%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:06:35 PM UTC 2026
% Result : Unsatisfiable 25.74s 3.68s
% Output : CNFRefutation 22.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 84 unt; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 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 : 221 ( 221 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : add(X,multiply(Y,multiply(X,Z))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : multiply(add(X,Y),add(X,inverse(Y))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : multiply(X,add(Y,add(X,Z))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : add(multiply(X,Y),multiply(X,inverse(Y))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : add(add(X,Y),Z) = add(X,add(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0,X1,X2] : add(X0,multiply(X1,multiply(X0,X2))) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0,X1,X2] : add(add(multiply(X0,X1),multiply(X1,X2)),X1) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1] : multiply(add(X0,X1),add(X0,inverse(X1))) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(X0,add(X1,add(X0,X2))) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(multiply(add(X0,X1),add(X1,X2)),X1) = X1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f22,plain,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0,X1,X2] : add(multiply(X0,X1),add(multiply(X1,X2),X1)) = X1,
inference(backward_demodulation,[status(thm)],[f20,f13]) ).
fof(f30,plain,
! [X0,X1,X2] : multiply(add(X0,X1),multiply(add(X1,X2),X1)) = X1,
inference(backward_demodulation,[status(thm)],[f21,f16]) ).
fof(f34,plain,
! [X0,X1,X2] : add(add(X0,X1),multiply(X2,X0)) = add(X0,X1),
inference(paramodulation,[status(thm)],[f14,f12]) ).
fof(f35,plain,
! [X0,X1,X2] : add(X0,add(X1,multiply(X2,X0))) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f20,f34]) ).
fof(f36,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),add(X2,X0)) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f37,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f12,f15]) ).
fof(f39,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f40,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,add(X2,X0))) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f21,f36]) ).
fof(f51,plain,
! [X0,X1,X2,X3] : add(X0,X1) = add(X0,add(X1,multiply(X2,multiply(add(X0,X1),X3)))),
inference(paramodulation,[status(thm)],[f12,f20]) ).
fof(f54,plain,
! [X0,X1,X2] : add(X0,X1) = add(multiply(X0,X2),add(multiply(X0,inverse(X2)),X1)),
inference(paramodulation,[status(thm)],[f17,f20]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(add(add(X0,X1),X2),add(X0,add(X1,inverse(X2)))) = add(X0,X1),
inference(paramodulation,[status(thm)],[f20,f14]) ).
fof(f64,plain,
! [X0,X1,X2] : multiply(add(X0,add(X1,X2)),add(X0,add(X1,inverse(X2)))) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f20,f57]) ).
fof(f67,plain,
! [X0,X1,X2] : X0 = add(add(multiply(X0,X1),X0),multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f29,f18]) ).
fof(f81,plain,
! [X0,X1] : multiply(add(X0,X1),add(X1,inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f18,f14]) ).
fof(f90,plain,
! [X0,X1,X2] : X0 = add(multiply(X0,X1),add(X0,multiply(X2,X0))),
inference(forward_demodulation,[status(thm)],[f20,f67]) ).
fof(f91,plain,
! [X0,X1] : add(multiply(X0,X1),X1) = X1,
inference(backward_demodulation,[status(thm)],[f96,f29]) ).
fof(f96,plain,
! [X0,X1] : X0 = add(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f39,f90]) ).
fof(f125,plain,
! [X0,X1,X2] : add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,inverse(X2)))) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f21,f17]) ).
fof(f142,plain,
! [X0,X1,X2] : add(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,inverse(X2)))) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f21,f125]) ).
fof(f147,plain,
! [X0,X1,X2,X3] : multiply(add(X0,add(X1,X2)),multiply(add(X2,X3),X2)) = X2,
inference(paramodulation,[status(thm)],[f20,f30]) ).
fof(f168,plain,
! [X0,X1,X2] : X0 = multiply(multiply(add(X0,X1),X0),add(X2,X0)),
inference(paramodulation,[status(thm)],[f30,f19]) ).
fof(f176,plain,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(a,c)),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f199,plain,
! [X0,X1,X2] : X0 = multiply(add(X0,X1),multiply(X0,add(X2,X0))),
inference(forward_demodulation,[status(thm)],[f21,f168]) ).
fof(f200,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(backward_demodulation,[status(thm)],[f208,f30]) ).
fof(f207,plain,
! [X0,X1,X2] : multiply(add(X0,add(X1,X2)),X2) = X2,
inference(backward_demodulation,[status(thm)],[f208,f147]) ).
fof(f208,plain,
! [X0,X1] : X0 = multiply(add(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f37,f199]) ).
fof(f250,plain,
! [X0,X1,X2] : add(X0,X1) = add(X0,add(multiply(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f39,f20]) ).
fof(f308,plain,
! [X0] : multiply(X0,X0) = X0,
inference(paramodulation,[status(thm)],[f91,f37]) ).
fof(f417,plain,
! [X0,X1,X2] : add(multiply(X0,add(X1,X2)),multiply(X2,X0)) = multiply(X0,add(X1,X2)),
inference(paramodulation,[status(thm)],[f40,f39]) ).
fof(f475,plain,
! [X0,X1,X2] : multiply(add(add(X0,X1),X2),add(X2,add(X0,inverse(X1)))) = add(X2,X0),
inference(paramodulation,[status(thm)],[f18,f64]) ).
fof(f505,plain,
! [X0,X1,X2] : multiply(add(X0,add(X1,X2)),add(X2,add(X0,inverse(X1)))) = add(X2,X0),
inference(forward_demodulation,[status(thm)],[f20,f475]) ).
fof(f542,plain,
! [X0,X1] : add(X0,inverse(X1)) = add(multiply(X0,X1),inverse(X1)),
inference(paramodulation,[status(thm)],[f91,f54]) ).
fof(f780,plain,
! [X0,X1,X2,X3] : multiply(add(X0,X1),add(add(X1,multiply(X2,multiply(add(X0,X1),X3))),inverse(X0))) = add(X1,multiply(X2,multiply(add(X0,X1),X3))),
inference(paramodulation,[status(thm)],[f51,f81]) ).
fof(f781,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(add(X1,multiply(X2,X0)),inverse(X0))) = add(X1,multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f35,f81]) ).
fof(f806,plain,
! [X0,X1,X2,X3] : multiply(add(X0,X1),add(X1,add(multiply(X2,multiply(add(X0,X1),X3)),inverse(X0)))) = add(X1,multiply(X2,multiply(add(X0,X1),X3))),
inference(forward_demodulation,[status(thm)],[f20,f780]) ).
fof(f807,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(X1,add(multiply(X2,X0),inverse(X0)))) = add(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f20,f781]) ).
fof(f808,plain,
! [X0,X1,X2,X3] : add(X0,multiply(multiply(X1,multiply(add(X2,X0),X3)),X2)) = add(X0,multiply(X1,multiply(add(X2,X0),X3))),
inference(backward_demodulation,[status(thm)],[f809,f806]) ).
fof(f809,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(X1,add(X2,inverse(X0)))) = add(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f542,f807]) ).
fof(f824,plain,
! [X0,X1,X2,X3] : add(X0,multiply(X1,multiply(multiply(add(X2,X0),X3),X2))) = add(X0,multiply(X1,multiply(add(X2,X0),X3))),
inference(forward_demodulation,[status(thm)],[f21,f808]) ).
fof(f825,plain,
! [X0,X1,X2,X3] : add(X0,multiply(X1,multiply(add(X2,X0),multiply(X3,X2)))) = add(X0,multiply(X1,multiply(add(X2,X0),X3))),
inference(forward_demodulation,[status(thm)],[f21,f824]) ).
fof(f1410,plain,
! [X0,X1,X2] : add(multiply(X0,X1),multiply(add(X2,multiply(X0,X1)),multiply(X0,inverse(X1)))) = multiply(add(X2,multiply(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f200,f142]) ).
fof(f2163,plain,
multiply(a,add(b,c)) != add(multiply(a,b),multiply(a,c)),
inference(paramodulation,[status(thm)],[f19,f176]) ).
fof(f3357,plain,
! [X0,X1,X2] : multiply(add(X0,X1),multiply(X2,X0)) = multiply(X2,X0),
inference(paramodulation,[status(thm)],[f35,f207]) ).
fof(f3432,plain,
! [X0,X1,X2,X3] : add(X0,multiply(X1,multiply(X2,X3))) = add(X0,multiply(X1,multiply(add(X3,X0),X2))),
inference(backward_demodulation,[status(thm)],[f3357,f825]) ).
fof(f7756,plain,
! [X0,X1,X2] : add(multiply(X0,X1),multiply(X2,multiply(X0,inverse(X1)))) = add(multiply(X0,X1),multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f142,f250]) ).
fof(f7892,plain,
! [X0,X1,X2] : add(multiply(X0,X1),multiply(add(X2,multiply(X0,X1)),X0)) = multiply(add(X2,multiply(X0,X1)),X0),
inference(backward_demodulation,[status(thm)],[f7756,f1410]) ).
fof(f9157,plain,
! [X0,X1,X2] : add(multiply(X0,add(X1,X2)),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(paramodulation,[status(thm)],[f19,f417]) ).
fof(f10524,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(X1,add(multiply(add(X0,X1),X2),inverse(X0)))) = add(X1,multiply(add(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f96,f505]) ).
fof(f10525,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(X1,add(multiply(X2,add(X0,X1)),inverse(X0)))) = add(X1,multiply(X2,add(X0,X1))),
inference(paramodulation,[status(thm)],[f91,f505]) ).
fof(f10668,plain,
! [X0,X1,X2] : add(X0,multiply(multiply(add(X1,X0),X2),X1)) = add(X0,multiply(add(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f809,f10524]) ).
fof(f10669,plain,
! [X0,X1,X2] : add(X0,multiply(add(X1,X0),multiply(X2,X1))) = add(X0,multiply(add(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f21,f10668]) ).
fof(f10672,plain,
! [X0,X1,X2] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(add(X2,multiply(X0,X1)),X0),
inference(backward_demodulation,[status(thm)],[f10685,f7892]) ).
fof(f10685,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = add(X0,multiply(add(X2,X0),X1)),
inference(forward_demodulation,[status(thm)],[f3357,f10669]) ).
fof(f10686,plain,
! [X0,X1,X2] : add(X0,multiply(multiply(X1,add(X2,X0)),X2)) = add(X0,multiply(X1,add(X2,X0))),
inference(forward_demodulation,[status(thm)],[f809,f10525]) ).
fof(f10687,plain,
! [X0,X1,X2] : add(X0,multiply(X1,multiply(add(X2,X0),X2))) = add(X0,multiply(X1,add(X2,X0))),
inference(forward_demodulation,[status(thm)],[f21,f10686]) ).
fof(f10688,plain,
! [X0,X1,X2] : add(X0,multiply(X1,multiply(X2,X2))) = add(X0,multiply(X1,add(X2,X0))),
inference(forward_demodulation,[status(thm)],[f3432,f10687]) ).
fof(f10696,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = add(X0,multiply(X1,add(X2,X0))),
inference(forward_demodulation,[status(thm)],[f308,f10688]) ).
fof(f10927,plain,
multiply(a,add(b,c)) != multiply(add(c,multiply(a,b)),a),
inference(backward_demodulation,[status(thm)],[f10672,f2163]) ).
fof(f10993,plain,
! [X0,X1,X2] : multiply(add(X0,multiply(X1,add(X2,X0))),X1) = multiply(X1,add(X2,X0)),
inference(backward_demodulation,[status(thm)],[f10672,f9157]) ).
fof(f11239,plain,
multiply(a,add(b,c)) != multiply(a,add(b,c)),
inference(backward_demodulation,[status(thm)],[f11291,f10927]) ).
fof(f11291,plain,
! [X0,X1,X2] : multiply(add(X0,multiply(X1,X2)),X1) = multiply(X1,add(X2,X0)),
inference(forward_demodulation,[status(thm)],[f10696,f10993]) ).
fof(f11446,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f11239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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 13:51:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 25.74/3.68 % Refutation found
% 25.74/3.68 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 25.74/3.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 22.74/3.75 % Elapsed time: 3.370622 seconds
% 22.74/3.75 % CPU time: 26.437763 seconds
% 22.74/3.75 % Total memory used: 254.924 MB
% 22.74/3.75 % Net memory used: 246.457 MB
%------------------------------------------------------------------------------