%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:08:41 PM UTC 2026
% Result : Unsatisfiable 33.04s 10.03s
% Output : CNFRefutation 33.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 17 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 8 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : apply(k(X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : apply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] : apply(k(X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0] : apply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f13,f18]) ).
fof(f578,plain,
! [X0,X1,X2] : apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2) = apply(X1,apply(apply(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f18,f25]) ).
fof(f6739,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)],[f18,f578]) ).
fof(f7329,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) != identity,
inference(paramodulation,[status(thm)],[f578,f24]) ).
fof(f7448,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = X2,
inference(forward_demodulation,[status(thm)],[f13,f6739]) ).
fof(f9647,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)) != apply(identity,n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)),
inference(resolution,[status(thm)],[f7329,f21]) ).
fof(f9649,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)) != n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity),
inference(forward_demodulation,[status(thm)],[f23,f9647]) ).
fof(f12920,plain,
n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity) != n(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity),
inference(forward_demodulation,[status(thm)],[f7448,f9649]) ).
fof(f12921,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f12920]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n004.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Mon Sep 21 14:09:26 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.46 % Drodi V4.1.1
% 33.04/10.03 % Refutation found
% 33.04/10.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 33.04/10.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.40/10.33 % Elapsed time: 4.876513 seconds
% 2.40/10.33 % CPU time: 36.414904 seconds
% 2.40/10.33 % Total memory used: 564.922 MB
% 2.40/10.33 % Net memory used: 517.144 MB
%------------------------------------------------------------------------------