%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:06:19 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 37 unt; 2 def)
% Number of atoms : 37 ( 36 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 : 4 ( 2 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 : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(f19,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
multiply(a,add(a,b)) != a,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f31,definition,
sF1_fnc = add(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f32,definition,
sF0_fnc = multiply(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f33,plain,
sF0_fnc != a,
inference(definition_folding,[],[f30,f32,f31]) ).
fof(f42,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X1,X2),add(X0,X2)),
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f52,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = add(multiply(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f18,f42]) ).
fof(f58,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = add(multiply(X2,X1),X0),
inference(paramodulation,[status(thm)],[f16,f52]) ).
fof(f91,plain,
! [X0] : add(X0,sF0_fnc) = add(multiply(sF1_fnc,a),X0),
inference(paramodulation,[status(thm)],[f32,f58]) ).
fof(f124,plain,
! [X0] : add(a,multiply(b,X0)) = multiply(sF1_fnc,add(a,X0)),
inference(paramodulation,[status(thm)],[f31,f19]) ).
fof(f311,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(paramodulation,[status(thm)],[f24,f21]) ).
fof(f317,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f28,f311]) ).
fof(f329,plain,
add(additive_identity,sF0_fnc) = multiply(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f28,f91]) ).
fof(f351,plain,
sF0_fnc = multiply(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f29,f329]) ).
fof(f728,plain,
add(a,multiply(b,additive_identity)) = multiply(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f28,f124]) ).
fof(f744,plain,
add(a,multiply(b,additive_identity)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f351,f728]) ).
fof(f1399,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f29,f317]) ).
fof(f1431,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f24,f1399]) ).
fof(f1480,plain,
add(a,additive_identity) = sF0_fnc,
inference(backward_demodulation,[status(thm)],[f1431,f744]) ).
fof(f1503,plain,
a = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f28,f1480]) ).
fof(f1504,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1503,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-2 : 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 : n002.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 13:50:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.060322 seconds
% 0.10/0.45 % CPU time: 0.255301 seconds
% 0.10/0.45 % Total memory used: 8.651 MB
% 0.10/0.45 % Net memory used: 8.499 MB
%------------------------------------------------------------------------------