%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% 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 12:06:21 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 36 unt; 2 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
inverse(inverse(x)) != x,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
sF1_fnc = inverse(x),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f20,definition,
sF0_fnc = inverse(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f21,plain,
sF0_fnc != x,
inference(definition_folding,[],[f18,f20,f19]) ).
fof(f30,plain,
! [X0] : X0 = multiply(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f51,plain,
add(sF1_fnc,sF0_fnc) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f20,f16]) ).
fof(f52,plain,
add(x,sF1_fnc) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f19,f16]) ).
fof(f54,plain,
add(sF0_fnc,sF1_fnc) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f10,f51]) ).
fof(f61,plain,
multiply(sF1_fnc,sF0_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f20,f17]) ).
fof(f62,plain,
multiply(x,sF1_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f19,f17]) ).
fof(f73,plain,
! [X0] : add(x,multiply(sF1_fnc,X0)) = multiply(multiplicative_identity,add(x,X0)),
inference(paramodulation,[status(thm)],[f52,f12]) ).
fof(f80,plain,
! [X0] : add(sF0_fnc,multiply(X0,sF1_fnc)) = multiply(add(sF0_fnc,X0),multiplicative_identity),
inference(paramodulation,[status(thm)],[f54,f12]) ).
fof(f93,plain,
! [X0] : add(x,multiply(sF1_fnc,X0)) = add(x,X0),
inference(forward_demodulation,[status(thm)],[f30,f73]) ).
fof(f97,plain,
! [X0] : add(sF0_fnc,multiply(X0,sF1_fnc)) = add(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f15,f80]) ).
fof(f273,plain,
add(x,additive_identity) = add(x,sF0_fnc),
inference(paramodulation,[status(thm)],[f61,f93]) ).
fof(f282,plain,
x = add(x,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f14,f273]) ).
fof(f315,plain,
add(sF0_fnc,additive_identity) = add(sF0_fnc,x),
inference(paramodulation,[status(thm)],[f62,f97]) ).
fof(f327,plain,
sF0_fnc = add(sF0_fnc,x),
inference(forward_demodulation,[status(thm)],[f14,f315]) ).
fof(f332,plain,
sF0_fnc = add(x,sF0_fnc),
inference(paramodulation,[status(thm)],[f10,f327]) ).
fof(f338,plain,
sF0_fnc = x,
inference(forward_demodulation,[status(thm)],[f282,f332]) ).
fof(f339,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f338,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 13:43:13 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.029078 seconds
% 0.11/0.40 % CPU time: 0.051524 seconds
% 0.11/0.40 % Total memory used: 1.909 MB
% 0.11/0.40 % Net memory used: 1.866 MB
%------------------------------------------------------------------------------