%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:08:26 PM UTC 2026
% Result : Unsatisfiable 279.93s 43.20s
% Output : CNFRefutation 245.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 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,Y] : apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y] : apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : apply(X0,apply(X1,X1)) = apply(apply(w,apply(b,X0)),X1),
inference(paramodulation,[status(thm)],[f5,f4]) ).
fof(f15,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)],[f4,f6]) ).
fof(f17,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)],[f4,f15]) ).
fof(f19,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)],[f4,f17]) ).
fof(f22,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)],[f4,f19]) ).
fof(f56,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)],[f4,f22]) ).
fof(f63,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)],[f4,f56]) ).
fof(f231,plain,
! [X0,X1,X2] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2),
inference(paramodulation,[status(thm)],[f12,f4]) ).
fof(f244,plain,
! [X0,X1] : apply(apply(w,apply(w,apply(b,X0))),X1) = apply(apply(X0,apply(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f12,f5]) ).
fof(f4064,plain,
! [X0,X1] : apply(apply(apply(w,apply(b,apply(b,X0))),X1),X1) = apply(X0,apply(apply(w,X1),X1)),
inference(paramodulation,[status(thm)],[f5,f231]) ).
fof(f32314,plain,
! [X0,X1] : apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1) = apply(X0,apply(apply(w,X1),X1)),
inference(forward_demodulation,[status(thm)],[f5,f4064]) ).
fof(f32316,plain,
! [X0,X1] : apply(X0,apply(apply(w,X1),X1)) = apply(apply(apply(b,X0),apply(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f244,f32314]) ).
fof(f33070,plain,
! [X0,X1] : apply(X0,apply(apply(w,X1),X1)) = apply(X0,apply(apply(X1,X1),X1)),
inference(forward_demodulation,[status(thm)],[f4,f32316]) ).
fof(f33154,plain,
! [X0,X1] : apply(X0,apply(apply(X1,X1),X1)) = apply(X0,apply(apply(w,w),X1)),
inference(paramodulation,[status(thm)],[f5,f33070]) ).
fof(f34474,plain,
! [X0,X1] : apply(X0,apply(apply(w,w),X1)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X1),
inference(paramodulation,[status(thm)],[f231,f33154]) ).
fof(f159076,plain,
! [X0,X1] : apply(X0,apply(apply(w,w),X1)) = apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1),
inference(forward_demodulation,[status(thm)],[f5,f34474]) ).
fof(f159095,plain,
! [X0] : apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))) = apply(apply(w,w),apply(w,apply(b,apply(b,X0)))),
inference(paramodulation,[status(thm)],[f5,f159076]) ).
fof(f159885,plain,
$false,
inference(resolution,[status(thm)],[f159095,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.46 % Computer : n015.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Mon Sep 21 14:06:41 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 % Drodi V4.1.1
% 279.93/43.20 % Refutation found
% 279.93/43.20 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 279.93/43.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 68.55/43.70 % Elapsed time: 38.150050 seconds
% 68.55/43.70 % CPU time: 283.307521 seconds
% 68.55/43.70 % Total memory used: 4.079 GB
% 68.55/43.70 % Net memory used: 4.015 GB
%------------------------------------------------------------------------------