%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:06:16 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 30 unt; 2 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V,W,X,Y,Z] : multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Y,X] : multiply(Y,X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : multiply(X,X,Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Y,X] : multiply(inverse(Y),Y,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : multiply(X,Y,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] : multiply(X0,X1,X1) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : multiply(X0,X0,X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : multiply(inverse(X0),X0,X1) = X1,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1,X0) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
multiply(a,inverse(a),b) != b,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
sF1_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF0_fnc = multiply(a,sF1_fnc,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != b,
inference(definition_folding,[],[f12,f14,f13]) ).
fof(f18,plain,
! [X0,X1] : multiply(sF0_fnc,X0,multiply(a,sF1_fnc,X1)) = multiply(a,sF1_fnc,multiply(b,X0,X1)),
inference(paramodulation,[status(thm)],[f14,f7]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1,X2),X3,X1) = multiply(X0,X1,multiply(X2,X3,X1)),
inference(paramodulation,[status(thm)],[f8,f7]) ).
fof(f44,plain,
! [X0] : multiply(sF1_fnc,a,X0) = X0,
inference(paramodulation,[status(thm)],[f13,f10]) ).
fof(f222,plain,
! [X0] : multiply(sF0_fnc,b,multiply(a,sF1_fnc,X0)) = multiply(a,sF1_fnc,b),
inference(paramodulation,[status(thm)],[f9,f18]) ).
fof(f237,plain,
! [X0] : multiply(sF0_fnc,b,multiply(a,sF1_fnc,X0)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f14,f222]) ).
fof(f274,plain,
multiply(sF0_fnc,b,a) = sF0_fnc,
inference(paramodulation,[status(thm)],[f11,f237]) ).
fof(f275,plain,
multiply(sF0_fnc,b,sF1_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f8,f237]) ).
fof(f953,plain,
! [X0,X1] : multiply(multiply(X0,X1,sF1_fnc),a,X1) = multiply(X0,X1,X1),
inference(paramodulation,[status(thm)],[f44,f22]) ).
fof(f972,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1,X2),X2,X1) = multiply(X0,X1,X2),
inference(paramodulation,[status(thm)],[f9,f22]) ).
fof(f1042,plain,
! [X0,X1] : multiply(multiply(X0,X1,sF1_fnc),a,X1) = X1,
inference(forward_demodulation,[status(thm)],[f8,f953]) ).
fof(f1100,plain,
multiply(sF0_fnc,a,b) = b,
inference(paramodulation,[status(thm)],[f275,f1042]) ).
fof(f1946,plain,
multiply(sF0_fnc,a,b) = multiply(sF0_fnc,b,a),
inference(paramodulation,[status(thm)],[f274,f972]) ).
fof(f2025,plain,
b = multiply(sF0_fnc,b,a),
inference(forward_demodulation,[status(thm)],[f1100,f1946]) ).
fof(f2026,plain,
b = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f274,f2025]) ).
fof(f2027,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2026,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n020.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 13:47:08 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Drodi V4.1.1
% 0.15/5.43 % Refutation found
% 0.15/5.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.59/6.65 % Elapsed time: 1.054058 seconds
% 1.59/6.65 % CPU time: 0.284806 seconds
% 1.59/6.65 % Total memory used: 9.166 MB
% 1.59/6.65 % Net memory used: 8.927 MB
%------------------------------------------------------------------------------