%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:32:22 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.54s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 60 ( 29 unt; 0 def)
% Number of atoms : 121 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 47 ~; 61 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,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(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(f11,axiom,
! [A] :
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C,D] :
( D = B
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,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(f16,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
! [A] : inverse(inverse(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f33,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [B,D] :
( D = B
| ! [A,C] :
( ~ product(A,D,C)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f42,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| product(A,element_in_O2(A,B),B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f44,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
~ subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
product(a,c,d),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup_member(inverse(X1))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f50,f34]) ).
fof(f61,plain,
subgroup_member(inverse(b)),
inference(resolution,[status(thm)],[f46,f36]) ).
fof(f79,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(inverse(X1))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f26,f52]) ).
fof(f84,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f24]) ).
fof(f91,plain,
! [X0] :
( subgroup_member(multiply(inverse(b),X0))
| ~ subgroup_member(inverse(X0)) ),
inference(resolution,[status(thm)],[f79,f61]) ).
fof(f162,plain,
! [X0] :
( X0 = c
| ~ product(a,X0,d) ),
inference(resolution,[status(thm)],[f38,f49]) ).
fof(f327,plain,
! [X0] :
( product(inverse(b),c,X0)
| ~ product(identity,inverse(a),X0) ),
inference(resolution,[status(thm)],[f85,f48]) ).
fof(f435,plain,
( subgroup_member(a)
| subgroup_member(d)
| element_in_O2(a,d) = c ),
inference(resolution,[status(thm)],[f162,f44]) ).
fof(f436,plain,
( subgroup_member(a)
| element_in_O2(a,d) = c ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f47]) ).
fof(f692,plain,
element_in_O2(a,d) = c,
inference(forward_subsumption_resolution,[status(thm)],[f436,f45]) ).
fof(f701,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(paramodulation,[status(thm)],[f692,f42]) ).
fof(f709,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference(forward_subsumption_resolution,[status(thm)],[f701,f47]) ).
fof(f710,plain,
subgroup_member(c),
inference(forward_subsumption_resolution,[status(thm)],[f709,f45]) ).
fof(f717,plain,
subgroup_member(inverse(c)),
inference(resolution,[status(thm)],[f710,f36]) ).
fof(f720,plain,
subgroup_member(multiply(inverse(b),c)),
inference(resolution,[status(thm)],[f717,f91]) ).
fof(f769,plain,
subgroup_member(inverse(multiply(inverse(b),c))),
inference(resolution,[status(thm)],[f720,f36]) ).
fof(f1317,plain,
product(inverse(b),c,inverse(a)),
inference(resolution,[status(thm)],[f327,f22]) ).
fof(f1518,plain,
multiply(inverse(b),c) = inverse(a),
inference(resolution,[status(thm)],[f1317,f84]) ).
fof(f1528,plain,
subgroup_member(inverse(inverse(a))),
inference(backward_demodulation,[status(thm)],[f1518,f769]) ).
fof(f1533,plain,
subgroup_member(a),
inference(forward_demodulation,[status(thm)],[f50,f1528]) ).
fof(f1534,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1533,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-4 : 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 : n003.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 19:57:15 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.14/0.54 % Refutation found
% 0.14/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.32/0.57 % Elapsed time: 0.205140 seconds
% 0.32/0.57 % CPU time: 1.383924 seconds
% 0.32/0.57 % Total memory used: 114.998 MB
% 0.32/0.57 % Net memory used: 111.558 MB
%------------------------------------------------------------------------------