%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% 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 12:32:21 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 89 ( 29 unt; 10 def)
% Number of atoms : 182 ( 31 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 155 ( 62 ~; 83 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( subgroup_member(element_in_O2(X,Y))
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( multiply(X,element_in_O2(X,Y)) = Y
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [Z] :
( subgroup_member(Z)
| ! [X,Y] :
( multiply(X,Y) != Z
| ~ subgroup_member(Y)
| ~ subgroup_member(X) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| multiply(X0,X1) != X2
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1] :
( multiply(X0,element_in_O2(X0,X1)) = X1
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
multiply(b,inverse(a)) = c,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
multiply(a,c) = d,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subgroup_member(X1)
| subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f28,f17]) ).
fof(f30,plain,
! [X0] :
( subgroup_member(multiply(X0,b))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f28,f24]) ).
fof(f32,plain,
( subgroup_member(identity)
| ~ subgroup_member(inverse(b)) ),
inference(paramodulation,[status(thm)],[f15,f30]) ).
fof(f33,definition,
( sQ0_spl
<=> subgroup_member(inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( sQ0_spl
| ~ subgroup_member(inverse(b)) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ1_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ1_spl
| subgroup_member(identity) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f33,f36]) ).
fof(f40,plain,
( sQ0_spl
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f35,f17]) ).
fof(f41,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f24]) ).
fof(f42,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f53,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f54,plain,
! [X0] : multiply(c,X0) = multiply(b,multiply(inverse(a),X0)),
inference(paramodulation,[status(thm)],[f25,f16]) ).
fof(f65,plain,
( ~ subgroup_member(a)
| subgroup_member(c)
| ~ subgroup_member(b) ),
inference(paramodulation,[status(thm)],[f25,f29]) ).
fof(f71,definition,
( sQ4_spl
<=> subgroup_member(b) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f74,definition,
( sQ5_spl
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ5_spl
| subgroup_member(c) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ6_spl
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ6_spl
| ~ subgroup_member(a) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( ~ sQ6_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f65,f71,f74,f77]) ).
fof(f81,definition,
! [X0] :
( sQ7_spl
<=> ( ~ subgroup_member(X0)
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f82,plain,
! [X0] :
( ~ sQ7_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f85,plain,
! [X0] :
( ~ sQ7_spl
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f82]) ).
fof(f86,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f37,f85]) ).
fof(f89,plain,
( ~ sQ1_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f102,plain,
! [X0] :
( multiply(X0,element_in_O2(X0,d)) = d
| subgroup_member(X0) ),
inference(resolution,[status(thm)],[f23,f27]) ).
fof(f104,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)],[f28,f22]) ).
fof(f110,plain,
( subgroup_member(b)
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f14,f30]) ).
fof(f113,plain,
( sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f110,f36,f71]) ).
fof(f115,plain,
! [X0] :
( ~ sQ5_spl
| subgroup_member(multiply(X0,c))
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f75,f28]) ).
fof(f116,plain,
multiply(c,a) = multiply(b,identity),
inference(paramodulation,[status(thm)],[f15,f54]) ).
fof(f120,plain,
multiply(c,a) = b,
inference(forward_demodulation,[status(thm)],[f20,f116]) ).
fof(f133,plain,
( ~ sQ5_spl
| subgroup_member(d)
| ~ subgroup_member(a) ),
inference(paramodulation,[status(thm)],[f26,f115]) ).
fof(f135,definition,
( sQ8_spl
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ8_spl
| ~ subgroup_member(inverse(c)) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f139,definition,
( sQ9_spl
<=> subgroup_member(d) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ9_spl
| subgroup_member(d) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ5_spl
| sQ9_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f133,f77,f139,f74]) ).
fof(f156,plain,
( sQ6_spl
| multiply(a,element_in_O2(a,d)) = d ),
inference(resolution,[status(thm)],[f102,f79]) ).
fof(f157,plain,
multiply(d,element_in_O2(d,d)) = d,
inference(resolution,[status(thm)],[f102,f27]) ).
fof(f203,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f14,f53]) ).
fof(f207,plain,
a = multiply(inverse(c),b),
inference(paramodulation,[status(thm)],[f120,f203]) ).
fof(f214,plain,
c = multiply(inverse(a),d),
inference(paramodulation,[status(thm)],[f26,f203]) ).
fof(f251,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(paramodulation,[status(thm)],[f207,f30]) ).
fof(f255,plain,
( sQ6_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f251,f135,f77]) ).
fof(f259,plain,
( sQ8_spl
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f137,f17]) ).
fof(f263,plain,
( sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f75]) ).
fof(f264,plain,
( sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f265,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f27]) ).
fof(f266,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f356,plain,
element_in_O2(d,d) = multiply(inverse(d),d),
inference(paramodulation,[status(thm)],[f157,f203]) ).
fof(f359,plain,
element_in_O2(d,d) = identity,
inference(forward_demodulation,[status(thm)],[f15,f356]) ).
fof(f416,plain,
( sQ6_spl
| element_in_O2(a,d) = multiply(inverse(a),d) ),
inference(paramodulation,[status(thm)],[f156,f203]) ).
fof(f418,plain,
( sQ6_spl
| element_in_O2(a,d) = c ),
inference(forward_demodulation,[status(thm)],[f214,f416]) ).
fof(f435,plain,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f14,f104]) ).
fof(f439,plain,
! [X0] :
( subgroup_member(d)
| subgroup_member(d)
| subgroup_member(multiply(X0,identity))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f359,f104]) ).
fof(f441,definition,
! [X0,X1] :
( sQ11_spl
<=> ( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ11_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f435,f36,f441]) ).
fof(f450,definition,
! [X0] :
( sQ13_spl
<=> ( subgroup_member(multiply(X0,identity))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f439,f450,f139]) ).
fof(f456,plain,
( sQ6_spl
| subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a) ),
inference(paramodulation,[status(thm)],[f418,f22]) ).
fof(f461,plain,
( sQ5_spl
| sQ9_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f456,f77,f139,f74]) ).
fof(f462,plain,
$false,
inference(sat_refutation,[status(thm)],[f39,f42,f80,f89,f113,f142,f255,f264,f266,f444,f453,f461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n011.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sun Sep 20 19:55:15 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.12/5.41 % Refutation found
% 0.12/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.43 % Elapsed time: 0.064663 seconds
% 0.12/5.43 % CPU time: 0.211466 seconds
% 0.12/5.43 % Total memory used: 103.536 MB
% 0.12/5.43 % Net memory used: 102.971 MB
%------------------------------------------------------------------------------