%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL038-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:08:31 PM UTC 2026
% Result : Unsatisfiable 0.13s 10.94s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 16 ( 4 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 : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : apply(m,X) = apply(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : apply(apply(apply(v,X),Y),Z) = apply(apply(Z,X),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(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0] : apply(m,X0) = apply(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1,X2] : apply(apply(apply(v,X0),X1),X2) = apply(apply(X2,X0),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(f12,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)],[f5,f8]) ).
fof(f13,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)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2)))) != apply(f(apply(apply(b,apply(apply(b,X0),X1)),X2)),apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2)))))),
inference(paramodulation,[status(thm)],[f5,f13]) ).
fof(f16,plain,
! [X0,X1,X2] : apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2))))) != apply(f(apply(apply(b,apply(apply(b,X0),X1)),X2)),apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2)))))),
inference(forward_demodulation,[status(thm)],[f5,f14]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : apply(apply(apply(b,X0),X1),apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3))))) != apply(f(apply(apply(b,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3)),apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3))))))),
inference(paramodulation,[status(thm)],[f5,f16]) ).
fof(f21,plain,
! [X0,X1,X2,X3] : apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3)))))) != apply(f(apply(apply(b,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3)),apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3))))))),
inference(forward_demodulation,[status(thm)],[f5,f18]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] : apply(apply(apply(v,X0),X1),apply(X2,apply(X3,apply(X4,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X0),X1)),X2)),X3)),X4)))))) != apply(f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X0),X1)),X2)),X3)),X4)),apply(apply(apply(X2,apply(X3,apply(X4,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X0),X1)),X2)),X3)),X4))))),X0),X1)),
inference(paramodulation,[status(thm)],[f7,f21]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] : apply(apply(apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),X0)),X1)),X2))))),X3),X4) != apply(f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),X0)),X1)),X2)),apply(apply(apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),X0)),X1)),X2))))),X3),X4)),
inference(forward_demodulation,[status(thm)],[f7,f37]) ).
fof(f64,plain,
! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1))),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f185,plain,
! [X0,X1,X2] : apply(X0,apply(apply(X1,apply(apply(b,apply(b,X0)),X1)),X2)) = apply(apply(m,apply(apply(b,apply(b,X0)),X1)),X2),
inference(paramodulation,[status(thm)],[f64,f5]) ).
fof(f755,plain,
! [X0,X1,X2,X3,X4] : apply(apply(apply(apply(b,X0),apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),apply(b,X0))),X1)),X2))))),X3),X4) != apply(f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),apply(b,X0))),X1)),X2)),apply(apply(X0,apply(apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),apply(b,X0))),X1)),X2)))),X3)),X4)),
inference(paramodulation,[status(thm)],[f5,f50]) ).
fof(f841,plain,
! [X0,X1,X2,X3,X4] : apply(apply(X0,apply(apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),apply(b,X0))),X1)),X2)))),X3)),X4) != apply(f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),apply(b,X0))),X1)),X2)),apply(apply(X0,apply(apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(apply(v,X3),X4)),apply(b,X0))),X1)),X2)))),X3)),X4)),
inference(forward_demodulation,[status(thm)],[f5,f755]) ).
fof(f842,plain,
$false,
inference(resolution,[status(thm)],[f841,f185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n017.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Mon Sep 21 14:01:08 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 % Drodi V4.1.1
% 0.13/10.94 % Refutation found
% 0.13/10.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/10.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.98 % Elapsed time: 0.585526 seconds
% 0.13/10.98 % CPU time: 4.538614 seconds
% 0.13/10.98 % Total memory used: 150.494 MB
% 0.13/10.98 % Net memory used: 148.017 MB
%------------------------------------------------------------------------------