%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 03:13:25 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [Y,Y2,Xs] : aux2(Y,Y2,Xs,bfalse) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Z] : leqNat(s(Z),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Y] : merge(nil,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
ord(nil) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Y,Y2,Xs] : ord(cons(Y,cons(Y2,Xs))) = aux2(Y,Y2,Xs,leqNat(Y,Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Q] : impl(btrue,Q) = Q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : prop_merge_ord_not3(X,Y) = impl(eq2(ord(X),btrue),impl(eq2(ord(Y),bfalse),eq2(ord(merge(X,Y)),btrue))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
eq2(bfalse,btrue) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X] : eq2(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
! [X,Y] : eq2(prop_merge_ord_not3(X,Y),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X0,X1,X2] : aux2(X0,X1,X2,bfalse) = bfalse,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
! [X0] : leqNat(s(X0),z) = bfalse,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
! [X0] : merge(nil,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
ord(nil) = btrue,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [X0,X1,X2] : ord(cons(X0,cons(X1,X2))) = aux2(X0,X1,X2,leqNat(X0,X1)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
! [X0] : impl(btrue,X0) = X0,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
! [X0,X1] : prop_merge_ord_not3(X0,X1) = impl(eq2(ord(X0),btrue),impl(eq2(ord(X1),bfalse),eq2(ord(merge(X0,X1)),btrue))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
eq2(bfalse,btrue) = bfalse,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
! [X0] : eq2(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f48,plain,
! [X0,X1] : eq2(prop_merge_ord_not3(X0,X1),bfalse) != btrue,
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f51,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))),
inference(paramodulation,[status(thm)],[f32,f40]) ).
fof(f59,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(eq2(btrue,btrue),impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))),
inference(backward_demodulation,[status(thm)],[f35,f51]) ).
fof(f62,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(btrue,impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))),
inference(forward_demodulation,[status(thm)],[f47,f59]) ).
fof(f66,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue)),
inference(forward_demodulation,[status(thm)],[f38,f62]) ).
fof(f130,plain,
! [X0,X1] : ord(cons(s(X0),cons(z,X1))) = aux2(s(X0),z,X1,bfalse),
inference(paramodulation,[status(thm)],[f30,f37]) ).
fof(f132,plain,
! [X0,X1] : ord(cons(s(X0),cons(z,X1))) = bfalse,
inference(forward_demodulation,[status(thm)],[f28,f130]) ).
fof(f140,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = impl(eq2(ord(cons(s(X0),cons(z,X1))),bfalse),eq2(bfalse,btrue)),
inference(paramodulation,[status(thm)],[f132,f66]) ).
fof(f148,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = impl(eq2(bfalse,bfalse),eq2(bfalse,btrue)),
inference(forward_demodulation,[status(thm)],[f132,f140]) ).
fof(f149,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = impl(btrue,eq2(bfalse,btrue)),
inference(forward_demodulation,[status(thm)],[f47,f148]) ).
fof(f150,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = eq2(bfalse,btrue),
inference(forward_demodulation,[status(thm)],[f38,f149]) ).
fof(f151,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = bfalse,
inference(forward_demodulation,[status(thm)],[f41,f150]) ).
fof(f168,plain,
eq2(bfalse,bfalse) != btrue,
inference(paramodulation,[status(thm)],[f151,f48]) ).
fof(f169,plain,
btrue != btrue,
inference(forward_demodulation,[status(thm)],[f47,f168]) ).
fof(f170,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 10:34:04 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.021893 seconds
% 0.12/0.38 % CPU time: 0.028515 seconds
% 0.12/0.38 % Total memory used: 807.664 KB
% 0.12/0.38 % Net memory used: 788.464 KB
%------------------------------------------------------------------------------