%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-2.003 : 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 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 63 ( 22 unt; 7 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 73 ~; 67 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(Y1,Y2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f39,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
! [Y1,Y2] :
( equalish(Y1,Y2)
| ! [X2,Z2] :
( ~ product(Z2,Y2,X2)
| ! [X1] :
( ~ product(Z2,Y1,X1)
| ! [Z1] :
( ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ) ) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5] :
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f33,f45]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f33,f43]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_2,X2)
| ~ product(X3,e_1,X0)
| ~ product(X2,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f33,f50]) ).
fof(f56,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f34,f45]) ).
fof(f57,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f34,f43]) ).
fof(f85,definition,
( sQ0_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( sQ0_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f95,definition,
( sQ3_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( sQ3_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f99,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f31]) ).
fof(f100,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f99]) ).
fof(f102,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f52,f46]) ).
fof(f109,plain,
! [X0] :
( ~ product(e_2,e_1,X0)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f54,f46]) ).
fof(f118,definition,
( sQ6_spl
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ6_spl
| ~ group_element(e_3) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f140,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f30]) ).
fof(f141,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f140]) ).
fof(f148,plain,
~ product(e_3,e_1,e_1),
inference(resolution,[status(thm)],[f56,f46]) ).
fof(f154,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f57,f46]) ).
fof(f159,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f32]) ).
fof(f160,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f154,f39]) ).
fof(f163,definition,
( sQ14_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ14_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,definition,
( sQ15_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f162,f118,f95,f163,f166]) ).
fof(f170,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f148]) ).
fof(f171,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f196,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2)
| ~ product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f109,f39]) ).
fof(f197,definition,
( sQ19_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ19_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
( sQ20_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( ~ sQ20_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( sQ20_spl
| sQ19_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f196,f166,f85,f95,f197,f200]) ).
fof(f205,plain,
( ~ sQ19_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f198,f51]) ).
fof(f212,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f46]) ).
fof(f213,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f214,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f102]) ).
fof(f215,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f214]) ).
fof(f216,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f141,f160,f169,f171,f203,f213,f215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n009.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 19:57:48 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.41 % Elapsed time: 0.038624 seconds
% 0.14/5.41 % CPU time: 0.108557 seconds
% 0.14/5.41 % Total memory used: 13.396 MB
% 0.14/5.41 % Net memory used: 13.095 MB
%------------------------------------------------------------------------------