%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP039-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:32:21 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 92 ( 29 unt; 11 def)
% Number of atoms : 189 ( 31 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 165 ( 68 ~; 86 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( subgroup_member(Z)
| multiply(X,Y) != Z
| ~ subgroup_member(Y)
| ~ subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : multiply(X,inverse(X)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( subgroup_member(element_in_O2(X,Y))
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( multiply(X,element_in_O2(X,Y)) = Y
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [Z] :
( subgroup_member(Z)
| ! [X,Y] :
( multiply(X,Y) != Z
| ~ subgroup_member(Y)
| ~ subgroup_member(X) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| multiply(X0,X1) != X2
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] :
( multiply(X0,element_in_O2(X0,X1)) = X1
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
multiply(b,inverse(a)) = c,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
multiply(a,c) = d,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f31,plain,
! [X0,X1] :
( ~ subgroup_member(X1)
| subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f30,f18]) ).
fof(f32,plain,
! [X0] :
( subgroup_member(multiply(X0,b))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f30,f26]) ).
fof(f34,plain,
( subgroup_member(identity)
| ~ subgroup_member(inverse(b)) ),
inference(paramodulation,[status(thm)],[f16,f32]) ).
fof(f35,definition,
( sQ0_spl
<=> subgroup_member(inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( sQ0_spl
| ~ subgroup_member(inverse(b)) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ1_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ1_spl
| subgroup_member(identity) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f35,f38]) ).
fof(f42,plain,
( sQ0_spl
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f37,f18]) ).
fof(f43,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f26]) ).
fof(f44,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f55,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f56,plain,
! [X0] : multiply(c,X0) = multiply(b,multiply(inverse(a),X0)),
inference(paramodulation,[status(thm)],[f27,f17]) ).
fof(f67,plain,
( ~ subgroup_member(a)
| subgroup_member(c)
| ~ subgroup_member(b) ),
inference(paramodulation,[status(thm)],[f27,f31]) ).
fof(f73,definition,
( sQ4_spl
<=> subgroup_member(b) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,definition,
( sQ5_spl
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ5_spl
| subgroup_member(c) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ6_spl
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( sQ6_spl
| ~ subgroup_member(a) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( ~ sQ6_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f67,f73,f76,f79]) ).
fof(f83,definition,
! [X0] :
( sQ7_spl
<=> ( ~ subgroup_member(X0)
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f84,plain,
! [X0] :
( ~ sQ7_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f87,plain,
! [X0] :
( ~ sQ7_spl
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f84]) ).
fof(f88,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f39,f87]) ).
fof(f91,plain,
( ~ sQ1_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f92,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f22,f15]) ).
fof(f104,plain,
! [X0] :
( multiply(X0,element_in_O2(X0,d)) = d
| subgroup_member(X0) ),
inference(resolution,[status(thm)],[f25,f29]) ).
fof(f106,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| subgroup_member(X1)
| subgroup_member(multiply(X0,element_in_O2(X1,X2)))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f30,f24]) ).
fof(f112,plain,
( subgroup_member(b)
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f15,f32]) ).
fof(f115,plain,
( sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f112,f38,f73]) ).
fof(f117,plain,
! [X0] :
( ~ sQ5_spl
| subgroup_member(multiply(X0,c))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f77,f30]) ).
fof(f118,plain,
multiply(c,a) = multiply(b,identity),
inference(paramodulation,[status(thm)],[f16,f56]) ).
fof(f122,plain,
multiply(c,a) = b,
inference(forward_demodulation,[status(thm)],[f21,f118]) ).
fof(f135,plain,
( ~ sQ5_spl
| subgroup_member(d)
| ~ subgroup_member(a) ),
inference(paramodulation,[status(thm)],[f28,f117]) ).
fof(f137,definition,
( sQ8_spl
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ8_spl
| ~ subgroup_member(inverse(c)) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f141,definition,
( sQ9_spl
<=> subgroup_member(d) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ9_spl
| subgroup_member(d) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( ~ sQ5_spl
| sQ9_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f135,f79,f141,f76]) ).
fof(f202,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f15,f55]) ).
fof(f206,plain,
a = multiply(inverse(c),b),
inference(paramodulation,[status(thm)],[f122,f202]) ).
fof(f213,plain,
c = multiply(inverse(a),d),
inference(paramodulation,[status(thm)],[f28,f202]) ).
fof(f248,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(paramodulation,[status(thm)],[f206,f32]) ).
fof(f252,plain,
( sQ6_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f248,f137,f79]) ).
fof(f256,plain,
( sQ8_spl
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f139,f18]) ).
fof(f259,plain,
( sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f77]) ).
fof(f260,plain,
( sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f261,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f29]) ).
fof(f262,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f332,plain,
( sQ6_spl
| multiply(a,element_in_O2(a,d)) = d ),
inference(resolution,[status(thm)],[f104,f81]) ).
fof(f410,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(X0))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f15,f31]) ).
fof(f417,plain,
! [X0] :
( ~ subgroup_member(identity)
| subgroup_member(multiply(X0,identity))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f92,f31]) ).
fof(f419,definition,
! [X0] :
( sQ12_spl
<=> ( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( sQ12_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f410,f38,f419]) ).
fof(f426,definition,
! [X0] :
( sQ13_spl
<=> ( subgroup_member(multiply(X0,identity))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( ~ sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f417,f426,f38]) ).
fof(f431,plain,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f15,f106]) ).
fof(f434,definition,
! [X0,X1] :
( sQ14_spl
<=> ( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ14_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f431,f38,f434]) ).
fof(f444,plain,
( sQ6_spl
| element_in_O2(a,d) = multiply(inverse(a),d) ),
inference(paramodulation,[status(thm)],[f332,f202]) ).
fof(f447,plain,
( sQ6_spl
| element_in_O2(a,d) = c ),
inference(forward_demodulation,[status(thm)],[f213,f444]) ).
fof(f450,plain,
( sQ6_spl
| subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a) ),
inference(paramodulation,[status(thm)],[f447,f24]) ).
fof(f455,plain,
( sQ5_spl
| sQ9_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f450,f79,f141,f76]) ).
fof(f456,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f44,f82,f91,f115,f144,f252,f260,f262,f422,f429,f437,f455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 19:53:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.059692 seconds
% 0.13/0.43 % CPU time: 0.183088 seconds
% 0.13/0.43 % Total memory used: 103.371 MB
% 0.13/0.43 % Net memory used: 102.831 MB
%------------------------------------------------------------------------------