%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:32:44 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 ( 15 unt; 6 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 148 ( 65 ~; 77 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0,X1] :
( product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0,X1] :
( product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
! [X,Z1,Z2] :
( product(Z1,Z2,X)
| ! [Y] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f55,plain,
! [X0] :
( product(e_3,X0,e_2)
| product(e_2,X0,e_2)
| product(e_1,X0,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f20,f27]) ).
fof(f57,plain,
! [X0] :
( product(X0,e_3,e_2)
| product(X0,e_2,e_2)
| product(X0,e_1,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f21,f27]) ).
fof(f61,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f37,f42]) ).
fof(f66,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f39,f42]) ).
fof(f67,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[f41,f42]) ).
fof(f72,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f55,f26]) ).
fof(f73,definition,
( sQ0_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ0_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f83,definition,
( sQ3_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ3_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f93,definition,
( sQ6_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ7_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ7_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ8_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f72,f93,f96,f99]) ).
fof(f106,plain,
! [X0] :
( ~ sQ8_spl
| product(X0,e_2,e_1)
| ~ product(e_1,e_3,X0) ),
inference(resolution,[status(thm)],[f100,f44]) ).
fof(f110,plain,
( ~ sQ7_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f97,f66]) ).
fof(f119,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f29]) ).
fof(f120,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f137,definition,
( sQ13_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ13_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f156,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f57,f26]) ).
fof(f159,plain,
( sQ0_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f156,f93,f83,f73]) ).
fof(f162,plain,
( ~ sQ6_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f94,f61]) ).
fof(f169,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f31]) ).
fof(f170,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f185,plain,
( ~ sQ3_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f84,f67]) ).
fof(f197,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f29]) ).
fof(f198,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f251,plain,
( ~ sQ13_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f138,f61]) ).
fof(f258,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f29]) ).
fof(f259,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f320,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f74,f106]) ).
fof(f328,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f320,f137,f73,f99]) ).
fof(f329,plain,
$false,
inference(sat_refutation,[status(thm)],[f102,f120,f159,f170,f198,f259,f328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n002.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 20:02:38 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % 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
% 0.13/5.42 % Elapsed time: 0.041325 seconds
% 0.13/5.42 % CPU time: 0.121088 seconds
% 0.13/5.42 % Total memory used: 16.508 MB
% 0.13/5.42 % Net memory used: 16.153 MB
%------------------------------------------------------------------------------