%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 12:32:39 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 63 ( 19 unt; 6 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 155 ( 78 ~; 71 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(Y1,Y2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
! [Y1,Y2] :
( equalish(Y1,Y2)
| ! [X2,Z2] :
( ~ product(Z2,Y2,X2)
| ! [X1] :
( ~ product(Z2,Y1,X1)
| ! [Z1] :
( ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ) ) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5] :
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f45,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f21,f32]) ).
fof(f46,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f21,f30]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_3,X2)
| ~ product(X3,e_1,X0)
| ~ product(X2,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f21,f37]) ).
fof(f55,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f23,f32]) ).
fof(f56,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f23,f30]) ).
fof(f71,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f26,f19]) ).
fof(f76,plain,
! [X0,X1] :
( ~ product(e_1,e_3,X1)
| ~ product(X1,e_3,X0)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f48,f33]) ).
fof(f79,plain,
~ product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[f46,f33]) ).
fof(f82,plain,
~ product(e_2,e_3,e_2),
inference(resolution,[status(thm)],[f56,f33]) ).
fof(f87,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f71,f18]) ).
fof(f88,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f71,f17]) ).
fof(f99,definition,
( sQ3_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ3_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ4_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ4_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
( sQ5_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ5_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f87,f99,f102,f105]) ).
fof(f109,definition,
( sQ6_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ6_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ7_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ7_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
( sQ8_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ8_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f88,f109,f112,f115]) ).
fof(f119,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f79]) ).
fof(f120,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f121,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f82]) ).
fof(f122,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f204,plain,
( ~ sQ8_spl
| ~ product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f116,f45]) ).
fof(f208,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f33]) ).
fof(f209,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f210,plain,
! [X0] :
( ~ sQ7_spl
| ~ product(e_2,e_3,X0)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f113,f76]) ).
fof(f219,plain,
( ~ sQ5_spl
| ~ product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f106,f55]) ).
fof(f220,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f33]) ).
fof(f221,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f100,f210]) ).
fof(f230,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f33]) ).
fof(f231,plain,
( ~ sQ7_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
$false,
inference(sat_refutation,[status(thm)],[f108,f118,f120,f122,f209,f221,f231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP123-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n006.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 19:57:42 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 0.20/0.50 % Refutation found
% 0.20/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.54 % Elapsed time: 0.075865 seconds
% 0.20/0.54 % CPU time: 0.226171 seconds
% 0.20/0.54 % Total memory used: 11.729 MB
% 0.20/0.54 % Net memory used: 11.569 MB
%------------------------------------------------------------------------------