%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:32:20 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 27 unt; 0 def)
% Number of atoms : 84 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f26,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
~ subgroup_member(c),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
! [X0] :
( c = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f20,f29]) ).
fof(f35,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f38,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f33,f18]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f22,f16]) ).
fof(f89,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[f26,f14]) ).
fof(f90,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f26,f17]) ).
fof(f91,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f26,f18]) ).
fof(f93,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f90]) ).
fof(f94,plain,
subgroup_member(identity),
inference(resolution,[status(thm)],[f93,f28]) ).
fof(f102,plain,
! [X0,X1] :
( product(inverse(inverse(X0)),identity,X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f44,f16]) ).
fof(f185,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f94]) ).
fof(f187,plain,
subgroup_member(inverse(b)),
inference(resolution,[status(thm)],[f185,f28]) ).
fof(f324,plain,
! [X0] :
( subgroup_member(multiply(a,inverse(X0)))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f91,f27]) ).
fof(f351,plain,
subgroup_member(multiply(a,inverse(inverse(b)))),
inference(resolution,[status(thm)],[f324,f187]) ).
fof(f573,plain,
! [X0] : product(inverse(inverse(X0)),identity,X0),
inference(resolution,[status(thm)],[f102,f14]) ).
fof(f711,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[f573,f35]) ).
fof(f732,plain,
subgroup_member(multiply(a,b)),
inference(backward_demodulation,[status(thm)],[f711,f351]) ).
fof(f751,plain,
subgroup_member(c),
inference(forward_demodulation,[status(thm)],[f38,f732]) ).
fof(f752,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f751,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 : Sun Sep 20 19:57:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.046029 seconds
% 0.09/0.42 % CPU time: 0.155377 seconds
% 0.09/0.42 % Total memory used: 28.735 MB
% 0.09/0.42 % Net memory used: 28.366 MB
%------------------------------------------------------------------------------