%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:32:40 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 79 ( 20 unt; 8 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 205 ( 101 ~; 96 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 81 ( 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] :
( product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1] :
( product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f40,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)],[f18]) ).
fof(f41,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)],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f24,f32]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_2,X2)
| ~ product(X3,e_1,X0)
| ~ product(X2,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f24,f41]) ).
fof(f49,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f44,f37]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(e_1,e_2,X1)
| ~ product(X1,e_2,X0)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f45,f37]) ).
fof(f57,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f25,f36]) ).
fof(f58,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f25,f34]) ).
fof(f59,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f25,f32]) ).
fof(f82,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f57,f37]) ).
fof(f101,plain,
! [X0] :
( product(e_3,X0,e_1)
| product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f19,f21]) ).
fof(f102,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f20,f23]) ).
fof(f111,definition,
( sQ0_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ0_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f121,definition,
( sQ3_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ3_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f131,definition,
( sQ6_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f168,definition,
( sQ15_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ15_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f185,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f101,f22]) ).
fof(f187,definition,
( sQ18_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ18_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f197,definition,
( sQ21_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ21_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
( sQ22_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( ~ sQ22_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,definition,
( sQ23_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ23_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f185,f197,f200,f203]) ).
fof(f217,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f49]) ).
fof(f218,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f223,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f102,f21]) ).
fof(f226,plain,
( sQ0_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f223,f131,f121,f111]) ).
fof(f227,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f82]) ).
fof(f228,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f269,plain,
( ~ sQ6_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f132,f59]) ).
fof(f270,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f269,f37]) ).
fof(f271,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f272,plain,
! [X0] :
( ~ sQ3_spl
| ~ product(e_3,e_2,X0)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f122,f52]) ).
fof(f280,plain,
( ~ sQ3_spl
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f122,f59]) ).
fof(f285,plain,
( ~ sQ15_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f169,f44]) ).
fof(f286,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f37]) ).
fof(f287,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f300,plain,
( ~ sQ18_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f188,f58]) ).
fof(f301,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f37]) ).
fof(f302,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f301]) ).
fof(f325,plain,
( ~ sQ3_spl
| ~ sQ23_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f204,f272]) ).
fof(f338,plain,
( ~ sQ3_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f37]) ).
fof(f339,plain,
( ~ sQ3_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f338]) ).
fof(f340,plain,
( ~ sQ21_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f280]) ).
fof(f341,plain,
( ~ sQ21_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f342,plain,
$false,
inference(sat_refutation,[status(thm)],[f206,f218,f226,f228,f271,f287,f302,f339,f341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n010.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 19:58:54 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.064053 seconds
% 0.17/0.50 % CPU time: 0.229835 seconds
% 0.17/0.50 % Total memory used: 13.480 MB
% 0.17/0.50 % Net memory used: 13.246 MB
%------------------------------------------------------------------------------