%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP039-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 138 ( 37 unt; 16 def)
% Number of atoms : 305 ( 31 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 300 ( 133 ~; 151 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 17 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 168 ( 168 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C,D] :
( D = B
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,C,D] :
( D = A
| ~ product(D,B,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : inverse(inverse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( subgroup_member(inverse(A))
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f33,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [B,D] :
( D = B
| ! [A,C] :
( ~ product(A,D,C)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [A,D] :
( D = A
| ! [B,C] :
( ~ product(D,B,C)
| ~ product(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( X3 = X0
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
subgroup_member(identity),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f41,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f42,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| product(A,element_in_O2(A,B),B) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f44,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
product(a,c,d),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
! [X0] :
( X0 = d
| ~ product(a,c,X0) ),
inference(resolution,[status(thm)],[f27,f47]) ).
fof(f56,plain,
! [X0] :
( inverse(a) = X0
| ~ product(b,X0,c) ),
inference(resolution,[status(thm)],[f35,f46]) ).
fof(f57,plain,
! [X0] :
( c = X0
| ~ product(a,X0,d) ),
inference(resolution,[status(thm)],[f35,f47]) ).
fof(f65,plain,
! [X0] :
( product(X0,c,c)
| ~ product(X0,b,b) ),
inference(resolution,[status(thm)],[f29,f46]) ).
fof(f72,plain,
! [X0,X1,X2] :
( product(X1,inverse(a),X2)
| ~ product(X0,c,X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f31,f46]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( product(X0,X3,X2)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[f21,f29]) ).
fof(f85,plain,
! [X0,X1] :
( identity = X0
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[f21,f37]) ).
fof(f86,plain,
! [X0,X1] :
( X1 = X0
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f21,f35]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X0)
| ~ product(X1,X3,identity)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f22,f31]) ).
fof(f96,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f22,f37]) ).
fof(f122,plain,
multiply(a,c) = d,
inference(resolution,[status(thm)],[f25,f51]) ).
fof(f130,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,X1,multiply(X0,X2)) ),
inference(resolution,[status(thm)],[f25,f35]) ).
fof(f131,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f132,plain,
identity = inverse(identity),
inference(resolution,[status(thm)],[f85,f23]) ).
fof(f140,definition,
( sQ0_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ0_spl
| ~ subgroup_member(identity) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f148,plain,
! [X0] : multiply(identity,X0) = X0,
inference(resolution,[status(thm)],[f86,f25]) ).
fof(f153,plain,
! [X0] : multiply(X0,identity) = X0,
inference(resolution,[status(thm)],[f96,f25]) ).
fof(f161,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[f33,f21]) ).
fof(f162,plain,
( subgroup_member(c)
| ~ subgroup_member(a)
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f33,f46]) ).
fof(f164,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f33,f25]) ).
fof(f165,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ product(X0,identity,X1)
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f132,f33]) ).
fof(f171,definition,
! [X0] :
( sQ2_spl
<=> ( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f161,f140,f171]) ).
fof(f175,definition,
( sQ3_spl
<=> subgroup_member(b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( sQ3_spl
| ~ subgroup_member(b) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ4_spl
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f181,definition,
( sQ5_spl
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ5_spl
| subgroup_member(c) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f162,f175,f178,f181]) ).
fof(f189,definition,
! [X0,X1] :
( sQ7_spl
<=> ( subgroup_member(X1)
| ~ product(X0,identity,X1)
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ0_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f165,f189,f140]) ).
fof(f198,plain,
( c = element_in_O2(a,d)
| subgroup_member(a)
| subgroup_member(d) ),
inference(resolution,[status(thm)],[f44,f57]) ).
fof(f217,definition,
( sQ10_spl
<=> subgroup_member(d) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ10_spl
| subgroup_member(d) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,definition,
( sQ11_spl
<=> c = element_in_O2(a,d) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( ~ sQ11_spl
| c = element_in_O2(a,d) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( sQ11_spl
| sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f198,f217,f178,f220]) ).
fof(f225,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f39]) ).
fof(f226,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f229,plain,
( ~ sQ11_spl
| subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(paramodulation,[status(thm)],[f221,f42]) ).
fof(f234,plain,
( ~ sQ11_spl
| sQ4_spl
| sQ10_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f229,f181,f217,f178,f220]) ).
fof(f235,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f48]) ).
fof(f236,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f345,definition,
( sQ17_spl
<=> subgroup_member(inverse(identity)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ17_spl
| ~ subgroup_member(inverse(identity)) ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f354,plain,
! [X0] :
( subgroup_member(multiply(X0,identity))
| ~ subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f132,f164]) ).
fof(f355,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(inverse(X1))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f38,f164]) ).
fof(f360,definition,
! [X0] :
( sQ18_spl
<=> ( subgroup_member(multiply(X0,identity))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( ~ sQ0_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f354,f360,f140]) ).
fof(f384,plain,
! [X0] :
( inverse(a) = inverse(a)
| ~ product(X0,c,c)
| ~ product(X0,b,b) ),
inference(resolution,[status(thm)],[f72,f56]) ).
fof(f412,definition,
! [X0] :
( sQ19_spl
<=> ( ~ product(X0,c,c)
| ~ product(X0,b,b) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f413,plain,
! [X0] :
( ~ sQ19_spl
| ~ product(X0,c,c)
| ~ product(X0,b,b) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f415,definition,
( sQ20_spl
<=> inverse(a) = inverse(a) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f384,f412,f415]) ).
fof(f438,plain,
! [X0] :
( ~ sQ19_spl
| ~ product(X0,b,b) ),
inference(forward_subsumption_resolution,[status(thm)],[f413,f65]) ).
fof(f439,plain,
( ~ sQ19_spl
| $false ),
inference(resolution,[status(thm)],[f438,f21]) ).
fof(f440,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f456,plain,
( subgroup_member(d)
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(a) ),
inference(paramodulation,[status(thm)],[f122,f355]) ).
fof(f457,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(identity) ),
inference(paramodulation,[status(thm)],[f148,f355]) ).
fof(f460,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(identity))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f153,f355]) ).
fof(f469,definition,
( sQ28_spl
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ28_spl
| ~ subgroup_member(inverse(c)) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( sQ10_spl
| ~ sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f456,f178,f469,f217]) ).
fof(f473,definition,
! [X0] :
( sQ29_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( sQ29_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f457,f140,f473]) ).
fof(f478,definition,
! [X0] :
( sQ30_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ17_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f460,f478,f345]) ).
fof(f482,plain,
( sQ17_spl
| ~ subgroup_member(identity) ),
inference(forward_demodulation,[status(thm)],[f132,f347]) ).
fof(f483,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f39]) ).
fof(f484,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( sQ28_spl
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f471,f40]) ).
fof(f487,plain,
( sQ28_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f182]) ).
fof(f488,plain,
( sQ28_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f540,plain,
! [X0,X1,X2] :
( product(X0,X2,X1)
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f82,f24]) ).
fof(f621,plain,
! [X0,X1] : product(X0,multiply(inverse(X0),X1),X1),
inference(resolution,[status(thm)],[f540,f25]) ).
fof(f647,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f45]) ).
fof(f648,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f647]) ).
fof(f787,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f621,f130]) ).
fof(f833,plain,
! [X0,X1,X2] :
( product(X2,X1,X0)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f89,f23]) ).
fof(f1102,plain,
product(c,a,b),
inference(resolution,[status(thm)],[f833,f46]) ).
fof(f1115,plain,
b = multiply(c,a),
inference(resolution,[status(thm)],[f1102,f131]) ).
fof(f1127,plain,
a = multiply(inverse(c),b),
inference(paramodulation,[status(thm)],[f1115,f787]) ).
fof(f1264,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c)) ),
inference(paramodulation,[status(thm)],[f1127,f355]) ).
fof(f1270,definition,
( sQ53_spl
<=> subgroup_member(inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1272,plain,
( sQ53_spl
| ~ subgroup_member(inverse(b)) ),
inference(component_clause,[status(thm)],[f1270]) ).
fof(f1273,plain,
( sQ4_spl
| ~ sQ53_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1264,f469,f1270,f178]) ).
fof(f1274,plain,
( sQ53_spl
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f1272,f40]) ).
fof(f1275,plain,
( sQ53_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1274,f175,f1270]) ).
fof(f1276,plain,
$false,
inference(sat_refutation,[status(thm)],[f174,f184,f192,f223,f226,f234,f236,f363,f418,f440,f472,f476,f481,f484,f488,f648,f1273,f1275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:50:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.080613 seconds
% 0.13/0.45 % CPU time: 0.403506 seconds
% 0.13/0.45 % Total memory used: 105.755 MB
% 0.13/0.45 % Net memory used: 104.721 MB
%------------------------------------------------------------------------------