%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 01:24:38 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
n2 = f(n1,n1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
n3 = f(n2,n1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
u = f(n2,n2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
f(f(n3,n2),u) != f(f(u,u),u),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0] : f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f18,plain,
! [X0] : f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(paramodulation,[status(thm)],[f8,f6]) ).
fof(f20,plain,
! [X0] : f(n2,f(X0,n2)) = f(f(n2,X0),u),
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f22,plain,
f(n2,f(n2,n2)) = f(u,u),
inference(paramodulation,[status(thm)],[f9,f17]) ).
fof(f23,plain,
f(n2,f(n2,n1)) = f(u,n3),
inference(paramodulation,[status(thm)],[f8,f17]) ).
fof(f26,plain,
f(f(n3,n2),u) != f(f(n2,u),u),
inference(backward_demodulation,[status(thm)],[f27,f10]) ).
fof(f27,plain,
f(n2,u) = f(u,u),
inference(forward_demodulation,[status(thm)],[f9,f22]) ).
fof(f28,plain,
f(n2,n3) = f(u,n3),
inference(forward_demodulation,[status(thm)],[f8,f23]) ).
fof(f29,plain,
f(f(n3,n2),u) != f(n2,f(u,n2)),
inference(forward_demodulation,[status(thm)],[f20,f26]) ).
fof(f35,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(paramodulation,[status(thm)],[f8,f18]) ).
fof(f38,plain,
f(n2,n2) = f(n3,n3),
inference(forward_demodulation,[status(thm)],[f7,f35]) ).
fof(f39,plain,
u = f(n3,n3),
inference(forward_demodulation,[status(thm)],[f9,f38]) ).
fof(f40,plain,
! [X0] : f(n3,f(X0,n3)) = f(f(n3,X0),u),
inference(paramodulation,[status(thm)],[f39,f6]) ).
fof(f41,plain,
! [X0] : f(n3,f(n3,X0)) = f(u,f(n3,X0)),
inference(paramodulation,[status(thm)],[f39,f6]) ).
fof(f42,plain,
f(n3,f(n2,n3)) != f(n2,f(u,n2)),
inference(backward_demodulation,[status(thm)],[f40,f29]) ).
fof(f43,plain,
f(n2,f(n1,n3)) != f(n2,f(u,n2)),
inference(forward_demodulation,[status(thm)],[f18,f42]) ).
fof(f84,plain,
f(n3,u) = f(u,f(n3,n3)),
inference(paramodulation,[status(thm)],[f39,f41]) ).
fof(f90,plain,
f(n3,u) = f(u,u),
inference(forward_demodulation,[status(thm)],[f39,f84]) ).
fof(f96,plain,
f(n3,u) = f(n2,u),
inference(forward_demodulation,[status(thm)],[f27,f90]) ).
fof(f107,plain,
f(n3,f(u,n3)) = f(f(n2,u),u),
inference(paramodulation,[status(thm)],[f96,f40]) ).
fof(f113,plain,
f(n3,f(n2,n3)) = f(f(n2,u),u),
inference(forward_demodulation,[status(thm)],[f28,f107]) ).
fof(f114,plain,
f(n2,f(n1,n3)) = f(f(n2,u),u),
inference(forward_demodulation,[status(thm)],[f18,f113]) ).
fof(f115,plain,
f(n2,f(n1,n3)) = f(n2,f(u,n2)),
inference(forward_demodulation,[status(thm)],[f20,f114]) ).
fof(f116,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f115,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 01:18:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.033865 seconds
% 0.10/0.41 % CPU time: 0.037122 seconds
% 0.10/0.41 % Total memory used: 1.461 MB
% 0.10/0.41 % Net memory used: 1.421 MB
%------------------------------------------------------------------------------