%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:32:16 PM UTC 2026
% Result : Theorem 0.07s 10.82s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 140 ( 44 ~; 39 |; 49 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 159 ( 145 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [E] :
( ( ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( ( product(X,V,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(U,Z,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(U,Z,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(X,V,W) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) )
=> ! [U,V,W,X] :
( ( product(V,U,X)
& product(inverse(U),inverse(V),W) )
=> product(inverse(W),inverse(X),E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [E] :
( ( ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( ( product(X,V,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(U,Z,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(U,Z,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(X,V,W) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) )
=> ! [U,V,W,X] :
( ( product(V,U,X)
& product(inverse(U),inverse(V),W) )
=> product(inverse(W),inverse(X),E) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [E] :
( ? [U,V,W,X] :
( ~ product(inverse(W),inverse(X),E)
& product(V,U,X)
& product(inverse(U),inverse(V),W) )
& ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
& ! [X,Y,Z,U,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [E] :
( ? [W,X] :
( ~ product(inverse(W),inverse(X),E)
& ? [U,V] :
( product(V,U,X)
& product(inverse(U),inverse(V),W) ) )
& ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [Z,U,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) )
& ! [X,V,W] :
( product(X,V,W)
| ! [Z,U] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f5,plain,
( ~ product(inverse(sK2_skl),inverse(sK3_skl),sK0_skl)
& product(sK5_skl,sK4_skl,sK3_skl)
& product(inverse(sK4_skl),inverse(sK5_skl),sK2_skl)
& ! [X] : product(inverse(X),X,sK0_skl)
& ! [X] : product(X,inverse(X),sK0_skl)
& ! [X] : product(sK0_skl,X,X)
& ! [X] : product(X,sK0_skl,X)
& ! [Z,U,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) )
& ! [X,V,W] :
( product(X,V,W)
| ! [Z,U] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) )
& ! [X,Y] : product(X,Y,sK1_skl(Y,X)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(E,sK0_skl),skolemize(Z,sK1_skl(Y,X)),skolemize(W,sK2_skl),skolemize(X,sK3_skl),skolemize(U,sK4_skl),skolemize(V,sK5_skl)],[f4]) ).
fof(f7,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)],[f5]) ).
fof(f8,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0] : product(X0,sK0_skl,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,plain,
! [X0] : product(sK0_skl,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0] : product(X0,inverse(X0),sK0_skl),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
product(inverse(sK4_skl),inverse(sK5_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
product(sK5_skl,sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
~ product(inverse(sK2_skl),inverse(sK3_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( product(X0,X3,X2)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,sK0_skl) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( product(X0,X2,X3)
| ~ product(X1,X2,X3)
| ~ product(X0,sK0_skl,X1) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( product(X0,X3,sK0_skl)
| ~ product(X1,inverse(X2),X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f11,f7]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( product(X1,X2,X3)
| ~ product(X0,X2,X3)
| ~ product(X0,sK0_skl,X1) ),
inference(resolution,[status(thm)],[f8,f10]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( product(X2,inverse(X1),X3)
| ~ product(X0,sK0_skl,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f8,f11]) ).
fof(f263,plain,
! [X0,X1] :
( product(X0,sK0_skl,inverse(X1))
| ~ product(X0,X1,sK0_skl) ),
inference(resolution,[status(thm)],[f27,f11]) ).
fof(f279,plain,
! [X0,X1] :
( product(X0,inverse(X1),sK0_skl)
| ~ product(X0,sK0_skl,X1) ),
inference(resolution,[status(thm)],[f29,f11]) ).
fof(f364,plain,
! [X0] :
( product(X0,sK2_skl,sK0_skl)
| ~ product(X0,inverse(sK4_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f33,f13]) ).
fof(f601,plain,
! [X0,X1] :
( product(X1,sK0_skl,X0)
| ~ product(X0,sK0_skl,X1) ),
inference(resolution,[status(thm)],[f47,f9]) ).
fof(f627,plain,
! [X0,X1,X2] :
( product(X2,inverse(X1),X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f48,f9]) ).
fof(f3392,plain,
product(sK3_skl,inverse(sK4_skl),sK5_skl),
inference(resolution,[status(thm)],[f627,f14]) ).
fof(f4719,plain,
product(sK3_skl,sK2_skl,sK0_skl),
inference(resolution,[status(thm)],[f364,f3392]) ).
fof(f4733,plain,
product(sK3_skl,sK0_skl,inverse(sK2_skl)),
inference(resolution,[status(thm)],[f4719,f263]) ).
fof(f4803,plain,
product(inverse(sK2_skl),sK0_skl,sK3_skl),
inference(resolution,[status(thm)],[f4733,f601]) ).
fof(f5294,plain,
product(inverse(sK2_skl),inverse(sK3_skl),sK0_skl),
inference(resolution,[status(thm)],[f4803,f279]) ).
fof(f5370,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5294,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/10.32 % Computer : n012.cluster.edu
% 0.04/10.32 % Model : x86_64 x86_64
% 0.04/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.32 % Memory : 8046.5625MB
% 0.04/10.32 % OS : Linux 6.8.0-71-generic
% 0.04/10.32 % CPULimit : 300
% 0.04/10.32 % WCLimit : 300
% 0.04/10.32 % DateTime : Sun Sep 20 19:53:35 UTC 2026
% 0.04/10.32 % CPUTime :
% 0.04/10.33 % Drodi V4.1.1
% 0.07/10.82 % Refutation found
% 0.07/10.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/10.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/10.84 % Elapsed time: 0.507969 seconds
% 0.07/10.84 % CPU time: 3.902383 seconds
% 0.07/10.84 % Total memory used: 104.766 MB
% 0.07/10.84 % Net memory used: 89.746 MB
%------------------------------------------------------------------------------