)),eq(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : eq(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : eq3(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] : eq(cons(X,Y),nil) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
! [X,Y,Z] : eq3(prop_drop_inj2(X,Y,Z),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0] : impl(btrue,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : drop(s(X0),nil) = nil,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] : drop(s(X0),cons(X1,X2)) = drop(X0,X2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : prop_drop_inj2(X0,X1,X2) = impl(eq(drop(X0,X1),drop(X0,X2)),eq(X1,X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [X0] : eq(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
! [X0] : eq3(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
! [X0,X1] : eq(cons(X0,X1),nil) = bfalse,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f40,plain,
! [X0,X1,X2] : eq3(prop_drop_inj2(X0,X1,X2),bfalse) != btrue,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f59,plain,
! [X0,X1] : prop_drop_inj2(s(X0),X1,nil) = impl(eq(drop(s(X0),X1),nil),eq(X1,nil)),
inference(paramodulation,[status(thm)],[f22,f25]) ).
fof(f65,plain,
! [X0,X1,X2] : prop_drop_inj2(s(X0),cons(X1,X2),nil) = impl(eq(drop(X0,X2),nil),eq(cons(X1,X2),nil)),
inference(paramodulation,[status(thm)],[f23,f59]) ).
fof(f68,plain,
! [X0,X1,X2] : prop_drop_inj2(s(X0),cons(X1,X2),nil) = impl(eq(drop(X0,X2),nil),bfalse),
inference(forward_demodulation,[status(thm)],[f39,f65]) ).
fof(f74,plain,
! [X0,X1] : eq3(impl(eq(drop(X0,X1),nil),bfalse),bfalse) != btrue,
inference(paramodulation,[status(thm)],[f68,f40]) ).
fof(f76,plain,
eq3(impl(eq(nil,nil),bfalse),bfalse) != btrue,
inference(paramodulation,[status(thm)],[f22,f74]) ).
fof(f78,plain,
eq3(impl(btrue,bfalse),bfalse) != btrue,
inference(forward_demodulation,[status(thm)],[f31,f76]) ).
fof(f79,plain,
eq3(bfalse,bfalse) != btrue,
inference(forward_demodulation,[status(thm)],[f20,f78]) ).
fof(f80,plain,
btrue != btrue,
inference(forward_demodulation,[status(thm)],[f33,f79]) ).
fof(f81,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWX186-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.49 % Computer : n012.cluster.edu
% 0.03/0.49 % Model : x86_64 x86_64
% 0.03/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.49 % Memory : 8046.5625MB
% 0.03/0.49 % OS : Linux 6.8.0-71-generic
% 0.03/0.49 % CPULimit : 300
% 0.03/0.49 % WCLimit : 300
% 0.03/0.49 % DateTime : Mon Sep 21 10:30:38 UTC 2026
% 0.03/0.49 % CPUTime :
% 0.03/0.50 % Drodi V4.1.1
% 0.03/0.52 % Refutation found
% 0.03/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.54 % Elapsed time: 0.039571 seconds
% 0.10/0.54 % CPU time: 0.090919 seconds
% 0.10/0.54 % Total memory used: 66.821 MB
% 0.10/0.54 % Net memory used: 66.450 MB
%------------------------------------------------------------------------------