%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:32:49 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 73 ( 7 unt; 8 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 223 ( 114 ~; 101 |; 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 : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,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(f10,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X1,X2] :
( equalish(X1,X2)
| ! [Y2,Z2] :
( ~ product(Z2,X2,Y2)
| ! [Y1] :
( ~ product(Z2,X1,Y1)
| ! [Z1] :
( ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5] :
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f20,f28]) ).
fof(f34,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f20,f26]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_2,X2)
| ~ product(X3,e_1,X0)
| ~ product(e_2,X2,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f20,f30]) ).
fof(f43,plain,
! [X0] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f22,f19]) ).
fof(f44,plain,
! [X0] :
( product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f45,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f43,f19]) ).
fof(f46,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f43,f18]) ).
fof(f47,definition,
( sQ0_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ0_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ1_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ1_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f47,f50]) ).
fof(f54,definition,
( sQ2_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ2_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ3_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ3_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f46,f54,f57]) ).
fof(f61,plain,
( ~ sQ2_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f55,f34]) ).
fof(f62,plain,
( ~ sQ0_spl
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f48,f33]) ).
fof(f63,plain,
( ~ sQ0_spl
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f48,f34]) ).
fof(f64,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f55]) ).
fof(f65,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f66,plain,
( ~ sQ3_spl
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f58,f34]) ).
fof(f68,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f44,f19]) ).
fof(f69,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f44,f18]) ).
fof(f70,definition,
( sQ4_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ4_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ5_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ5_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f68,f70,f73]) ).
fof(f77,definition,
( sQ6_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ7_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ7_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f69,f77,f80]) ).
fof(f85,plain,
( ~ sQ1_spl
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f51,f33]) ).
fof(f86,plain,
( ~ sQ1_spl
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f51,f34]) ).
fof(f88,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f58]) ).
fof(f89,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f90,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f61]) ).
fof(f91,plain,
( ~ sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ product(X1,e_2,e_1)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f71,f37]) ).
fof(f96,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f66]) ).
fof(f97,plain,
( ~ sQ7_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f106,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ4_spl
| ~ product(X0,e_2,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f92,f55]) ).
fof(f108,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f106,f55]) ).
fof(f109,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f81]) ).
fof(f110,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f86]) ).
fof(f113,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f114,plain,
( ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f63,f70,f47]) ).
fof(f118,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ product(X1,e_2,e_2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f48,f37]) ).
fof(f128,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f118,f78]) ).
fof(f129,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f128,f58]) ).
fof(f130,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f129,f77,f47,f57]) ).
fof(f131,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f60,f65,f76,f83,f89,f91,f97,f110,f113,f114,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 20:01:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.14/0.37 % Refutation found
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.043650 seconds
% 0.14/0.41 % CPU time: 0.119742 seconds
% 0.14/0.41 % Total memory used: 16.971 MB
% 0.14/0.41 % Net memory used: 16.524 MB
%------------------------------------------------------------------------------