%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO010-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:06:20 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.54s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 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,negated_conjecture,
add(a,multiply(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(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(f22,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f30,plain,
add(a,multiply(a,b)) != a,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X2,X1)),
inference(paramodulation,[status(thm)],[f16,f18]) ).
fof(f114,plain,
! [X0,X1] : multiply(X0,add(X1,multiplicative_identity)) = add(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f21]) ).
fof(f142,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(paramodulation,[status(thm)],[f22,f19]) ).
fof(f148,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f26,f142]) ).
fof(f243,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f27,f148]) ).
fof(f262,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),X0),
inference(backward_demodulation,[status(thm)],[f264,f114]) ).
fof(f264,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f22,f243]) ).
fof(f274,plain,
! [X0,X1] : X0 = add(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f26,f262]) ).
fof(f323,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f56]) ).
fof(f356,plain,
a != a,
inference(backward_demodulation,[status(thm)],[f358,f30]) ).
fof(f358,plain,
! [X0,X1] : X0 = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f274,f323]) ).
fof(f371,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 13:52:08 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.31/0.54 % Refutation found
% 0.31/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.31/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.75/0.57 % Elapsed time: 0.116096 seconds
% 0.75/0.57 % CPU time: 0.531394 seconds
% 0.75/0.57 % Total memory used: 14.312 MB
% 0.75/0.57 % Net memory used: 14.102 MB
%------------------------------------------------------------------------------