%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:06:20 PM UTC 2026
% Result : Unsatisfiable 23.00s 3.37s
% Output : CNFRefutation 23.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 63 ( 29 unt; 0 def)
% Number of atoms : 133 ( 37 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 143 ( 73 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 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 : 171 ( 171 !; 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(f8,axiom,
! [X] : product(X,multiplicative_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(f18,axiom,
! [X] : sum(X,inverse(X),multiplicative_identity),
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,
inverse(inverse(x)) != 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(f31,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
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(f49,plain,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f18]) ).
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,
inverse(inverse(x)) != x,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f53,f28]) ).
fof(f61,plain,
! [X0,X1,X2] :
( X2 = add(X0,X1)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f53,f24]) ).
fof(f68,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)],[f58,f33]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[f61,f26]) ).
fof(f121,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f110,f24]) ).
fof(f136,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(paramodulation,[status(thm)],[f121,f24]) ).
fof(f156,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f55,f31]) ).
fof(f157,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f55,f25]) ).
fof(f179,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(resolution,[status(thm)],[f156,f25]) ).
fof(f222,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X3,X6,X0)
| ~ product(X4,X5,X6)
| ~ sum(X3,X5,X2)
| ~ sum(X3,X4,X1)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[f157,f41]) ).
fof(f225,plain,
! [X0,X1,X2] :
( ~ product(X2,X1,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[f157,f27]) ).
fof(f237,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f225,f25]) ).
fof(f253,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f237,f25]) ).
fof(f300,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)],[f68,f51]) ).
fof(f308,plain,
! [X0,X1,X2] :
( ~ product(X2,multiplicative_identity,X0)
| ~ product(X2,inverse(inverse(X2)),X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f300,f49]) ).
fof(f310,plain,
! [X0,X1,X2,X3] :
( ~ product(X2,add(X3,inverse(X2)),X0)
| ~ product(X2,X3,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f300,f136]) ).
fof(f525,plain,
! [X0,X1] :
( ~ product(X1,multiplicative_identity,X0)
| X0 = multiply(inverse(inverse(X1)),X1) ),
inference(resolution,[status(thm)],[f308,f253]) ).
fof(f536,plain,
! [X0,X1] :
( ~ product(X1,multiplicative_identity,X0)
| X0 = multiply(X1,inverse(inverse(X1))) ),
inference(forward_demodulation,[status(thm)],[f237,f525]) ).
fof(f945,plain,
! [X0] : X0 = multiply(X0,inverse(inverse(X0))),
inference(resolution,[status(thm)],[f536,f31]) ).
fof(f976,plain,
! [X0] : product(inverse(inverse(X0)),X0,X0),
inference(paramodulation,[status(thm)],[f945,f253]) ).
fof(f1089,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| multiply(add(X0,inverse(X1)),X1) = X2 ),
inference(resolution,[status(thm)],[f310,f253]) ).
fof(f1105,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,add(X1,inverse(X0))) = X2 ),
inference(forward_demodulation,[status(thm)],[f237,f1089]) ).
fof(f1120,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = multiply(X1,X0),
inference(resolution,[status(thm)],[f1105,f253]) ).
fof(f2714,plain,
! [X0,X1,X2] :
( ~ product(X2,inverse(X1),inverse(X1))
| ~ sum(X1,X2,X0)
| multiplicative_identity = multiply(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f222,f49]) ).
fof(f2751,plain,
! [X0,X1,X2] :
( ~ product(X2,inverse(X1),inverse(X1))
| ~ sum(X1,X2,X0)
| multiplicative_identity = X0 ),
inference(forward_demodulation,[status(thm)],[f179,f2714]) ).
fof(f5073,plain,
! [X0,X1] :
( ~ sum(X1,inverse(inverse(inverse(X1))),X0)
| multiplicative_identity = X0 ),
inference(resolution,[status(thm)],[f2751,f976]) ).
fof(f6440,plain,
! [X0] : multiplicative_identity = add(inverse(inverse(inverse(X0))),X0),
inference(resolution,[status(thm)],[f5073,f136]) ).
fof(f6451,plain,
! [X0] : multiplicative_identity = add(X0,inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f121,f6440]) ).
fof(f6517,plain,
! [X0] : multiply(inverse(inverse(X0)),multiplicative_identity) = multiply(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f6451,f1120]) ).
fof(f6585,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f179,f6517]) ).
fof(f6586,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f945,f6585]) ).
fof(f6670,plain,
x != x,
inference(backward_demodulation,[status(thm)],[f6586,f56]) ).
fof(f6765,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f6670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:49:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 23.00/3.37 % Refutation found
% 23.00/3.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 23.00/3.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.86/3.41 % Elapsed time: 3.043990 seconds
% 2.86/3.41 % CPU time: 23.681059 seconds
% 2.86/3.41 % Total memory used: 94.845 MB
% 2.86/3.41 % Net memory used: 82.723 MB
%------------------------------------------------------------------------------