%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:32:41 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 75 ( 23 unt; 6 def)
% Number of atoms : 159 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 172 ( 88 ~; 78 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 85 ( 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] :
( product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f58,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f63,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f66,plain,
! [X0,X1] :
( product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f69,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f81,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
! [X,Y,Z2] :
( product2(Z2,X,Y)
| ! [Z1] :
( ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( product2(X1,X0,X1)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[f73,f83]) ).
fof(f91,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f60,f72]) ).
fof(f112,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f61,f78]) ).
fof(f115,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f61,f70]) ).
fof(f127,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f63,f76]) ).
fof(f128,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f63,f72]) ).
fof(f155,plain,
~ product2(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f112,f81]) ).
fof(f158,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f155,f84]) ).
fof(f166,plain,
! [X0] :
( product1(X0,e_3,e_3)
| product1(X0,e_3,e_2)
| product1(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f66,f59]) ).
fof(f185,plain,
! [X0,X1,X2] :
( ~ product1(X2,e_3,X0)
| ~ product1(X1,e_3,X2)
| ~ product2(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f127,f83]) ).
fof(f186,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f128,f73]) ).
fof(f279,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f166,f58]) ).
fof(f280,plain,
( product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f166,f57]) ).
fof(f291,definition,
( sQ17_spl
<=> product1(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( ~ sQ17_spl
| product1(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,definition,
( sQ18_spl
<=> product1(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ18_spl
| product1(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
( sQ19_spl
<=> product1(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ19_spl
| product1(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f279,f291,f294,f297]) ).
fof(f301,definition,
( sQ20_spl
<=> product1(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ20_spl
| product1(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ21_spl
<=> product1(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( ~ sQ21_spl
| product1(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ22_spl
<=> product1(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( ~ sQ22_spl
| product1(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,plain,
( sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f280,f301,f304,f307]) ).
fof(f311,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f158]) ).
fof(f312,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f186]) ).
fof(f314,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f403,plain,
! [X0] :
( ~ sQ21_spl
| ~ product1(X0,e_3,e_1)
| ~ product2(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f305,f185]) ).
fof(f418,plain,
( ~ sQ20_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f302,f115]) ).
fof(f420,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f73]) ).
fof(f421,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f424,plain,
( ~ sQ18_spl
| ~ product1(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f295,f91]) ).
fof(f434,plain,
( ~ sQ18_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f424,f305]) ).
fof(f435,plain,
( ~ sQ18_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f440,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| ~ product2(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f292,f403]) ).
fof(f448,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f81]) ).
fof(f449,plain,
( ~ sQ21_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f450,plain,
$false,
inference(sat_refutation,[status(thm)],[f300,f310,f312,f314,f421,f435,f449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:58:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.051437 seconds
% 0.12/0.41 % CPU time: 0.159605 seconds
% 0.12/0.41 % Total memory used: 10.522 MB
% 0.12/0.41 % Net memory used: 10.403 MB
%------------------------------------------------------------------------------