%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : 103 ( 31 unt; 11 def)
% Number of atoms : 210 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 223 ( 116 ~; 96 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 12 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 101 ( 101 !; 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,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product1(X,Y,Z)
| ~ product1(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,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)],[f10]) ).
fof(f31,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Y,Z)
| ~ product1(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product1(X0,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f46,plain,
! [X,Y,Z2] :
( product2(Z2,X,Y)
| ! [Z1] :
( ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( product2(X1,X0,X1)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[f37,f47]) ).
fof(f50,plain,
! [X0,X1] :
( ~ product2(X0,e_2,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f24,f42]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f24,f36]) ).
fof(f53,plain,
! [X0,X1] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f24,f34]) ).
fof(f54,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_2)
| ~ product1(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f24,f32]) ).
fof(f57,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f25,f40]) ).
fof(f58,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f25,f36]) ).
fof(f59,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f25,f34]) ).
fof(f68,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f27,f42]) ).
fof(f91,definition,
( sQ0_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( sQ0_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f98,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f22]) ).
fof(f99,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f102,plain,
! [X0] :
( ~ product1(e_2,X0,X0)
| ~ product2(X0,e_1,X0) ),
inference(resolution,[status(thm)],[f50,f48]) ).
fof(f109,plain,
~ product2(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f102,f37]) ).
fof(f113,definition,
( sQ4_spl
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( sQ4_spl
| ~ group_element(e_3) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,definition,
( sQ5_spl
<=> product1(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( ~ sQ5_spl
| product1(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,definition,
( sQ6_spl
<=> product1(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ6_spl
| product1(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f123,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f109,f48]) ).
fof(f138,definition,
( sQ8_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ8_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f142,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f21]) ).
fof(f143,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f150,plain,
~ product1(e_1,e_1,e_2),
inference(resolution,[status(thm)],[f54,f37]) ).
fof(f159,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f23]) ).
fof(f160,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f185,plain,
~ product2(e_1,e_1,e_3),
inference(resolution,[status(thm)],[f57,f45]) ).
fof(f189,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f58,f37]) ).
fof(f195,plain,
~ product1(e_1,e_3,e_1),
inference(resolution,[status(thm)],[f59,f37]) ).
fof(f202,definition,
( sQ16_spl
<=> product2(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ16_spl
| ~ product2(e_3,e_3,e_3) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ17_spl
<=> product1(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ17_spl
| product1(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
( sQ18_spl
<=> product1(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ18_spl
| product1(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f212,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f45]) ).
fof(f213,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f216,plain,
( ~ sQ18_spl
| ~ product1(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[f209,f52]) ).
fof(f218,plain,
( ~ sQ18_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f120]) ).
fof(f219,plain,
( ~ sQ18_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f224,plain,
! [X0] :
( ~ product1(X0,e_3,e_1)
| ~ product1(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f185,f47]) ).
fof(f232,plain,
( product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f189,f30]) ).
fof(f233,plain,
( sQ18_spl
| sQ17_spl
| ~ sQ4_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f232,f138,f113,f205,f208]) ).
fof(f235,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f195]) ).
fof(f236,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f251,definition,
( sQ24_spl
<=> product1(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ24_spl
| product1(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f255,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f150]) ).
fof(f256,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f282,plain,
! [X0] :
( ~ product1(e_2,X0,X0)
| ~ product2(X0,e_3,X0) ),
inference(resolution,[status(thm)],[f68,f48]) ).
fof(f309,plain,
( product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2)
| ~ product2(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f282,f30]) ).
fof(f311,plain,
( sQ6_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f309,f202,f91,f113,f116,f119]) ).
fof(f316,definition,
( sQ30_spl
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( ~ sQ30_spl
| product1(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,definition,
( sQ31_spl
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( ~ sQ31_spl
| product1(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f323,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f123]) ).
fof(f324,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f336,plain,
( ~ sQ30_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f317,f53]) ).
fof(f340,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f336,f37]) ).
fof(f341,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f359,plain,
( ~ sQ5_spl
| ~ product1(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f224,f117]) ).
fof(f360,plain,
( ~ sQ5_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f359,f208,f116]) ).
fof(f361,plain,
$false,
inference(sat_refutation,[status(thm)],[f99,f143,f160,f213,f219,f233,f236,f256,f311,f324,f341,f360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:58:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % 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: 0.049972 seconds
% 0.13/0.40 % CPU time: 0.150640 seconds
% 0.13/0.40 % Total memory used: 17.539 MB
% 0.13/0.40 % Net memory used: 17.177 MB
%------------------------------------------------------------------------------