%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL046-1 : 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 12:08:34 PM UTC 2026
% Result : Unsatisfiable 56.45s 7.63s
% Output : CNFRefutation 56.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 3 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 : 57 ( 57 !; 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] : apply(m,X) = apply(X,X),
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(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : apply(X0,apply(X1,X2)) = apply(apply(apply(b,X0),X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0] : apply(X0,X0) = apply(m,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(f13,plain,
! [X0,X1,X2,X3] : apply(apply(apply(apply(s,X0),X1),X2),apply(X3,apply(X1,X2))) = apply(apply(apply(s,apply(X0,X2)),X3),apply(X1,X2)),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f17,plain,
! [X0,X1,X2] : apply(X0,apply(X1,apply(X2,X1))) = apply(apply(apply(s,apply(b,X0)),X2),X1),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f18,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(f22,plain,
! [X0,X1,X2,X3] : apply(apply(X0,apply(X1,X2)),apply(X3,X2)) = apply(apply(apply(s,apply(apply(b,X0),X1)),X3),X2),
inference(paramodulation,[status(thm)],[f6,f5]) ).
fof(f24,plain,
! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1))),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f25,plain,
! [X0,X1] : apply(apply(apply(s,X0),X0),X1) = apply(m,apply(X0,X1)),
inference(paramodulation,[status(thm)],[f5,f7]) ).
fof(f80,plain,
! [X0] : apply(apply(apply(s,X0),X0),f(apply(apply(s,X0),X0))) != apply(f(apply(apply(s,X0),X0)),apply(m,apply(X0,f(apply(apply(s,X0),X0))))),
inference(paramodulation,[status(thm)],[f25,f8]) ).
fof(f87,plain,
! [X0] : apply(m,apply(X0,f(apply(apply(s,X0),X0)))) != apply(f(apply(apply(s,X0),X0)),apply(m,apply(X0,f(apply(apply(s,X0),X0))))),
inference(forward_demodulation,[status(thm)],[f25,f80]) ).
fof(f632,plain,
! [X0,X1] : apply(apply(apply(apply(s,b),X0),X1),apply(X0,X1)) = apply(X1,apply(m,apply(X0,X1))),
inference(paramodulation,[status(thm)],[f7,f18]) ).
fof(f753,plain,
! [X0] : apply(apply(apply(s,apply(apply(s,b),X0)),X0),f(apply(apply(s,X0),X0))) != apply(m,apply(X0,f(apply(apply(s,X0),X0)))),
inference(backward_demodulation,[status(thm)],[f754,f87]) ).
fof(f754,plain,
! [X0,X1] : apply(X0,apply(m,apply(X1,X0))) = apply(apply(apply(s,apply(apply(s,b),X1)),X1),X0),
inference(forward_demodulation,[status(thm)],[f5,f632]) ).
fof(f830,plain,
! [X0,X1,X2] : apply(m,apply(apply(X0,apply(X1,X0)),X2)) = apply(apply(apply(apply(apply(s,apply(b,s)),X1),X0),apply(X0,apply(X1,X0))),X2),
inference(paramodulation,[status(thm)],[f17,f25]) ).
fof(f935,plain,
! [X0,X1,X2] : apply(m,apply(apply(X0,apply(X1,X0)),X2)) = apply(apply(apply(apply(s,apply(apply(b,s),X0)),X0),apply(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f13,f830]) ).
fof(f936,plain,
! [X0,X1,X2] : apply(m,apply(apply(X0,apply(X1,X0)),X2)) = apply(apply(apply(apply(s,apply(s,apply(apply(b,s),X0))),X1),X0),X2),
inference(forward_demodulation,[status(thm)],[f5,f935]) ).
fof(f2521,plain,
! [X0] : apply(m,apply(apply(X0,apply(apply(b,apply(s,b)),X0)),f(apply(apply(s,apply(X0,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0)))))) != apply(apply(apply(s,apply(m,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))),f(apply(apply(s,apply(X0,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))))),
inference(paramodulation,[status(thm)],[f24,f753]) ).
fof(f2532,plain,
! [X0] : apply(m,apply(apply(X0,apply(apply(b,apply(s,b)),X0)),f(apply(apply(apply(s,apply(apply(b,s),X0)),X0),apply(apply(b,apply(s,b)),X0))))) != apply(apply(apply(s,apply(m,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))),f(apply(apply(s,apply(X0,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))))),
inference(forward_demodulation,[status(thm)],[f22,f2521]) ).
fof(f2533,plain,
! [X0] : apply(m,apply(apply(X0,apply(apply(b,apply(s,b)),X0)),f(apply(apply(apply(s,apply(s,apply(apply(b,s),X0))),apply(b,apply(s,b))),X0)))) != apply(apply(apply(s,apply(m,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))),f(apply(apply(s,apply(X0,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))))),
inference(forward_demodulation,[status(thm)],[f5,f2532]) ).
fof(f2534,plain,
! [X0] : apply(m,apply(apply(X0,apply(apply(b,apply(s,b)),X0)),f(apply(apply(apply(s,apply(s,apply(apply(b,s),X0))),apply(b,apply(s,b))),X0)))) != apply(apply(apply(apply(s,apply(apply(b,s),m)),X0),apply(apply(b,apply(s,b)),X0)),f(apply(apply(s,apply(X0,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))))),
inference(forward_demodulation,[status(thm)],[f22,f2533]) ).
fof(f2535,plain,
! [X0] : apply(m,apply(apply(X0,apply(apply(b,apply(s,b)),X0)),f(apply(apply(apply(s,apply(s,apply(apply(b,s),X0))),apply(b,apply(s,b))),X0)))) != apply(apply(apply(apply(s,apply(s,apply(apply(b,s),m))),apply(b,apply(s,b))),X0),f(apply(apply(s,apply(X0,apply(apply(b,apply(s,b)),X0))),apply(X0,apply(apply(b,apply(s,b)),X0))))),
inference(forward_demodulation,[status(thm)],[f5,f2534]) ).
fof(f2536,plain,
! [X0] : apply(m,apply(apply(X0,apply(apply(b,apply(s,b)),X0)),f(apply(apply(apply(s,apply(s,apply(apply(b,s),X0))),apply(b,apply(s,b))),X0)))) != apply(apply(apply(apply(s,apply(s,apply(apply(b,s),m))),apply(b,apply(s,b))),X0),f(apply(apply(apply(s,apply(apply(b,s),X0)),X0),apply(apply(b,apply(s,b)),X0)))),
inference(forward_demodulation,[status(thm)],[f22,f2535]) ).
fof(f2537,plain,
! [X0] : apply(m,apply(apply(X0,apply(apply(b,apply(s,b)),X0)),f(apply(apply(apply(s,apply(s,apply(apply(b,s),X0))),apply(b,apply(s,b))),X0)))) != apply(apply(apply(apply(s,apply(s,apply(apply(b,s),m))),apply(b,apply(s,b))),X0),f(apply(apply(apply(s,apply(s,apply(apply(b,s),X0))),apply(b,apply(s,b))),X0))),
inference(forward_demodulation,[status(thm)],[f5,f2536]) ).
fof(f2538,plain,
$false,
inference(resolution,[status(thm)],[f2537,f936]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL046-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:09:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 56.45/7.63 % Refutation found
% 56.45/7.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 56.45/7.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.79/7.74 % Elapsed time: 7.357145 seconds
% 3.79/7.74 % CPU time: 58.069751 seconds
% 3.79/7.74 % Total memory used: 979.380 MB
% 3.79/7.74 % Net memory used: 950.806 MB
%------------------------------------------------------------------------------