%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 1.03s 0.71s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 23 unt; 0 def)
% Number of atoms : 118 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 69 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 157 ( 157 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ product(x,add(x,y),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f40,plain,
! [V1,V2,V4] :
( product(V1,V2,V4)
| ! [X,V3] :
( ~ sum(X,V3,V4)
| ! [Y,Z] :
( ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f51,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f52,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
~ product(x,add(x,y),x),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f57,plain,
~ product(add(x,y),x,x),
inference(resolution,[status(thm)],[f27,f56]) ).
fof(f60,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f53,f28]) ).
fof(f63,plain,
! [X0,X1,X2] :
( X2 = add(X0,X1)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f53,f24]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X2,X5,X0)
| ~ sum(X3,X4,X5)
| ~ product(X2,X4,X1)
| ~ product(X2,X3,additive_identity)
| X0 = X1 ),
inference(resolution,[status(thm)],[f60,f33]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[f63,f26]) ).
fof(f125,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f120,f24]) ).
fof(f140,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(paramodulation,[status(thm)],[f125,f24]) ).
fof(f163,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f55,f25]) ).
fof(f196,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( X7 = X6
| ~ product(X2,X4,X7)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f41,f55]) ).
fof(f233,plain,
! [X0,X1,X2] :
( ~ product(X2,X1,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[f163,f27]) ).
fof(f245,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f233,f25]) ).
fof(f261,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f245,f25]) ).
fof(f310,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X2,X4,X0)
| ~ sum(inverse(X2),X3,X4)
| ~ product(X2,X3,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f70,f51]) ).
fof(f319,plain,
! [X0,X1,X2] :
( ~ product(X2,inverse(X2),X0)
| ~ product(X2,additive_identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f310,f29]) ).
fof(f400,plain,
! [X0,X1] :
( ~ product(X1,inverse(X1),X0)
| X0 = multiply(additive_identity,X1) ),
inference(resolution,[status(thm)],[f319,f261]) ).
fof(f414,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f400,f51]) ).
fof(f439,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f414,f261]) ).
fof(f755,plain,
! [X0,X1,X2,X3] :
( X3 = X0
| ~ product(X2,X0,X3)
| ~ product(X1,additive_identity,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f196,f29]) ).
fof(f782,plain,
! [X0,X1,X2,X3] :
( X3 = X0
| ~ product(X2,X0,X3)
| ~ sum(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f755,f439]) ).
fof(f806,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(add(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f782,f140]) ).
fof(f815,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(resolution,[status(thm)],[f806,f261]) ).
fof(f895,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f125,f815]) ).
fof(f914,plain,
! [X0,X1] : product(add(X0,X1),X0,X0),
inference(paramodulation,[status(thm)],[f895,f261]) ).
fof(f1000,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f57,f914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:47:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.03/0.71 % Refutation found
% 1.03/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.03/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.28/0.74 % Elapsed time: 0.365728 seconds
% 2.28/0.74 % CPU time: 2.536768 seconds
% 2.28/0.74 % Total memory used: 60.478 MB
% 2.28/0.74 % Net memory used: 56.682 MB
%------------------------------------------------------------------------------