%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 107 ( 30 unt; 12 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 225 ( 112 ~; 101 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 13 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f37,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f38,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,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)],[f16]) ).
fof(f46,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f52,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f59,plain,
! [X,Y,Z2] :
( product2(Z2,X,Y)
| ! [Z1] :
( ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( product2(X1,X0,X1)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[f50,f60]) ).
fof(f65,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f37,f49]) ).
fof(f66,plain,
! [X0,X1] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f37,f47]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f38,f55]) ).
fof(f70,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f71,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f38,f49]) ).
fof(f72,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f38,f47]) ).
fof(f81,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f40,f55]) ).
fof(f108,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f66,f50]) ).
fof(f120,plain,
~ product2(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f69,f58]) ).
fof(f123,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f120,f61]) ).
fof(f125,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)],[f43,f36]) ).
fof(f127,plain,
! [X0] :
( product1(X0,e_1,e_3)
| product1(X0,e_1,e_2)
| product1(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f43,f34]) ).
fof(f131,plain,
~ product2(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f70,f58]) ).
fof(f137,plain,
! [X0] :
( ~ product1(X0,e_1,e_3)
| ~ product1(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[f131,f60]) ).
fof(f139,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f72,f50]) ).
fof(f145,plain,
~ product2(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f81,f58]) ).
fof(f148,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f145,f61]) ).
fof(f161,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)],[f125,f35]) ).
fof(f162,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)],[f125,f34]) ).
fof(f173,definition,
( sQ3_spl
<=> product1(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ3_spl
| product1(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ4_spl
<=> product1(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ4_spl
| product1(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,definition,
( sQ5_spl
<=> product1(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ5_spl
| product1(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f161,f173,f176,f179]) ).
fof(f183,definition,
( sQ6_spl
<=> product1(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ6_spl
| product1(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ7_spl
<=> product1(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ7_spl
| product1(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ8_spl
<=> product1(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ8_spl
| product1(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f162,f183,f186,f189]) ).
fof(f193,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f123]) ).
fof(f194,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f148]) ).
fof(f196,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f236,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f127,f36]) ).
fof(f237,plain,
( product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f127,f35]) ).
fof(f239,definition,
( sQ18_spl
<=> product1(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ18_spl
| product1(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ19_spl
<=> product1(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ19_spl
| product1(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ20_spl
<=> product1(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ20_spl
| product1(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f236,f239,f242,f245]) ).
fof(f249,definition,
( sQ21_spl
<=> product1(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( ~ sQ21_spl
| product1(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,definition,
( sQ22_spl
<=> product1(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ22_spl
| product1(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ23_spl
<=> product1(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( ~ sQ23_spl
| product1(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f237,f249,f252,f255]) ).
fof(f269,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f108]) ).
fof(f270,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f271,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f246,f139]) ).
fof(f272,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f271]) ).
fof(f292,plain,
( ~ sQ6_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f184,f72]) ).
fof(f294,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f292,f50]) ).
fof(f295,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f298,plain,
( ~ sQ4_spl
| ~ product1(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f177,f65]) ).
fof(f306,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f187]) ).
fof(f307,plain,
( ~ sQ4_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f314,plain,
( ~ sQ3_spl
| ~ product1(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f174,f72]) ).
fof(f499,plain,
( ~ sQ21_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f314]) ).
fof(f500,plain,
( ~ sQ21_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f501,plain,
( ~ sQ19_spl
| ~ product1(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f243,f137]) ).
fof(f509,plain,
( ~ sQ19_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f256]) ).
fof(f510,plain,
( ~ sQ19_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f516,plain,
( ~ sQ18_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f240,f71]) ).
fof(f519,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f50]) ).
fof(f520,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f521,plain,
$false,
inference(sat_refutation,[status(thm)],[f182,f192,f194,f196,f248,f258,f270,f272,f295,f307,f500,f510,f520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n018.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:00:28 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.045287 seconds
% 0.13/0.40 % CPU time: 0.152290 seconds
% 0.13/0.40 % Total memory used: 17.801 MB
% 0.13/0.40 % Net memory used: 17.505 MB
%------------------------------------------------------------------------------