%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:32:40 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 94 ( 31 unt; 11 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 205 ( 108 ~; 86 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 82 ( 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,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(f27,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,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(f53,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f55,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f56,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f57,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f59,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f62,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)],[f26]) ).
fof(f63,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f72,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)],[f32]) ).
fof(f73,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)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f56,f68]) ).
fof(f75,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f56,f66]) ).
fof(f76,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f56,f64]) ).
fof(f79,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f57,f68]) ).
fof(f80,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f57,f66]) ).
fof(f108,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f74,f69]) ).
fof(f109,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f75,f69]) ).
fof(f110,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f76,f69]) ).
fof(f111,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f79,f69]) ).
fof(f112,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f80,f69]) ).
fof(f127,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f59,f68]) ).
fof(f128,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f59,f66]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_3,X2)
| ~ product(X3,e_2,X0)
| ~ product(X2,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f59,f73]) ).
fof(f199,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f127,f69]) ).
fof(f211,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f128,f69]) ).
fof(f213,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f62,f55]) ).
fof(f246,plain,
! [X0,X1] :
( ~ product(e_2,e_3,X1)
| ~ product(X1,e_3,X0)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f130,f69]) ).
fof(f338,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f213,f54]) ).
fof(f339,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f213,f53]) ).
fof(f350,definition,
( sQ32_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( ~ sQ32_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,definition,
( sQ33_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ33_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
( sQ34_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( ~ sQ34_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( sQ34_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f338,f350,f353,f356]) ).
fof(f360,definition,
( sQ35_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( ~ sQ35_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
( sQ36_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f366,definition,
( sQ37_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( ~ sQ37_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( sQ37_spl
| sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f339,f360,f363,f366]) ).
fof(f370,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f111]) ).
fof(f371,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f372,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f357,f199]) ).
fof(f373,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f396,plain,
( ~ sQ33_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f354,f128]) ).
fof(f403,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f69]) ).
fof(f404,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f405,plain,
! [X0] :
( ~ sQ32_spl
| ~ product(e_1,e_3,X0)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f351,f246]) ).
fof(f424,plain,
( ~ sQ35_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f361,f80]) ).
fof(f425,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f424,f69]) ).
fof(f426,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f445,definition,
( sQ40_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ40_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f449,definition,
( sQ41_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ41_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f462,definition,
( sQ45_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ45_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f469,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f108]) ).
fof(f470,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f471,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f110]) ).
fof(f472,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f473,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f211]) ).
fof(f474,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f484,definition,
( sQ49_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( ~ sQ49_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f491,definition,
( sQ51_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ51_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f508,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f109]) ).
fof(f509,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f512,plain,
( ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f112]) ).
fof(f513,plain,
~ sQ49_spl,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f529,plain,
( ~ sQ32_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f405,f69]) ).
fof(f530,plain,
( ~ sQ32_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f529,f363,f350]) ).
fof(f531,plain,
$false,
inference(sat_refutation,[status(thm)],[f359,f369,f371,f373,f404,f426,f470,f472,f474,f509,f513,f530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:01:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.048589 seconds
% 0.13/0.42 % CPU time: 0.150222 seconds
% 0.13/0.42 % Total memory used: 17.898 MB
% 0.13/0.42 % Net memory used: 17.644 MB
%------------------------------------------------------------------------------