%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL036-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:08:31 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : apply(apply(t,X),Y) = apply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y] : apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1] : apply(apply(apply(b,X0),X1),f(apply(apply(b,X0),X1))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f15,plain,
! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(forward_demodulation,[status(thm)],[f6,f14]) ).
fof(f17,plain,
! [X0,X1] : apply(apply(t,X0),apply(X1,f(apply(apply(b,apply(t,X0)),X1)))) != apply(f(apply(apply(b,apply(t,X0)),X1)),apply(apply(X1,f(apply(apply(b,apply(t,X0)),X1))),X0)),
inference(paramodulation,[status(thm)],[f7,f15]) ).
fof(f21,plain,
! [X0,X1] : apply(apply(X0,f(apply(apply(b,apply(t,X1)),X0))),X1) != apply(f(apply(apply(b,apply(t,X1)),X0)),apply(apply(X0,f(apply(apply(b,apply(t,X1)),X0))),X1)),
inference(forward_demodulation,[status(thm)],[f7,f17]) ).
fof(f26,plain,
! [X0,X1,X2] : apply(apply(apply(apply(b,X0),X1),f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),X2) != apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))),apply(apply(X0,apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))),X2)),
inference(paramodulation,[status(thm)],[f6,f21]) ).
fof(f30,plain,
! [X0,X1,X2] : apply(apply(X0,apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))),X2) != apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))),apply(apply(X0,apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))),X2)),
inference(forward_demodulation,[status(thm)],[f6,f26]) ).
fof(f64,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,apply(b,X0)),X1))))),X2) != apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,apply(b,X0)),X1))),apply(X0,apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,apply(b,X0)),X1)))),X2))),
inference(paramodulation,[status(thm)],[f6,f30]) ).
fof(f70,plain,
! [X0,X1,X2] : apply(X0,apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,apply(b,X0)),X1)))),X2)) != apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,apply(b,X0)),X1))),apply(X0,apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,apply(b,X0)),X1)))),X2))),
inference(forward_demodulation,[status(thm)],[f6,f64]) ).
fof(f86,plain,
! [X0,X1] : apply(apply(apply(s,t),X0),X1) = apply(apply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f162,plain,
! [X0] : apply(apply(apply(s,t),t),X0) = apply(X0,X0),
inference(paramodulation,[status(thm)],[f7,f86]) ).
fof(f220,plain,
! [X0,X1] : apply(apply(apply(s,t),t),apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1))),
inference(paramodulation,[status(thm)],[f6,f162]) ).
fof(f251,plain,
$false,
inference(resolution,[status(thm)],[f220,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL036-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 14:06:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.49 % Refutation found
% 0.14/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.120459 seconds
% 0.14/0.50 % CPU time: 0.828908 seconds
% 0.14/0.50 % Total memory used: 36.008 MB
% 0.14/0.50 % Net memory used: 35.409 MB
%------------------------------------------------------------------------------