%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:32:22 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 66
% Syntax : Number of formulae : 252 ( 51 unt; 51 def)
% Number of atoms : 623 ( 74 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 615 ( 244 ~; 320 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 54 ( 52 usr; 52 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 194 ( 194 !; 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(f8,axiom,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] :
( subgroup_member(element_in_O2(X,Y))
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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(f13,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [Z] :
( subgroup_member(Z)
| ! [X,Y] :
( multiply(X,Y) != Z
| ~ subgroup_member(Y)
| ~ subgroup_member(X) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| multiply(X0,X1) != X2
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
inverse(identity) = identity,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0,X1] :
( multiply(X0,element_in_O2(X0,X1)) = X1
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
multiply(b,inverse(a)) = c,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f32,plain,
multiply(a,c) = d,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f40,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f25,f20]) ).
fof(f41,definition,
( sQ0_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f52,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f18,f34]) ).
fof(f53,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(paramodulation,[status(thm)],[f31,f34]) ).
fof(f54,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(paramodulation,[status(thm)],[f32,f34]) ).
fof(f57,definition,
! [X0] :
( sQ1_spl
<=> ( ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f58,plain,
! [X0] :
( ~ sQ1_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f52,f57,f41]) ).
fof(f61,definition,
( sQ2_spl
<=> subgroup_member(b) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ2_spl
| ~ subgroup_member(b) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ3_spl
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( sQ3_spl
| ~ subgroup_member(inverse(a)) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,definition,
( sQ4_spl
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f53,f61,f64,f67]) ).
fof(f71,definition,
( sQ5_spl
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f74,definition,
( sQ6_spl
<=> subgroup_member(d) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ6_spl
| subgroup_member(d) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f54,f71,f67,f74]) ).
fof(f79,plain,
! [X0] :
( ~ sQ1_spl
| ~ subgroup_member(inverse(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f40]) ).
fof(f80,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f33]) ).
fof(f81,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ sQ1_spl
| ~ subgroup_member(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f20,f79]) ).
fof(f85,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(paramodulation,[status(thm)],[f24,f19]) ).
fof(f88,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f89,plain,
! [X0] : multiply(c,X0) = multiply(b,multiply(inverse(a),X0)),
inference(paramodulation,[status(thm)],[f31,f19]) ).
fof(f90,plain,
! [X0] : multiply(d,X0) = multiply(a,multiply(c,X0)),
inference(paramodulation,[status(thm)],[f32,f19]) ).
fof(f93,plain,
! [X0,X1,X2] :
( subgroup_member(multiply(X0,multiply(X1,X2)))
| ~ subgroup_member(X2)
| ~ subgroup_member(multiply(X0,X1)) ),
inference(paramodulation,[status(thm)],[f19,f34]) ).
fof(f96,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f30,f82]) ).
fof(f97,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f118,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(X0)
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f17,f34]) ).
fof(f124,definition,
! [X0] :
( sQ7_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f118,f41,f124]) ).
fof(f133,plain,
! [X0,X1,X2] :
( multiply(X0,multiply(X1,element_in_O2(multiply(X0,X1),X2))) = X2
| subgroup_member(X2)
| subgroup_member(multiply(X0,X1)) ),
inference(paramodulation,[status(thm)],[f19,f29]) ).
fof(f138,plain,
! [X0,X1,X2] :
( subgroup_member(X0)
| subgroup_member(X2)
| multiply(X0,X1) = multiply(X2,multiply(element_in_O2(X2,X0),X1)) ),
inference(paramodulation,[status(thm)],[f29,f19]) ).
fof(f155,plain,
! [X0,X1,X2] : identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(multiply(X0,X1),X2))))),
inference(paramodulation,[status(thm)],[f19,f85]) ).
fof(f165,plain,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| identity = multiply(X0,multiply(element_in_O2(X0,X1),inverse(X1))) ),
inference(paramodulation,[status(thm)],[f29,f85]) ).
fof(f172,plain,
! [X0,X1,X2] : identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[status(thm)],[f19,f155]) ).
fof(f193,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f88]) ).
fof(f196,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f25,f193]) ).
fof(f203,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f85,f193]) ).
fof(f209,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(multiply(X0,X1))
| ~ subgroup_member(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f193,f34]) ).
fof(f215,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f23,f203]) ).
fof(f221,plain,
! [X0] : multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(paramodulation,[status(thm)],[f193,f89]) ).
fof(f222,plain,
multiply(c,a) = multiply(b,identity),
inference(paramodulation,[status(thm)],[f18,f89]) ).
fof(f230,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| ~ subgroup_member(multiply(inverse(a),X0))
| ~ subgroup_member(b) ),
inference(paramodulation,[status(thm)],[f89,f34]) ).
fof(f233,plain,
multiply(c,a) = b,
inference(forward_demodulation,[status(thm)],[f23,f222]) ).
fof(f245,definition,
! [X0] :
( sQ13_spl
<=> ( subgroup_member(multiply(c,X0))
| ~ subgroup_member(multiply(inverse(a),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ13_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f230,f61,f245]) ).
fof(f251,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f30]) ).
fof(f252,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f254,plain,
a = multiply(inverse(c),b),
inference(paramodulation,[status(thm)],[f233,f193]) ).
fof(f267,plain,
multiply(d,a) = multiply(a,b),
inference(paramodulation,[status(thm)],[f233,f90]) ).
fof(f271,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(paramodulation,[status(thm)],[f24,f90]) ).
fof(f284,plain,
multiply(d,inverse(c)) = a,
inference(forward_demodulation,[status(thm)],[f23,f271]) ).
fof(f294,plain,
( sQ3_spl
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[f66,f20]) ).
fof(f315,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(multiply(inverse(X0),X1))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f196,f34]) ).
fof(f331,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(paramodulation,[status(thm)],[f254,f34]) ).
fof(f335,definition,
( sQ16_spl
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ16_spl
| ~ subgroup_member(inverse(c)) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,plain,
( sQ5_spl
| ~ sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f331,f335,f61,f71]) ).
fof(f339,plain,
( sQ16_spl
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f337,f20]) ).
fof(f340,plain,
inverse(c) = multiply(inverse(d),a),
inference(paramodulation,[status(thm)],[f284,f193]) ).
fof(f353,definition,
( sQ17_spl
<=> subgroup_member(inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ17_spl
| ~ subgroup_member(inverse(b)) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f357,plain,
( sQ17_spl
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f355,f20]) ).
fof(f358,plain,
( sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f357,f61,f353]) ).
fof(f359,plain,
( sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f294,f71,f64]) ).
fof(f362,plain,
( sQ16_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f339,f67,f335]) ).
fof(f370,plain,
multiply(inverse(c),inverse(a)) = inverse(d),
inference(paramodulation,[status(thm)],[f284,f215]) ).
fof(f371,plain,
multiply(a,inverse(b)) = inverse(c),
inference(paramodulation,[status(thm)],[f233,f215]) ).
fof(f386,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f215,f215]) ).
fof(f412,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f25,f386]) ).
fof(f441,definition,
( sQ20_spl
<=> subgroup_member(inverse(d)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ20_spl
| ~ subgroup_member(inverse(d)) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f479,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f196,f412]) ).
fof(f519,plain,
! [X0,X1] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X1))
| ~ subgroup_member(inverse(inverse(multiply(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f412,f209]) ).
fof(f525,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(identity)
| ~ subgroup_member(inverse(inverse(X0))) ),
inference(paramodulation,[status(thm)],[f18,f209]) ).
fof(f527,plain,
! [X0] :
( subgroup_member(multiply(inverse(a),X0))
| ~ subgroup_member(multiply(c,X0))
| ~ subgroup_member(inverse(b)) ),
inference(paramodulation,[status(thm)],[f89,f209]) ).
fof(f537,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(identity)
| ~ subgroup_member(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f24,f209]) ).
fof(f542,definition,
( sQ21_spl
<=> subgroup_member(inverse(identity)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f546,plain,
! [X0,X1] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X1))
| ~ subgroup_member(multiply(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f25,f519]) ).
fof(f551,definition,
( sQ23_spl
<=> subgroup_member(inverse(inverse(b))) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f564,definition,
! [X0] :
( sQ26_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(inverse(inverse(X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f525,f564,f41]) ).
fof(f569,definition,
! [X0] :
( sQ27_spl
<=> ( subgroup_member(multiply(inverse(a),X0))
| ~ subgroup_member(multiply(c,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( sQ27_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f527,f353,f569]) ).
fof(f582,definition,
! [X0] :
( sQ29_spl
<=> ( subgroup_member(inverse(X0))
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( ~ sQ0_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f537,f582,f41]) ).
fof(f603,plain,
! [X0] :
( subgroup_member(multiply(X0,a))
| ~ subgroup_member(b)
| ~ subgroup_member(multiply(X0,inverse(c))) ),
inference(paramodulation,[status(thm)],[f254,f93]) ).
fof(f606,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,identity))
| ~ subgroup_member(X1)
| ~ subgroup_member(multiply(X0,inverse(X1))) ),
inference(paramodulation,[status(thm)],[f18,f93]) ).
fof(f610,plain,
! [X0] :
( subgroup_member(multiply(X0,inverse(c)))
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(multiply(X0,a)) ),
inference(paramodulation,[status(thm)],[f371,f93]) ).
fof(f611,plain,
! [X0] :
( subgroup_member(multiply(X0,multiply(d,a)))
| ~ subgroup_member(b)
| ~ subgroup_member(multiply(X0,a)) ),
inference(paramodulation,[status(thm)],[f267,f93]) ).
fof(f616,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(identity)
| ~ subgroup_member(multiply(X0,X1)) ),
inference(paramodulation,[status(thm)],[f23,f93]) ).
fof(f638,definition,
( sQ34_spl
<=> subgroup_member(multiply(a,c)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( ~ sQ34_spl
| subgroup_member(multiply(a,c)) ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f670,definition,
! [X0] :
( sQ42_spl
<=> ( subgroup_member(multiply(X0,a))
| ~ subgroup_member(multiply(X0,inverse(c))) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( ~ sQ2_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f603,f670,f61]) ).
fof(f678,plain,
! [X0,X1] :
( subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ subgroup_member(multiply(X0,inverse(X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f606]) ).
fof(f687,definition,
! [X0] :
( sQ46_spl
<=> ( subgroup_member(multiply(X0,inverse(c)))
| ~ subgroup_member(multiply(X0,a)) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f690,plain,
( ~ sQ17_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f610,f687,f353]) ).
fof(f691,definition,
! [X0] :
( sQ47_spl
<=> ( subgroup_member(multiply(X0,multiply(d,a)))
| ~ subgroup_member(multiply(X0,a)) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f694,plain,
( ~ sQ2_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f611,f691,f61]) ).
fof(f700,definition,
! [X0,X1] :
( sQ49_spl
<=> ( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(multiply(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f703,plain,
( ~ sQ0_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f616,f700,f41]) ).
fof(f711,plain,
! [X0] :
( multiply(d,element_in_O2(multiply(a,c),X0)) = X0
| subgroup_member(X0)
| subgroup_member(multiply(a,c)) ),
inference(paramodulation,[status(thm)],[f90,f133]) ).
fof(f733,plain,
! [X0] :
( multiply(a,multiply(c,element_in_O2(d,X0))) = X0
| subgroup_member(X0)
| subgroup_member(multiply(a,c)) ),
inference(paramodulation,[status(thm)],[f32,f133]) ).
fof(f767,definition,
! [X0] :
( sQ51_spl
<=> ( multiply(d,element_in_O2(multiply(a,c),X0)) = X0
| subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f768,plain,
! [X0] :
( ~ sQ51_spl
| multiply(d,element_in_O2(multiply(a,c),X0)) = X0
| subgroup_member(X0) ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f770,plain,
( sQ51_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f711,f638,f767]) ).
fof(f789,definition,
( sQ56_spl
<=> subgroup_member(multiply(c,a)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f791,plain,
( sQ56_spl
| ~ subgroup_member(multiply(c,a)) ),
inference(component_clause,[status(thm)],[f789]) ).
fof(f865,definition,
! [X0] :
( sQ73_spl
<=> ( multiply(a,multiply(c,element_in_O2(d,X0))) = X0
| subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f868,plain,
( sQ73_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f733,f638,f865]) ).
fof(f915,plain,
! [X0] :
( ~ sQ51_spl
| multiply(d,element_in_O2(d,X0)) = X0
| subgroup_member(X0) ),
inference(forward_demodulation,[status(thm)],[f32,f768]) ).
fof(f934,plain,
! [X0] :
( ~ sQ51_spl
| subgroup_member(X0)
| subgroup_member(d)
| X0 = X0
| subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f29,f915]) ).
fof(f938,plain,
! [X0] :
( ~ sQ51_spl
| subgroup_member(X0)
| subgroup_member(element_in_O2(d,X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(d)) ),
inference(paramodulation,[status(thm)],[f915,f209]) ).
fof(f941,plain,
! [X0] :
( ~ sQ51_spl
| subgroup_member(X0)
| element_in_O2(d,X0) = multiply(inverse(d),X0) ),
inference(paramodulation,[status(thm)],[f915,f193]) ).
fof(f944,definition,
! [X0] :
( sQ74_spl
<=> ( subgroup_member(X0)
| X0 = X0
| subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f947,plain,
( ~ sQ51_spl
| sQ6_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f934,f944,f74,f767]) ).
fof(f949,definition,
! [X0] :
( sQ75_spl
<=> ( subgroup_member(X0)
| subgroup_member(element_in_O2(d,X0))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f952,plain,
( ~ sQ51_spl
| sQ75_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f938,f441,f949,f767]) ).
fof(f992,plain,
! [X0] :
( subgroup_member(multiply(b,X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(multiply(c,a)) ),
inference(paramodulation,[status(thm)],[f221,f93]) ).
fof(f1013,definition,
! [X0] :
( sQ81_spl
<=> ( subgroup_member(multiply(b,X0))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1014,plain,
! [X0] :
( ~ sQ81_spl
| subgroup_member(multiply(b,X0))
| ~ subgroup_member(X0) ),
inference(component_clause,[status(thm)],[f1013]) ).
fof(f1016,plain,
( sQ81_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f992,f789,f1013]) ).
fof(f1034,plain,
( sQ56_spl
| ~ subgroup_member(b) ),
inference(forward_demodulation,[status(thm)],[f233,f791]) ).
fof(f1035,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1034,f30]) ).
fof(f1036,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f1035]) ).
fof(f1041,plain,
! [X0] :
( ~ sQ81_spl
| subgroup_member(X0)
| ~ subgroup_member(multiply(inverse(b),X0)) ),
inference(paramodulation,[status(thm)],[f196,f1014]) ).
fof(f1045,plain,
! [X0] :
( ~ sQ81_spl
| subgroup_member(inverse(X0))
| ~ subgroup_member(inverse(multiply(X0,b))) ),
inference(paramodulation,[status(thm)],[f215,f1014]) ).
fof(f1067,plain,
( ~ sQ81_spl
| subgroup_member(inverse(inverse(b)))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f24,f1041]) ).
fof(f1077,plain,
( ~ sQ81_spl
| sQ23_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1067,f41,f551,f1013]) ).
fof(f1094,plain,
! [X0] :
( subgroup_member(inverse(inverse(X0)))
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f24,f315]) ).
fof(f1095,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(multiply(identity,X0))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f26,f315]) ).
fof(f1105,definition,
! [X0] :
( sQ86_spl
<=> ( subgroup_member(inverse(inverse(X0)))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1108,plain,
( ~ sQ0_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1094,f1105,f41]) ).
fof(f1109,definition,
! [X0] :
( sQ87_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(multiply(identity,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
( sQ87_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1095,f41,f1109]) ).
fof(f1177,plain,
! [X0] :
( multiply(inverse(c),multiply(inverse(a),element_in_O2(inverse(d),X0))) = X0
| subgroup_member(X0)
| subgroup_member(multiply(inverse(c),inverse(a))) ),
inference(paramodulation,[status(thm)],[f370,f133]) ).
fof(f1186,definition,
( sQ94_spl
<=> subgroup_member(multiply(inverse(c),inverse(a))) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1187,plain,
( ~ sQ94_spl
| subgroup_member(multiply(inverse(c),inverse(a))) ),
inference(component_clause,[status(thm)],[f1186]) ).
fof(f1189,definition,
! [X0] :
( sQ95_spl
<=> ( multiply(inverse(c),multiply(inverse(a),element_in_O2(inverse(d),X0))) = X0
| subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1192,plain,
( sQ95_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1177,f1186,f1189]) ).
fof(f1204,plain,
( ~ sQ94_spl
| subgroup_member(inverse(d)) ),
inference(forward_demodulation,[status(thm)],[f370,f1187]) ).
fof(f1205,plain,
( ~ sQ94_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1204,f443]) ).
fof(f1206,plain,
( ~ sQ94_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f1205]) ).
fof(f1507,plain,
! [X0] :
( ~ sQ51_spl
| subgroup_member(X0)
| subgroup_member(d)
| ~ subgroup_member(inverse(element_in_O2(d,X0)))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f915,f546]) ).
fof(f1541,definition,
! [X0] :
( sQ106_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(inverse(element_in_O2(d,X0)))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1544,plain,
( ~ sQ51_spl
| sQ6_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1507,f1541,f74,f767]) ).
fof(f1592,plain,
( ~ sQ34_spl
| subgroup_member(d) ),
inference(forward_demodulation,[status(thm)],[f32,f639]) ).
fof(f1593,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1592,f33]) ).
fof(f1594,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f1593]) ).
fof(f1667,plain,
! [X0,X1] :
( ~ sQ81_spl
| subgroup_member(multiply(X0,multiply(X1,inverse(multiply(inverse(b),multiply(X0,X1))))))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f172,f1041]) ).
fof(f1671,plain,
! [X0,X1,X2] :
( subgroup_member(multiply(X1,multiply(X2,inverse(multiply(inverse(X0),multiply(X1,X2))))))
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f172,f315]) ).
fof(f1680,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ subgroup_member(inverse(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1)))))))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f172,f546]) ).
fof(f1683,plain,
! [X0,X1,X2] :
( subgroup_member(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2))))))
| ~ subgroup_member(identity)
| ~ subgroup_member(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f172,f209]) ).
fof(f1816,definition,
! [X0,X1] :
( sQ113_spl
<=> subgroup_member(multiply(X0,multiply(X1,inverse(multiply(inverse(b),multiply(X0,X1)))))) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1819,plain,
( ~ sQ81_spl
| sQ113_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1667,f41,f1816,f1013]) ).
fof(f1826,definition,
! [X0,X1,X2] :
( sQ114_spl
<=> ( subgroup_member(multiply(X1,multiply(X2,inverse(multiply(inverse(X0),multiply(X1,X2))))))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1829,plain,
( ~ sQ0_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1671,f1826,f41]) ).
fof(f1846,definition,
! [X0,X1,X2] :
( sQ117_spl
<=> ( subgroup_member(X2)
| ~ subgroup_member(inverse(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1))))))) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1849,plain,
( sQ117_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1680,f41,f1846]) ).
fof(f1854,definition,
! [X0,X1,X2] :
( sQ118_spl
<=> ( subgroup_member(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2))))))
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1857,plain,
( ~ sQ0_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f1683,f1854,f41]) ).
fof(f1927,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(identity)
| ~ subgroup_member(multiply(X0,identity)) ),
inference(paramodulation,[status(thm)],[f26,f678]) ).
fof(f1939,definition,
! [X0] :
( sQ120_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(multiply(X0,identity)) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1942,plain,
( ~ sQ0_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f1927,f1939,f41]) ).
fof(f1943,plain,
! [X0] :
( ~ sQ81_spl
| ~ subgroup_member(multiply(X0,b))
| subgroup_member(inverse(X0)) ),
inference(resolution,[status(thm)],[f1045,f20]) ).
fof(f1946,plain,
( ~ sQ81_spl
| subgroup_member(inverse(identity))
| ~ subgroup_member(inverse(b)) ),
inference(paramodulation,[status(thm)],[f17,f1045]) ).
fof(f1952,plain,
( ~ sQ81_spl
| sQ21_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1946,f353,f542,f1013]) ).
fof(f1960,plain,
! [X0] :
( ~ sQ81_spl
| ~ subgroup_member(b)
| ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ),
inference(resolution,[status(thm)],[f1943,f34]) ).
fof(f1963,plain,
! [X0] :
( ~ sQ81_spl
| ~ subgroup_member(inverse(X0))
| subgroup_member(inverse(inverse(multiply(b,X0)))) ),
inference(paramodulation,[status(thm)],[f412,f1943]) ).
fof(f1968,definition,
! [X0] :
( sQ121_spl
<=> ( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1971,plain,
( ~ sQ81_spl
| ~ sQ2_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1960,f1968,f61,f1013]) ).
fof(f1973,plain,
! [X0] :
( ~ sQ81_spl
| ~ subgroup_member(inverse(X0))
| subgroup_member(multiply(b,X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f1963]) ).
fof(f1980,plain,
! [X0] :
( ~ sQ81_spl
| subgroup_member(X0)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(X0)) ),
inference(resolution,[status(thm)],[f1973,f209]) ).
fof(f1985,plain,
! [X0] :
( ~ sQ81_spl
| ~ subgroup_member(inverse(multiply(inverse(b),X0)))
| subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f196,f1973]) ).
fof(f2001,definition,
! [X0] :
( sQ124_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f2004,plain,
( ~ sQ81_spl
| ~ sQ17_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1980,f2001,f353,f1013]) ).
fof(f2012,plain,
! [X0] :
( ~ sQ81_spl
| ~ subgroup_member(multiply(inverse(X0),b))
| subgroup_member(X0) ),
inference(forward_demodulation,[status(thm)],[f479,f1985]) ).
fof(f2027,plain,
( ~ sQ81_spl
| ~ subgroup_member(a)
| subgroup_member(c) ),
inference(paramodulation,[status(thm)],[f254,f2012]) ).
fof(f2034,plain,
( ~ sQ81_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f2027,f67,f71,f1013]) ).
fof(f2056,plain,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(inverse(X0))
| subgroup_member(multiply(element_in_O2(inverse(X0),X1),inverse(X1)))
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f165,f315]) ).
fof(f2065,plain,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(X0)
| ~ subgroup_member(inverse(multiply(element_in_O2(X0,X1),inverse(X1))))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f165,f546]) ).
fof(f2068,plain,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(multiply(element_in_O2(X0,X1),inverse(X1)))
| ~ subgroup_member(identity)
| ~ subgroup_member(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f165,f209]) ).
fof(f2106,definition,
! [X0,X1] :
( sQ136_spl
<=> ( subgroup_member(X1)
| subgroup_member(inverse(X0))
| subgroup_member(multiply(element_in_O2(inverse(X0),X1),inverse(X1)))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f2109,plain,
( ~ sQ0_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f2056,f2106,f41]) ).
fof(f2134,definition,
! [X0,X1] :
( sQ141_spl
<=> ( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(X0)
| ~ subgroup_member(inverse(multiply(element_in_O2(X0,X1),inverse(X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( sQ141_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2065,f41,f2134]) ).
fof(f2140,definition,
! [X0,X1] :
( sQ142_spl
<=> ( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(multiply(element_in_O2(X0,X1),inverse(X1)))
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f2143,plain,
( ~ sQ0_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f2068,f2140,f41]) ).
fof(f3014,plain,
( ~ sQ51_spl
| subgroup_member(a)
| element_in_O2(d,a) = inverse(c) ),
inference(paramodulation,[status(thm)],[f340,f941]) ).
fof(f3017,plain,
( ~ sQ51_spl
| subgroup_member(d)
| element_in_O2(d,d) = identity ),
inference(paramodulation,[status(thm)],[f18,f941]) ).
fof(f3018,plain,
! [X0] :
( ~ sQ51_spl
| subgroup_member(X0)
| subgroup_member(inverse(d))
| subgroup_member(element_in_O2(inverse(d),X0))
| element_in_O2(d,element_in_O2(inverse(d),X0)) = X0 ),
inference(paramodulation,[status(thm)],[f29,f941]) ).
fof(f3019,plain,
! [X0,X1] :
( ~ sQ51_spl
| subgroup_member(X0)
| subgroup_member(inverse(d))
| subgroup_member(multiply(element_in_O2(inverse(d),X0),X1))
| element_in_O2(d,multiply(element_in_O2(inverse(d),X0),X1)) = multiply(X0,X1) ),
inference(paramodulation,[status(thm)],[f138,f941]) ).
fof(f3047,plain,
! [X0] :
( ~ sQ51_spl
| subgroup_member(inverse(X0))
| subgroup_member(inverse(d))
| ~ subgroup_member(X0)
| ~ subgroup_member(element_in_O2(d,inverse(X0))) ),
inference(paramodulation,[status(thm)],[f941,f678]) ).
fof(f3051,plain,
! [X0] :
( ~ sQ51_spl
| subgroup_member(X0)
| subgroup_member(inverse(d))
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(element_in_O2(d,X0)) ),
inference(paramodulation,[status(thm)],[f941,f546]) ).
fof(f3059,definition,
( sQ162_spl
<=> element_in_O2(d,a) = inverse(c) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f3060,plain,
( ~ sQ162_spl
| element_in_O2(d,a) = inverse(c) ),
inference(component_clause,[status(thm)],[f3059]) ).
fof(f3062,plain,
( ~ sQ51_spl
| sQ5_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f3014,f3059,f71,f767]) ).
fof(f3063,definition,
( sQ163_spl
<=> element_in_O2(d,d) = identity ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f3064,plain,
( ~ sQ163_spl
| element_in_O2(d,d) = identity ),
inference(component_clause,[status(thm)],[f3063]) ).
fof(f3066,plain,
( ~ sQ51_spl
| sQ6_spl
| sQ163_spl ),
inference(split_clause,[status(thm)],[f3017,f3063,f74,f767]) ).
fof(f3067,definition,
! [X0] :
( sQ164_spl
<=> ( subgroup_member(X0)
| subgroup_member(element_in_O2(inverse(d),X0))
| element_in_O2(d,element_in_O2(inverse(d),X0)) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f3070,plain,
( ~ sQ51_spl
| sQ20_spl
| sQ164_spl ),
inference(split_clause,[status(thm)],[f3018,f3067,f441,f767]) ).
fof(f3071,definition,
! [X0,X1] :
( sQ165_spl
<=> ( subgroup_member(X0)
| subgroup_member(multiply(element_in_O2(inverse(d),X0),X1))
| element_in_O2(d,multiply(element_in_O2(inverse(d),X0),X1)) = multiply(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f3074,plain,
( ~ sQ51_spl
| sQ20_spl
| sQ165_spl ),
inference(split_clause,[status(thm)],[f3019,f3071,f441,f767]) ).
fof(f3110,definition,
! [X0] :
( sQ170_spl
<=> ( subgroup_member(inverse(X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(element_in_O2(d,inverse(X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f3113,plain,
( ~ sQ51_spl
| sQ20_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f3047,f3110,f441,f767]) ).
fof(f3117,definition,
! [X0] :
( sQ171_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(element_in_O2(d,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f3120,plain,
( ~ sQ51_spl
| sQ20_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f3051,f3117,f441,f767]) ).
fof(f3217,plain,
! [X0] :
( ~ sQ163_spl
| subgroup_member(d)
| subgroup_member(d)
| multiply(d,X0) = multiply(d,multiply(identity,X0)) ),
inference(paramodulation,[status(thm)],[f3064,f138]) ).
fof(f3219,plain,
( ~ sQ163_spl
| multiply(d,identity) = d
| subgroup_member(d)
| subgroup_member(d) ),
inference(paramodulation,[status(thm)],[f3064,f29]) ).
fof(f3220,definition,
( sQ173_spl
<=> multiply(d,identity) = d ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f3224,definition,
! [X0] :
( sQ174_spl
<=> multiply(d,X0) = multiply(d,multiply(identity,X0)) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f3227,plain,
( ~ sQ163_spl
| sQ6_spl
| sQ174_spl ),
inference(split_clause,[status(thm)],[f3217,f3224,f74,f3063]) ).
fof(f3229,plain,
( ~ sQ163_spl
| sQ173_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f3219,f74,f3220,f3063]) ).
fof(f3232,plain,
( ~ sQ162_spl
| subgroup_member(inverse(c))
| subgroup_member(a)
| subgroup_member(d) ),
inference(paramodulation,[status(thm)],[f3060,f28]) ).
fof(f3242,plain,
( ~ sQ162_spl
| sQ16_spl
| sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f3232,f74,f71,f335,f3059]) ).
fof(f3244,plain,
$false,
inference(sat_refutation,[status(thm)],[f60,f70,f77,f81,f97,f127,f248,f252,f338,f358,f359,f362,f567,f572,f585,f673,f690,f694,f703,f770,f868,f947,f952,f1016,f1036,f1077,f1108,f1112,f1192,f1206,f1544,f1594,f1819,f1829,f1849,f1857,f1942,f1952,f1971,f2004,f2034,f2109,f2137,f2143,f3062,f3066,f3070,f3074,f3113,f3120,f3227,f3229,f3242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.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 19:55:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.49 % Refutation found
% 0.14/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.52 % Elapsed time: 0.148245 seconds
% 0.14/0.52 % CPU time: 0.869082 seconds
% 0.14/0.52 % Total memory used: 117.758 MB
% 0.14/0.52 % Net memory used: 115.975 MB
%------------------------------------------------------------------------------