%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:32:22 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.58s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 23 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 123 ( 52 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subgroup_member(B)
| ~ subgroup_member(A)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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(f15,axiom,
! [A,B,C,D] :
( equalish(D,B)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [B] :
( subgroup_member(B)
| ! [A] :
( ~ subgroup_member(A)
| ~ equalish(A,B) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f31,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f33,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f37,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f38,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)],[f11]) ).
fof(f39,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)],[f38]) ).
fof(f45,plain,
! [B,D] :
( equalish(D,B)
| ! [A,C] :
( ~ product(A,D,C)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f50,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| product(A,element_in_O2(A,B),B) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f52,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
product(a,c,d),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
subgroup_member(inverse(b)),
inference(resolution,[status(thm)],[f31,f53]) ).
fof(f63,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f33,f54]) ).
fof(f64,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[f33,f55]) ).
fof(f67,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f53]) ).
fof(f68,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f56]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f39,f36]) ).
fof(f116,plain,
! [X0] :
( product(inverse(b),c,X0)
| ~ product(identity,inverse(a),X0) ),
inference(resolution,[status(thm)],[f75,f54]) ).
fof(f154,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(inverse(X0),X1,identity) ),
inference(resolution,[status(thm)],[f46,f36]) ).
fof(f156,plain,
! [X0] :
( equalish(X0,c)
| ~ product(a,X0,d) ),
inference(resolution,[status(thm)],[f46,f55]) ).
fof(f179,plain,
( subgroup_member(a)
| subgroup_member(d)
| equalish(element_in_O2(a,d),c) ),
inference(resolution,[status(thm)],[f156,f52]) ).
fof(f180,plain,
( subgroup_member(a)
| equalish(element_in_O2(a,d),c) ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f56]) ).
fof(f190,plain,
! [X0] : equalish(inverse(inverse(X0)),X0),
inference(resolution,[status(thm)],[f154,f37]) ).
fof(f194,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(inverse(X0))) ),
inference(resolution,[status(thm)],[f190,f24]) ).
fof(f334,plain,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(a,d))
| subgroup_member(a) ),
inference(resolution,[status(thm)],[f180,f24]) ).
fof(f617,plain,
product(inverse(b),c,inverse(a)),
inference(resolution,[status(thm)],[f116,f34]) ).
fof(f630,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(c)
| ~ subgroup_member(inverse(b)) ),
inference(resolution,[status(thm)],[f617,f33]) ).
fof(f631,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(c) ),
inference(forward_subsumption_resolution,[status(thm)],[f630,f57]) ).
fof(f2393,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[f334,f50]) ).
fof(f2394,plain,
( subgroup_member(d)
| subgroup_member(c)
| subgroup_member(a) ),
inference(duplicate_literals_removal,[status(thm)],[f2393]) ).
fof(f2395,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[f2394,f56]) ).
fof(f2397,plain,
( subgroup_member(inverse(a))
| subgroup_member(a) ),
inference(resolution,[status(thm)],[f2395,f631]) ).
fof(f2401,plain,
subgroup_member(inverse(a)),
inference(forward_subsumption_resolution,[status(thm)],[f2397,f31]) ).
fof(f2402,plain,
subgroup_member(c),
inference(backward_subsumption_resolution,[status(thm)],[f67,f2401]) ).
fof(f2404,plain,
subgroup_member(inverse(inverse(a))),
inference(resolution,[status(thm)],[f2401,f31]) ).
fof(f2406,plain,
~ subgroup_member(a),
inference(backward_subsumption_resolution,[status(thm)],[f68,f2402]) ).
fof(f2416,plain,
subgroup_member(a),
inference(resolution,[status(thm)],[f2404,f194]) ).
fof(f2419,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2416,f2406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:58:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.15/0.58 % Refutation found
% 0.15/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.36/0.60 % Elapsed time: 0.228988 seconds
% 1.36/0.60 % CPU time: 1.647738 seconds
% 1.36/0.60 % Total memory used: 30.760 MB
% 1.36/0.60 % Net memory used: 27.136 MB
%------------------------------------------------------------------------------