%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:32:21 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.56s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 64 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 67 ( 35 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
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(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(f11,hypothesis,
! [A] :
( product(A,another_identity,A)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
! [A] :
( product(A,another_inverse(A),another_identity)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [A,B,C,D] :
( D = B
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f32,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] :
( product(X0,another_identity,X0)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,plain,
! [X0] :
( product(X0,another_inverse(X0),another_identity)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
! [B,D] :
( D = B
| ! [A,C] :
( ~ product(A,D,C)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f44,plain,
inverse(a) != another_inverse(a),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f46,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f32,f23]) ).
fof(f47,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f46]) ).
fof(f49,plain,
subgroup_member(identity),
inference(resolution,[status(thm)],[f47,f42]) ).
fof(f57,plain,
! [X0,X1] :
( X1 = X0
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f66,plain,
( ~ subgroup_member(identity)
| identity = another_identity ),
inference(resolution,[status(thm)],[f57,f34]) ).
fof(f71,plain,
identity = another_identity,
inference(forward_subsumption_resolution,[status(thm)],[f66,f49]) ).
fof(f77,plain,
! [X0] : product(X0,inverse(X0),another_identity),
inference(backward_demodulation,[status(thm)],[f71,f23]) ).
fof(f153,plain,
! [X0,X1] :
( inverse(X0) = X1
| ~ product(X0,X1,another_identity) ),
inference(resolution,[status(thm)],[f39,f77]) ).
fof(f208,plain,
! [X0] :
( ~ subgroup_member(X0)
| inverse(X0) = another_inverse(X0) ),
inference(resolution,[status(thm)],[f153,f35]) ).
fof(f224,plain,
~ subgroup_member(a),
inference(resolution,[status(thm)],[f208,f44]) ).
fof(f226,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f224,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n019.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Sun Sep 20 19:55:21 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.52 % Drodi V4.1.1
% 0.15/0.56 % Refutation found
% 0.15/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.58 % Elapsed time: 0.057929 seconds
% 0.15/0.58 % CPU time: 0.172767 seconds
% 0.15/0.58 % Total memory used: 44.912 MB
% 0.15/0.58 % Net memory used: 44.464 MB
%------------------------------------------------------------------------------