%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL037-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 9 ( 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 : 42 ( 42 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y] : apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox2/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,X2] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
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(f74,plain,
! [X0,X1] : apply(apply(apply(c,X0),X1),f(apply(apply(c,X0),X1))) != apply(f(apply(apply(c,X0),X1)),apply(apply(X0,f(apply(apply(c,X0),X1))),X1)),
inference(paramodulation,[status(thm)],[f7,f8]) ).
fof(f95,plain,
! [X0,X1] : apply(apply(X0,f(apply(apply(c,X0),X1))),X1) != apply(f(apply(apply(c,X0),X1)),apply(apply(X0,f(apply(apply(c,X0),X1))),X1)),
inference(forward_demodulation,[status(thm)],[f7,f74]) ).
fof(f98,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(c,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f138,plain,
! [X0,X1,X2] : apply(apply(apply(apply(s,b),X0),X1),X2) = apply(X1,apply(apply(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f153,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(c,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f6,f98]) ).
fof(f526,plain,
! [X0,X1] : apply(apply(X0,f(apply(apply(c,X0),X1))),X1) != apply(apply(apply(apply(s,b),X0),f(apply(apply(c,X0),X1))),X1),
inference(paramodulation,[status(thm)],[f138,f95]) ).
fof(f783,plain,
! [X0,X1] : apply(apply(X0,f(apply(apply(c,X0),apply(X1,X0)))),apply(X1,X0)) != apply(apply(apply(apply(s,b),X0),f(apply(apply(apply(s,c),X1),X0))),apply(X1,X0)),
inference(paramodulation,[status(thm)],[f5,f526]) ).
fof(f796,plain,
! [X0,X1] : apply(apply(X0,f(apply(apply(apply(s,c),X1),X0))),apply(X1,X0)) != apply(apply(apply(apply(s,b),X0),f(apply(apply(apply(s,c),X1),X0))),apply(X1,X0)),
inference(paramodulation,[status(thm)],[f5,f783]) ).
fof(f1585,plain,
! [X0,X1,X2] : apply(apply(apply(apply(X0,X1),X1),f(apply(apply(apply(s,c),X2),apply(apply(X0,X1),X1)))),apply(X2,apply(apply(X0,X1),X1))) != apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X0),X1),f(apply(apply(apply(s,c),X2),apply(apply(X0,X1),X1)))),apply(X2,apply(apply(X0,X1),X1))),
inference(paramodulation,[status(thm)],[f153,f796]) ).
fof(f1710,plain,
$false,
inference(destructive_equality_resolution,[status(thm)],[f1585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 14:07:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.48 % Elapsed time: 0.119971 seconds
% 0.13/0.48 % CPU time: 0.823853 seconds
% 0.13/0.48 % Total memory used: 43.196 MB
% 0.13/0.48 % Net memory used: 42.716 MB
%------------------------------------------------------------------------------