%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:32:49 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 7 unt; 8 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 214 ( 109 ~; 97 |; 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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(f11,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,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)],[f10]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f13,f21]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f13,f19]) ).
fof(f29,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)],[f13,f25]) ).
fof(f36,plain,
! [X0] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f37,plain,
! [X0] :
( product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f15,f11]) ).
fof(f38,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f36,f12]) ).
fof(f39,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f36,f11]) ).
fof(f40,definition,
( sQ0_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( ~ sQ0_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f40]) ).
fof(f43,definition,
( sQ1_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ1_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f40,f43]) ).
fof(f47,definition,
( sQ2_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ2_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ3_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ3_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f39,f47,f50]) ).
fof(f54,plain,
! [X0] :
( ~ sQ2_spl
| ~ product(e_1,e_1,X0)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f48,f29]) ).
fof(f58,plain,
( ~ sQ2_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f48,f27]) ).
fof(f59,plain,
( ~ sQ0_spl
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f41,f26]) ).
fof(f62,plain,
( ~ sQ0_spl
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f41,f27]) ).
fof(f63,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f48]) ).
fof(f64,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ product(e_1,e_1,X0)
| ~ product(e_2,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f51,f29]) ).
fof(f69,plain,
( ~ sQ1_spl
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f44,f26]) ).
fof(f74,plain,
( ~ sQ1_spl
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f44,f27]) ).
fof(f76,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f51]) ).
fof(f77,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f37,f12]) ).
fof(f79,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f37,f11]) ).
fof(f80,definition,
( sQ4_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ4_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ5_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ5_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f78,f80,f83]) ).
fof(f87,definition,
( sQ6_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ7_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ7_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f79,f87,f90]) ).
fof(f102,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f58]) ).
fof(f103,plain,
( ~ sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f102]) ).
fof(f112,plain,
( ~ sQ3_spl
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f51,f27]) ).
fof(f114,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f91]) ).
fof(f115,plain,
( ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f129,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f54,f91]) ).
fof(f130,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f81]) ).
fof(f131,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f74]) ).
fof(f134,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f62,f80,f40]) ).
fof(f148,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ3_spl
| ~ product(e_1,e_1,X0)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f65,f41]) ).
fof(f149,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f148,f88]) ).
fof(f150,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f149,f87,f50,f40]) ).
fof(f151,plain,
$false,
inference(sat_refutation,[status(thm)],[f46,f53,f64,f77,f86,f93,f103,f115,f131,f134,f135,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Sep 20 20:01:55 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.043925 seconds
% 0.13/0.41 % CPU time: 0.131223 seconds
% 0.13/0.41 % Total memory used: 17.036 MB
% 0.13/0.41 % Net memory used: 16.543 MB
%------------------------------------------------------------------------------