%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO016-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:06:23 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 36 unt; 1 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 : 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 : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(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(f7,axiom,
! [X] : add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : multiply(multiplicative_identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
multiply(x,y) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
add(x,z) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f27,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
multiply(x,y) = z,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
add(x,z) != x,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF0_fnc = add(x,z),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f34,plain,
sF0_fnc != x,
inference(definition_folding,[],[f32,f33]) ).
fof(f44,plain,
! [X0] : add(multiply(x,X0),z) = multiply(sF0_fnc,add(X0,z)),
inference(paramodulation,[status(thm)],[f33,f19]) ).
fof(f51,plain,
! [X0,X1] : add(X0,multiply(X1,X1)) = add(multiply(X0,X0),X1),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f63,plain,
! [X0,X1] : add(multiply(X0,X0),X1) = add(multiply(X1,X1),X0),
inference(paramodulation,[status(thm)],[f17,f51]) ).
fof(f155,plain,
! [X0] : add(multiply(X0,X0),multiplicative_identity) = add(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f27,f63]) ).
fof(f243,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(paramodulation,[status(thm)],[f23,f20]) ).
fof(f249,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f27,f243]) ).
fof(f459,plain,
! [X0] : multiply(x,add(X0,y)) = add(multiply(x,X0),z),
inference(paramodulation,[status(thm)],[f31,f22]) ).
fof(f463,plain,
! [X0] : multiply(x,add(X0,y)) = multiply(sF0_fnc,add(X0,z)),
inference(forward_demodulation,[status(thm)],[f44,f459]) ).
fof(f764,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f28,f249]) ).
fof(f793,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f23,f764]) ).
fof(f828,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(backward_demodulation,[status(thm)],[f793,f155]) ).
fof(f965,plain,
multiply(x,multiplicative_identity) = multiply(sF0_fnc,add(multiplicative_identity,z)),
inference(paramodulation,[status(thm)],[f828,f463]) ).
fof(f980,plain,
x = multiply(sF0_fnc,add(multiplicative_identity,z)),
inference(forward_demodulation,[status(thm)],[f27,f965]) ).
fof(f981,plain,
x = multiply(sF0_fnc,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f828,f980]) ).
fof(f982,plain,
x = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f27,f981]) ).
fof(f983,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f982,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:48:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.039203 seconds
% 0.10/0.41 % CPU time: 0.170795 seconds
% 0.10/0.41 % Total memory used: 5.646 MB
% 0.10/0.41 % Net memory used: 5.530 MB
%------------------------------------------------------------------------------