%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:32:41 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of formulae : 110 ( 29 unt; 14 def)
% Number of atoms : 275 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 302 ( 137 ~; 151 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 15 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_3),
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_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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(f14,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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(f25,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f34,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)],[f12]) ).
fof(f37,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f43,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
! [X,Y,Z2] :
( product2(Z2,X,Y)
| ! [Z1] :
( ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( product2(X1,X0,X1)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[f41,f51]) ).
fof(f60,plain,
! [X0,X1] :
( ~ product2(X0,e_2,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f28,f46]) ).
fof(f61,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f28,f44]) ).
fof(f62,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f28,f40]) ).
fof(f63,plain,
! [X0,X1] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f28,f38]) ).
fof(f66,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f29,f46]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f29,f38]) ).
fof(f95,plain,
! [X0,X1,X2] :
( product2(e_3,X2,X1)
| ~ product1(X2,X1,X0)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f34,f51]) ).
fof(f96,plain,
! [X0,X1] :
( product1(X1,X0,e_2)
| product1(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product2(e_3,X1,X0)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f95,f34]) ).
fof(f98,definition,
( sQ0_spl
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( sQ0_spl
| ~ group_element(e_3) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,definition,
! [X0,X1] :
( sQ1_spl
<=> ( product1(X1,X0,e_2)
| product1(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product2(e_3,X1,X0)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f102,plain,
! [X0,X1] :
( ~ sQ1_spl
| product1(X1,X0,e_2)
| product1(X1,X0,e_1)
| ~ group_element(X0)
| ~ group_element(X1)
| product2(e_3,X1,X0)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f96,f98,f101]) ).
fof(f106,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f27]) ).
fof(f107,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ~ sQ1_spl
| product1(X1,X0,e_2)
| product1(X1,X0,e_1)
| ~ group_element(X1)
| product2(e_3,X1,X0)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f102]) ).
fof(f116,definition,
( sQ3_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( sQ3_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f124,plain,
~ product2(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f60,f49]) ).
fof(f145,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f26]) ).
fof(f146,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f147,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f124,f52]) ).
fof(f157,definition,
( sQ10_spl
<=> product1(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ10_spl
| product1(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
( sQ11_spl
<=> product1(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( ~ sQ11_spl
| product1(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f176,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f63,f41]) ).
fof(f185,definition,
( sQ15_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ15_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
( sQ16_spl
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ16_spl
| product1(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,definition,
( sQ17_spl
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ17_spl
| product1(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f198,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f147]) ).
fof(f199,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f200,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f25]) ).
fof(f201,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f204,definition,
( sQ19_spl
<=> product1(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ19_spl
| product1(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ20_spl
<=> product1(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ20_spl
| product1(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,definition,
( sQ21_spl
<=> product1(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( ~ sQ21_spl
| product1(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,definition,
( sQ22_spl
<=> product1(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ22_spl
| product1(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f220,definition,
( sQ23_spl
<=> product2(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( ~ sQ23_spl
| product2(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( sQ23_spl
| ~ product2(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f226,plain,
( ~ sQ16_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f189,f63]) ).
fof(f229,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f41]) ).
fof(f230,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f231,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f176]) ).
fof(f232,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f233,plain,
( ~ sQ21_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f211,f62]) ).
fof(f236,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f41]) ).
fof(f237,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ sQ20_spl
| product2(e_3,e_3,e_1)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f208,f95]) ).
fof(f240,definition,
( sQ24_spl
<=> product2(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ24_spl
| product2(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( ~ sQ20_spl
| sQ24_spl
| sQ22_spl
| sQ21_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f238,f116,f185,f210,f213,f240,f207]) ).
fof(f253,plain,
( ~ sQ23_spl
| ~ product2(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f221,f61]) ).
fof(f255,plain,
( ~ sQ10_spl
| product2(e_3,e_3,e_2)
| product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f158,f95]) ).
fof(f278,plain,
( ~ sQ23_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f241]) ).
fof(f279,plain,
( ~ sQ23_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f287,plain,
( ~ sQ11_spl
| ~ product1(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f161,f63]) ).
fof(f291,plain,
( ~ sQ11_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f208]) ).
fof(f292,plain,
( ~ sQ11_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f296,plain,
( ~ sQ1_spl
| sQ23_spl
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1)
| ~ group_element(e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f222,f108]) ).
fof(f298,plain,
( ~ sQ1_spl
| sQ23_spl
| ~ sQ0_spl
| sQ11_spl
| sQ10_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f296,f116,f157,f160,f98,f220,f101]) ).
fof(f299,plain,
( ~ sQ10_spl
| sQ23_spl
| sQ17_spl
| sQ16_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f255,f185,f116,f188,f191,f220,f157]) ).
fof(f303,plain,
~ product2(e_1,e_3,e_1),
inference(resolution,[status(thm)],[f66,f49]) ).
fof(f349,plain,
~ product1(e_3,e_1,e_1),
inference(resolution,[status(thm)],[f303,f52]) ).
fof(f351,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f205]) ).
fof(f352,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f383,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f69,f41]) ).
fof(f418,plain,
( product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f383,f34]) ).
fof(f419,plain,
( sQ20_spl
| sQ19_spl
| ~ sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f418,f98,f185,f204,f207]) ).
fof(f420,plain,
$false,
inference(sat_refutation,[status(thm)],[f104,f107,f146,f199,f201,f230,f232,f237,f243,f279,f292,f298,f299,f352,f419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:02:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.043971 seconds
% 0.14/0.42 % CPU time: 0.139473 seconds
% 0.14/0.42 % Total memory used: 14.394 MB
% 0.14/0.42 % Net memory used: 14.157 MB
%------------------------------------------------------------------------------