%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:32:43 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 65 ( 17 unt; 6 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 145 ( 67 ~; 72 |; 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 : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f6,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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(f11,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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(f17,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,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)],[f10]) ).
fof(f26,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f33,plain,
! [X,Z1,Z2] :
( product(Z1,Z2,X)
| ! [Y] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f27,f32]) ).
fof(f39,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f29,f32]) ).
fof(f40,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[f31,f32]) ).
fof(f42,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f25,f18]) ).
fof(f43,plain,
! [X0] :
( product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f25,f17]) ).
fof(f46,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f42,f17]) ).
fof(f58,definition,
( sQ3_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ3_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ4_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ4_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ5_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ5_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f46,f58,f61,f64]) ).
fof(f78,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)],[f43,f18]) ).
fof(f81,definition,
( sQ9_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ9_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ10_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ10_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ11_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ11_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f78,f81,f84,f87]) ).
fof(f163,plain,
( ~ sQ5_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f65,f39]) ).
fof(f168,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f22]) ).
fof(f169,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f170,plain,
( ~ sQ4_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f62,f40]) ).
fof(f175,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f24]) ).
fof(f176,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f180,plain,
! [X0] :
( ~ sQ3_spl
| product(X0,e_1,e_2)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f59,f34]) ).
fof(f216,plain,
( ~ sQ11_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f88,f40]) ).
fof(f221,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f22]) ).
fof(f222,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( ~ sQ10_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f85,f39]) ).
fof(f230,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f24]) ).
fof(f231,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f82,f180]) ).
fof(f239,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f232,f37]) ).
fof(f243,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f21]) ).
fof(f244,plain,
( ~ sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f243]) ).
fof(f245,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f90,f169,f176,f222,f231,f244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n011.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 19:59:15 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.13/5.51 % Refutation found
% 0.13/5.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.53 % Elapsed time: 0.144767 seconds
% 0.13/5.53 % CPU time: 0.918243 seconds
% 0.13/5.53 % Total memory used: 21.144 MB
% 0.13/5.53 % Net memory used: 20.424 MB
%------------------------------------------------------------------------------