%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:08:42 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 17 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : apply(k(X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : apply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1] : apply(k(X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : apply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( X0 != apply(X1,n(k(X0),X1))
| k(X0) = X1 ),
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f13,plain,
! [X0,X1] :
( apply(X0,n(X0,k(X1))) != X1
| X0 = k(X1) ),
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f14,plain,
! [X0] :
( apply(X0,n(X0,identity)) != n(X0,identity)
| X0 = identity ),
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f22,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f101,plain,
! [X0,X1,X2] : apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2) = apply(X1,apply(apply(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f7,f22]) ).
fof(f105,plain,
! [X0,X1,X2] :
( X0 != apply(X1,apply(X2,n(k(X0),apply(apply(abstraction,k(X1)),X2))))
| k(X0) = apply(apply(abstraction,k(X1)),X2) ),
inference(paramodulation,[status(thm)],[f22,f11]) ).
fof(f867,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = apply(k(X2),apply(apply(X0,k(X2)),apply(X1,X2))),
inference(paramodulation,[status(thm)],[f7,f101]) ).
fof(f936,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = X2,
inference(forward_demodulation,[status(thm)],[f6,f867]) ).
fof(f1120,plain,
! [X0,X1] : apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1) = identity,
inference(resolution,[status(thm)],[f936,f14]) ).
fof(f1171,plain,
! [X0] : apply(abstraction,apply(apply(abstraction,abstraction),X0)) = k(identity),
inference(resolution,[status(thm)],[f1120,f13]) ).
fof(f1524,plain,
k(k(identity)) = apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)),
inference(resolution,[status(thm)],[f105,f1171]) ).
fof(f1547,plain,
k(k(identity)) = apply(apply(apply(abstraction,abstraction),abstraction),abstraction),
inference(forward_demodulation,[status(thm)],[f7,f1524]) ).
fof(f1548,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1547,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n010.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
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 14:09:41 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Drodi V4.1.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.54 % Elapsed time: 0.109112 seconds
% 0.16/0.54 % CPU time: 0.523481 seconds
% 0.16/0.54 % Total memory used: 61.591 MB
% 0.16/0.54 % Net memory used: 61.390 MB
%------------------------------------------------------------------------------