%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:06:24 PM UTC 2026
% Result : Unsatisfiable 3.16s 0.81s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 62 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 153 ( 153 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : multiply(add(X,Y),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : add(multiply(X,Y),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : multiply(X,inverse(X)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : add(multiply(X0,X1),X1) = X1,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X2,X0)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0] : multiply(X0,inverse(X0)) = n0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0] : add(X0,X0) = X0,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f22,plain,
! [X0] : multiply(X0,X0) = X0,
inference(paramodulation,[status(thm)],[f11,f8]) ).
fof(f25,plain,
! [X0,X1,X2] : multiply(multiply(X0,add(X1,X2)),multiply(X2,X0)) = multiply(X2,X0),
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f27,plain,
! [X0,X1] : multiply(X0,add(X1,X1)) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f9,f21]) ).
fof(f30,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f21,f27]) ).
fof(f32,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X1,X0),X0),
inference(paramodulation,[status(thm)],[f22,f9]) ).
fof(f35,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f11,f32]) ).
fof(f42,plain,
! [X0] : n0 = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f13,f30]) ).
fof(f53,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f30,f9]) ).
fof(f54,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = X0,
inference(paramodulation,[status(thm)],[f30,f11]) ).
fof(f79,plain,
! [X0] : add(n0,X0) = X0,
inference(paramodulation,[status(thm)],[f42,f11]) ).
fof(f90,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X2,X0),add(X1,X0)),
inference(paramodulation,[status(thm)],[f30,f12]) ).
fof(f92,plain,
! [X0,X1] : add(X0,multiply(X1,X1)) = add(X1,X0),
inference(paramodulation,[status(thm)],[f22,f12]) ).
fof(f94,plain,
! [X0,X1,X2,X3] : add(multiply(X0,X1),multiply(multiply(X2,X1),X3)) = multiply(multiply(X1,add(X2,X0)),add(X3,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f95,plain,
! [X0,X1,X2] : add(X0,multiply(multiply(X1,X0),X2)) = multiply(X0,add(X2,X0)),
inference(paramodulation,[status(thm)],[f11,f12]) ).
fof(f97,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f12]) ).
fof(f99,plain,
! [X0,X1,X2,X3] : add(multiply(X0,X1),multiply(X2,multiply(X3,X1))) = multiply(add(X2,multiply(X0,X1)),multiply(X1,add(X3,X0))),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f109,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = add(X0,multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f12,f90]) ).
fof(f111,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f92]) ).
fof(f113,plain,
! [X0,X1,X2] : add(X0,multiply(multiply(X1,X0),X2)) = X0,
inference(forward_demodulation,[status(thm)],[f35,f95]) ).
fof(f114,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f35,f97]) ).
fof(f155,plain,
! [X0] : X0 = add(X0,n0),
inference(paramodulation,[status(thm)],[f79,f111]) ).
fof(f158,plain,
! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f11,f111]) ).
fof(f198,plain,
! [X0] : multiply(n0,X0) = n0,
inference(paramodulation,[status(thm)],[f54,f155]) ).
fof(f486,plain,
! [X0,X1] : multiply(multiply(X0,X1),multiply(X1,X0)) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f79,f25]) ).
fof(f845,plain,
! [X0,X1,X2] : add(multiply(n0,X0),multiply(multiply(X1,X0),X2)) = multiply(multiply(X0,X1),add(X2,multiply(n0,X0))),
inference(paramodulation,[status(thm)],[f155,f94]) ).
fof(f857,plain,
! [X0,X1,X2] : add(multiply(X0,X1),multiply(multiply(X2,X1),X0)) = multiply(multiply(X1,add(X2,X0)),X0),
inference(paramodulation,[status(thm)],[f114,f94]) ).
fof(f947,plain,
! [X0,X1,X2] : add(n0,multiply(multiply(X0,X1),X2)) = multiply(multiply(X1,X0),add(X2,multiply(n0,X1))),
inference(forward_demodulation,[status(thm)],[f198,f845]) ).
fof(f948,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X1,X0),add(X2,multiply(n0,X1))),
inference(forward_demodulation,[status(thm)],[f79,f947]) ).
fof(f949,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X1,X0),add(X2,n0)),
inference(forward_demodulation,[status(thm)],[f198,f948]) ).
fof(f950,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f155,f949]) ).
fof(f965,plain,
! [X0,X1,X2] : multiply(X0,add(X1,multiply(X2,X1))) = multiply(multiply(X1,add(X2,X0)),X0),
inference(forward_demodulation,[status(thm)],[f53,f857]) ).
fof(f967,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(X1,add(X2,X0)),X0),
inference(forward_demodulation,[status(thm)],[f158,f965]) ).
fof(f1440,plain,
! [X0,X1,X2,X3] : add(multiply(multiply(X0,X1),X2),multiply(X3,X1)) = multiply(add(X3,multiply(multiply(X0,X1),X2)),X1),
inference(paramodulation,[status(thm)],[f113,f12]) ).
fof(f1471,plain,
! [X0,X1,X2] : add(multiply(X0,X1),multiply(X0,multiply(X2,X1))) = multiply(X0,multiply(X1,add(X2,X0))),
inference(paramodulation,[status(thm)],[f114,f99]) ).
fof(f1850,plain,
! [X0,X1,X2,X3] : add(multiply(X0,X1),multiply(X2,X3)) = multiply(add(X2,multiply(X0,X1)),add(X3,multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f109,f12]) ).
fof(f2106,plain,
! [X0,X1,X2,X3] : multiply(add(multiply(X0,X1),multiply(multiply(X2,X1),X3)),multiply(add(X3,multiply(X0,X1)),multiply(X1,add(X2,X0)))) = multiply(add(X3,multiply(X0,X1)),multiply(X1,add(X2,X0))),
inference(paramodulation,[status(thm)],[f94,f486]) ).
fof(f2188,plain,
! [X0,X1,X2,X3] : multiply(add(multiply(X0,X1),multiply(multiply(X2,X1),X3)),add(multiply(X0,X1),multiply(X3,multiply(X2,X1)))) = multiply(add(X3,multiply(X0,X1)),multiply(X1,add(X2,X0))),
inference(forward_demodulation,[status(thm)],[f99,f2106]) ).
fof(f2189,plain,
! [X0,X1,X2,X3] : add(multiply(multiply(X0,X1),X2),multiply(multiply(X3,X1),multiply(X3,X1))) = multiply(add(X2,multiply(X3,X1)),multiply(X1,add(X0,X3))),
inference(forward_demodulation,[status(thm)],[f1850,f2188]) ).
fof(f2190,plain,
! [X0,X1,X2,X3] : add(multiply(multiply(X0,X1),X2),multiply(X3,X1)) = multiply(add(X2,multiply(X3,X1)),multiply(X1,add(X0,X3))),
inference(forward_demodulation,[status(thm)],[f22,f2189]) ).
fof(f2191,plain,
! [X0,X1,X2,X3] : multiply(add(X0,multiply(multiply(X1,X2),X3)),X2) = multiply(add(X3,multiply(X0,X2)),multiply(X2,add(X1,X0))),
inference(forward_demodulation,[status(thm)],[f1440,f2190]) ).
fof(f2222,plain,
! [X0,X1,X2] : multiply(add(X0,multiply(multiply(X1,X2),X0)),X2) = multiply(X0,multiply(X2,add(X1,X0))),
inference(backward_demodulation,[status(thm)],[f2223,f1471]) ).
fof(f2223,plain,
! [X0,X1,X2,X3] : multiply(add(X0,multiply(multiply(X1,X2),X3)),X2) = add(multiply(X0,X2),multiply(X3,multiply(X1,X2))),
inference(forward_demodulation,[status(thm)],[f99,f2191]) ).
fof(f2332,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X0,multiply(X1,add(X2,X0))),
inference(forward_demodulation,[status(thm)],[f158,f2222]) ).
fof(f2354,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X2,X1),X0),
inference(paramodulation,[status(thm)],[f30,f950]) ).
fof(f2609,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X2,X1),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f158,f967]) ).
fof(f3227,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X1),multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f158,f2332]) ).
fof(f3291,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X2,X1),X0),
inference(forward_demodulation,[status(thm)],[f2609,f3227]) ).
fof(f3438,plain,
multiply(multiply(a,b),c) != multiply(multiply(c,b),a),
inference(paramodulation,[status(thm)],[f2354,f14]) ).
fof(f3574,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3438,f3291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n003.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 13:50:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 3.16/0.81 % Refutation found
% 3.16/0.81 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.16/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.34/14.06 % Elapsed time: 13.712981 seconds
% 26.34/14.06 % CPU time: 75.922633 seconds
% 26.34/14.06 % Total memory used: 48.957 GB
% 26.34/14.06 % Net memory used: 48.956 GB
%------------------------------------------------------------------------------