%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.14s 1.10s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 101 ( 101 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 204 ( 204 !; 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(f5,axiom,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,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(f9,axiom,
! [X] : multiply(X,inverse(X)) = additive_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(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,
add(a,add(b,c)) != add(add(a,b),c),
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(f20,plain,
! [X0,X1,X2] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f9]) ).
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(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,
add(a,add(b,c)) != add(add(a,b),c),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
add(a,add(b,c)) != add(c,add(a,b)),
inference(forward_demodulation,[status(thm)],[f16,f30]) ).
fof(f71,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X1,X2),add(X0,X2)),
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f76,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X2,X0),add(X1,X2)),
inference(paramodulation,[status(thm)],[f16,f18]) ).
fof(f79,plain,
! [X0,X1] : add(multiply(X0,X1),inverse(X1)) = multiply(add(X0,inverse(X1)),multiplicative_identity),
inference(paramodulation,[status(thm)],[f22,f18]) ).
fof(f81,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X2,X1)),
inference(paramodulation,[status(thm)],[f16,f18]) ).
fof(f85,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = add(multiply(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f18,f71]) ).
fof(f92,plain,
! [X0,X1] : add(inverse(X0),multiply(X1,X0)) = multiply(add(X1,inverse(X0)),multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f16,f79]) ).
fof(f93,plain,
! [X0,X1] : add(inverse(X0),multiply(X1,X0)) = add(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f26,f92]) ).
fof(f122,plain,
! [X0] : add(inverse(inverse(X0)),additive_identity) = add(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f24,f93]) ).
fof(f131,plain,
! [X0] : inverse(inverse(X0)) = add(X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f28,f122]) ).
fof(f144,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),X0) = multiply(multiplicative_identity,add(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f76]) ).
fof(f170,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f16,f144]) ).
fof(f171,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f27,f170]) ).
fof(f202,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),X1) = multiply(add(X0,X1),multiplicative_identity),
inference(paramodulation,[status(thm)],[f22,f81]) ).
fof(f232,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X1,X0),multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f16,f202]) ).
fof(f233,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f26,f232]) ).
fof(f261,plain,
! [X0] : add(X0,additive_identity) = add(inverse(inverse(X0)),X0),
inference(paramodulation,[status(thm)],[f24,f171]) ).
fof(f262,plain,
! [X0] : add(X0,inverse(X0)) = add(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f26,f171]) ).
fof(f277,plain,
! [X0] : X0 = add(inverse(inverse(X0)),X0),
inference(forward_demodulation,[status(thm)],[f28,f261]) ).
fof(f278,plain,
! [X0] : X0 = add(X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f16,f277]) ).
fof(f286,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f131,f278]) ).
fof(f290,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(forward_demodulation,[status(thm)],[f22,f262]) ).
fof(f427,plain,
! [X0,X1] : multiply(add(multiplicative_identity,X0),X1) = add(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f20]) ).
fof(f428,plain,
! [X0,X1] : multiply(add(X0,X1),inverse(X0)) = add(additive_identity,multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f24,f20]) ).
fof(f436,plain,
! [X0,X1] : multiply(add(X0,X1),inverse(X1)) = add(multiply(X0,inverse(X1)),additive_identity),
inference(paramodulation,[status(thm)],[f24,f20]) ).
fof(f454,plain,
! [X0,X1] : multiply(multiplicative_identity,X0) = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f290,f427]) ).
fof(f458,plain,
! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f27,f454]) ).
fof(f459,plain,
! [X0,X1] : multiply(inverse(X0),add(X0,X1)) = add(additive_identity,multiply(X1,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f17,f428]) ).
fof(f460,plain,
! [X0,X1] : multiply(inverse(X0),add(X0,X1)) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f29,f459]) ).
fof(f466,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,X0)) = add(multiply(X1,inverse(X0)),additive_identity),
inference(forward_demodulation,[status(thm)],[f17,f436]) ).
fof(f467,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,X0)) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f28,f466]) ).
fof(f484,plain,
! [X0,X1,X2] : add(X0,X1) = add(add(X0,X1),add(multiply(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f76,f458]) ).
fof(f556,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),add(X1,inverse(X0))) = multiply(multiply(X1,X0),inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f93,f460]) ).
fof(f568,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = add(add(X0,X1),X0),
inference(paramodulation,[status(thm)],[f460,f171]) ).
fof(f579,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(multiply(X0,X1),inverse(inverse(X1))),
inference(forward_demodulation,[status(thm)],[f467,f556]) ).
fof(f580,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),inverse(inverse(X1))),
inference(forward_demodulation,[status(thm)],[f286,f579]) ).
fof(f581,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f286,f580]) ).
fof(f582,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f17,f581]) ).
fof(f603,plain,
! [X0,X1] : add(X0,X1) = add(add(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f233,f568]) ).
fof(f604,plain,
! [X0,X1] : add(X0,X1) = add(X1,add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f16,f603]) ).
fof(f617,plain,
! [X0] : multiply(multiplicative_identity,X0) = multiply(X0,X0),
inference(paramodulation,[status(thm)],[f27,f582]) ).
fof(f640,plain,
! [X0] : X0 = multiply(X0,X0),
inference(forward_demodulation,[status(thm)],[f27,f617]) ).
fof(f671,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = add(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f640,f20]) ).
fof(f672,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f640,f20]) ).
fof(f687,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f17,f671]) ).
fof(f688,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f16,f687]) ).
fof(f693,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f458,f688]) ).
fof(f694,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f672]) ).
fof(f695,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f458,f694]) ).
fof(f740,plain,
! [X0,X1,X2] : add(X0,X1) = add(add(X0,X1),add(X0,multiply(X2,X1))),
inference(paramodulation,[status(thm)],[f19,f458]) ).
fof(f981,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,add(X2,X1)),X1),
inference(paramodulation,[status(thm)],[f693,f20]) ).
fof(f1006,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = add(multiply(X0,add(X1,X2)),X2),
inference(forward_demodulation,[status(thm)],[f18,f981]) ).
fof(f1007,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = add(X2,multiply(X0,add(X1,X2))),
inference(forward_demodulation,[status(thm)],[f16,f1006]) ).
fof(f3759,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(add(add(X0,X1),X2),add(X1,X2)),
inference(paramodulation,[status(thm)],[f693,f484]) ).
fof(f3760,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(add(add(X0,X1),X2),add(X0,X2)),
inference(paramodulation,[status(thm)],[f695,f484]) ).
fof(f3872,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(add(X1,X2),add(add(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f16,f3759]) ).
fof(f3873,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(add(X0,X2),add(add(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f16,f3760]) ).
fof(f4781,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,add(X1,X2)),add(X0,X2)),
inference(paramodulation,[status(thm)],[f693,f740]) ).
fof(f4782,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,add(X1,X2)),add(X0,X1)),
inference(paramodulation,[status(thm)],[f695,f740]) ).
fof(f4945,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X2),add(X0,add(X1,X2))),
inference(forward_demodulation,[status(thm)],[f16,f4781]) ).
fof(f4946,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),add(X0,add(X1,X2))),
inference(forward_demodulation,[status(thm)],[f16,f4782]) ).
fof(f5943,plain,
! [X0,X1,X2] : add(multiply(add(X0,X1),X0),X2) = add(X2,add(X0,multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f19,f1007]) ).
fof(f6063,plain,
! [X0,X1,X2] : add(multiply(X0,add(X0,X1)),X2) = add(X2,add(X0,multiply(X1,X2))),
inference(forward_demodulation,[status(thm)],[f85,f5943]) ).
fof(f6067,plain,
! [X0,X1,X2] : add(X0,X1) = add(X1,add(X0,multiply(X2,X1))),
inference(forward_demodulation,[status(thm)],[f695,f6063]) ).
fof(f6255,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X1,X2),add(X0,X2)),
inference(paramodulation,[status(thm)],[f693,f6067]) ).
fof(f6352,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(add(X0,X1),add(X0,X2)),
inference(backward_demodulation,[status(thm)],[f6255,f3873]) ).
fof(f6353,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(add(X0,X1),add(X1,X2)),
inference(backward_demodulation,[status(thm)],[f6255,f3872]) ).
fof(f6487,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),add(X1,X2)),
inference(backward_demodulation,[status(thm)],[f6352,f4946]) ).
fof(f6488,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X2),add(X1,X2)),
inference(backward_demodulation,[status(thm)],[f6352,f4945]) ).
fof(f6671,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X1,add(X1,X2))),
inference(backward_demodulation,[status(thm)],[f6722,f6353]) ).
fof(f6722,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f6353,f6487]) ).
fof(f6724,plain,
add(a,add(b,c)) != add(a,add(c,b)),
inference(backward_demodulation,[status(thm)],[f6744,f38]) ).
fof(f6744,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(forward_demodulation,[status(thm)],[f6255,f6488]) ).
fof(f7024,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X1,add(X1,X2))),
inference(forward_demodulation,[status(thm)],[f6722,f6671]) ).
fof(f7025,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
inference(forward_demodulation,[status(thm)],[f604,f7024]) ).
fof(f7078,plain,
add(a,add(b,c)) != add(a,add(b,c)),
inference(forward_demodulation,[status(thm)],[f7025,f6724]) ).
fof(f7079,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f7078]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.59 % Computer : n014.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Mon Sep 21 13:46:35 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.60 % Drodi V4.1.1
% 0.14/1.10 % Refutation found
% 0.14/1.10 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.70/2.32 % Elapsed time: 1.511177 seconds
% 9.70/2.32 % CPU time: 3.647021 seconds
% 9.70/2.32 % Total memory used: 50.460 MB
% 9.70/2.32 % Net memory used: 49.144 MB
%------------------------------------------------------------------------------