%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.12s 0.49s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 21 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 12 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 3 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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : apply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/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(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f26,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f13,f18]) ).
fof(f38,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,f26]) ).
fof(f298,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,f38]) ).
fof(f386,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = X2,
inference(forward_demodulation,[status(thm)],[f13,f298]) ).
fof(f758,plain,
apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))) != apply(k(k(identity)),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))),
inference(resolution,[status(thm)],[f21,f24]) ).
fof(f761,plain,
apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))) != k(identity),
inference(forward_demodulation,[status(thm)],[f13,f758]) ).
fof(f1397,plain,
apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))) != k(identity),
inference(paramodulation,[status(thm)],[f38,f761]) ).
fof(f1400,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))) != apply(k(identity),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),
inference(resolution,[status(thm)],[f1397,f21]) ).
fof(f1402,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))) != identity,
inference(forward_demodulation,[status(thm)],[f13,f1400]) ).
fof(f1413,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity)) != apply(identity,n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity)),
inference(resolution,[status(thm)],[f1402,f21]) ).
fof(f1415,plain,
n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity) != apply(identity,n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity)),
inference(forward_demodulation,[status(thm)],[f386,f1413]) ).
fof(f1416,plain,
n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity) != n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity),
inference(forward_demodulation,[status(thm)],[f23,f1415]) ).
fof(f1417,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 14:04:42 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.49 % Refutation found
% 0.12/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.52 % Elapsed time: 0.152223 seconds
% 0.12/0.52 % CPU time: 0.957205 seconds
% 0.12/0.52 % Total memory used: 133.881 MB
% 0.12/0.52 % Net memory used: 131.892 MB
%------------------------------------------------------------------------------