%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:32:51 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.44s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 9 unt; 8 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 197 ( 92 ~; 97 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,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(f22,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f28,plain,
! [Y,X,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0] :
( product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f21,f18]) ).
fof(f31,plain,
! [X0] :
( product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f21,f17]) ).
fof(f32,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f30,f18]) ).
fof(f33,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f30,f17]) ).
fof(f34,definition,
( sQ0_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( ~ sQ0_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,definition,
( sQ1_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( ~ sQ1_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f34,f37]) ).
fof(f41,definition,
( sQ2_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ2_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,definition,
( sQ3_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ3_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f33,f41,f44]) ).
fof(f50,plain,
! [X0] :
( ~ sQ2_spl
| equalish(X0,e_1)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f42,f25]) ).
fof(f52,plain,
! [X0] :
( ~ sQ2_spl
| product(e_1,e_1,X0)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f42,f29]) ).
fof(f58,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f50,f35]) ).
fof(f60,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f20]) ).
fof(f61,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f31,f18]) ).
fof(f63,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f31,f17]) ).
fof(f64,definition,
( sQ4_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ4_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,definition,
( sQ5_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ5_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f62,f64,f67]) ).
fof(f71,definition,
( sQ6_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,definition,
( sQ7_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ7_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f63,f71,f74]) ).
fof(f82,plain,
! [X0] :
( ~ sQ3_spl
| product(e_2,e_1,X0)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f45,f29]) ).
fof(f86,plain,
! [X0] :
( ~ sQ1_spl
| product(e_2,e_2,X0)
| ~ product(e_2,X0,e_2) ),
inference(resolution,[status(thm)],[f38,f29]) ).
fof(f88,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f86,f45]) ).
fof(f91,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| equalish(X0,e_1)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f88,f23]) ).
fof(f96,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f91,f38]) ).
fof(f97,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f20]) ).
fof(f98,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f103,plain,
! [X0] :
( ~ sQ6_spl
| product(e_1,e_1,X0)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f72,f29]) ).
fof(f105,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f65,f103]) ).
fof(f114,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| equalish(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f105,f23]) ).
fof(f120,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f114,f72]) ).
fof(f121,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f19]) ).
fof(f122,plain,
( ~ sQ6_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f132,plain,
! [X0] :
( ~ sQ5_spl
| product(e_2,e_2,X0)
| ~ product(e_2,X0,e_1) ),
inference(resolution,[status(thm)],[f68,f29]) ).
fof(f144,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f132,f42]) ).
fof(f145,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f144,f34,f67,f41]) ).
fof(f154,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f75,f52]) ).
fof(f160,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f154,f71,f74,f41]) ).
fof(f161,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f82,f75]) ).
fof(f162,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f161,f41,f44,f74]) ).
fof(f163,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f35,f132]) ).
fof(f168,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f163,f37,f34,f67]) ).
fof(f169,plain,
$false,
inference(sat_refutation,[status(thm)],[f40,f47,f61,f70,f77,f98,f122,f145,f160,f162,f168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:06:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.44 % Refutation found
% 0.08/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.46 % Elapsed time: 0.093277 seconds
% 0.08/0.46 % CPU time: 0.513478 seconds
% 0.08/0.46 % Total memory used: 17.722 MB
% 0.08/0.46 % Net memory used: 17.536 MB
%------------------------------------------------------------------------------