%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO012-2 : 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 12:06:21 PM UTC 2026
% Result : Unsatisfiable 0.17s 10.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% 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 : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
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] : add(inverse(X),X) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : multiply(inverse(X),X) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : multiply(multiplicative_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0] : add(inverse(X0),X0) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0] : multiply(inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
inverse(inverse(x)) != x,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f31,definition,
sF1_fnc = inverse(x),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f32,definition,
sF0_fnc = inverse(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f33,plain,
sF0_fnc != x,
inference(definition_folding,[],[f30,f32,f31]) ).
fof(f63,plain,
add(sF1_fnc,sF0_fnc) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f32,f22]) ).
fof(f74,plain,
! [X0] : add(multiply(sF1_fnc,X0),sF0_fnc) = multiply(multiplicative_identity,add(X0,sF0_fnc)),
inference(paramodulation,[status(thm)],[f63,f18]) ).
fof(f94,plain,
! [X0] : add(multiply(sF1_fnc,X0),sF0_fnc) = add(X0,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f27,f74]) ).
fof(f110,plain,
add(sF1_fnc,x) = multiplicative_identity,
inference(paramodulation,[status(thm)],[f31,f23]) ).
fof(f131,plain,
multiply(sF0_fnc,sF1_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f32,f25]) ).
fof(f132,plain,
multiply(sF1_fnc,x) = additive_identity,
inference(paramodulation,[status(thm)],[f31,f25]) ).
fof(f138,plain,
! [X0] : add(multiply(X0,sF1_fnc),x) = multiply(add(X0,x),multiplicative_identity),
inference(paramodulation,[status(thm)],[f110,f18]) ).
fof(f142,plain,
! [X0] : add(multiply(X0,sF1_fnc),x) = add(X0,x),
inference(forward_demodulation,[status(thm)],[f26,f138]) ).
fof(f412,plain,
add(additive_identity,sF0_fnc) = add(x,sF0_fnc),
inference(paramodulation,[status(thm)],[f132,f94]) ).
fof(f426,plain,
sF0_fnc = add(x,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f29,f412]) ).
fof(f520,plain,
add(additive_identity,x) = add(sF0_fnc,x),
inference(paramodulation,[status(thm)],[f131,f142]) ).
fof(f532,plain,
x = add(sF0_fnc,x),
inference(forward_demodulation,[status(thm)],[f29,f520]) ).
fof(f539,plain,
x = add(x,sF0_fnc),
inference(paramodulation,[status(thm)],[f16,f532]) ).
fof(f547,plain,
x = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f426,f539]) ).
fof(f548,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f547,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.45 % Computer : n015.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Mon Sep 21 13:51:32 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.46 % Drodi V4.1.1
% 0.17/10.48 % Refutation found
% 0.17/10.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/10.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/10.53 % Elapsed time: 0.071182 seconds
% 0.21/10.53 % CPU time: 0.103584 seconds
% 0.21/10.53 % Total memory used: 3.519 MB
% 0.21/10.53 % Net memory used: 3.472 MB
%------------------------------------------------------------------------------