%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP384-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:33:35 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 70
% Syntax : Number of formulae : 336 ( 12 unt; 30 def)
% Number of atoms : 1191 ( 407 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1579 ( 724 ~; 825 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 31 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 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,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != X4
| multiply(X3,X4) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f66,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f67,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f108,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f109,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f110,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f111,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f112,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f113,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f118,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f119,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f120,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f121,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f122,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f123,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f128,plain,
! [X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X4] :
( multiply(X4,sk_c9) != sk_c10
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,definition,
( sQ0_spl
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ0_spl
| inverse(sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( sQ0_spl
| inverse(sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f130,f133]) ).
fof(f137,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f130,f137]) ).
fof(f141,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f130,f141]) ).
fof(f145,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f130,f145]) ).
fof(f149,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f130,f149]) ).
fof(f153,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f130,f153]) ).
fof(f173,definition,
( sQ11_spl
<=> multiply(sk_c10,sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f175,plain,
( sQ11_spl
| multiply(sk_c10,sk_c9) != sk_c11 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f173,f133]) ).
fof(f177,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f173,f137]) ).
fof(f178,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f173,f141]) ).
fof(f179,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f173,f145]) ).
fof(f180,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f173,f149]) ).
fof(f181,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f173,f153]) ).
fof(f186,definition,
( sQ12_spl
<=> multiply(sk_c11,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ12_spl
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f188,plain,
( sQ12_spl
| multiply(sk_c11,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f186,f133]) ).
fof(f190,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f186,f137]) ).
fof(f191,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f186,f141]) ).
fof(f192,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f186,f145]) ).
fof(f193,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f186,f149]) ).
fof(f194,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f186,f153]) ).
fof(f199,definition,
( sQ13_spl
<=> multiply(sk_c1,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ13_spl
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f199,f133]) ).
fof(f203,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f199,f137]) ).
fof(f204,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f199,f141]) ).
fof(f205,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f199,f145]) ).
fof(f206,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f199,f149]) ).
fof(f207,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f199,f153]) ).
fof(f212,definition,
( sQ14_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ14_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f108,f212,f133]) ).
fof(f216,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f109,f212,f137]) ).
fof(f217,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f110,f212,f141]) ).
fof(f218,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f212,f145]) ).
fof(f219,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f212,f149]) ).
fof(f220,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f113,f212,f153]) ).
fof(f225,definition,
( sQ15_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f118,f225,f133]) ).
fof(f229,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f119,f225,f137]) ).
fof(f230,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f120,f225,f141]) ).
fof(f231,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f121,f225,f145]) ).
fof(f232,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f122,f225,f149]) ).
fof(f233,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f123,f225,f153]) ).
fof(f238,definition,
! [X0,X1] :
( sQ16_spl
<=> ( multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0,X1] :
( ~ sQ16_spl
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
! [X2] :
( sQ17_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f242,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
! [X3] :
( sQ18_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f245,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
! [X4,X5,X6,X7] :
( sQ19_spl
<=> ( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f130,f173,f186,f238,f241,f244,f247]) ).
fof(f251,plain,
! [X0,X1] :
( ~ sQ19_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f248]) ).
fof(f254,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f187,f67]) ).
fof(f285,definition,
( sQ24_spl
<=> multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ24_spl
| multiply(inverse(sk_c3),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f352,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f66,f67]) ).
fof(f353,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f65,f352]) ).
fof(f360,plain,
( ~ sQ18_spl
| inverse(identity) != sk_c10
| sk_c10 != sk_c9 ),
inference(paramodulation,[status(thm)],[f65,f245]) ).
fof(f362,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| inverse(sk_c4) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f142,f245]) ).
fof(f371,definition,
( sQ43_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ43_spl
| sk_c10 = sk_c9 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f373,plain,
( sQ43_spl
| sk_c10 != sk_c9 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,definition,
( sQ44_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ44_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,plain,
( ~ sQ18_spl
| ~ sQ44_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f360,f371,f374,f244]) ).
fof(f378,definition,
( sQ45_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( sQ45_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f362,f378,f145,f244,f141]) ).
fof(f389,plain,
( sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f380]) ).
fof(f390,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f391,plain,
! [X0] :
( ~ sQ16_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f239]) ).
fof(f397,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f134,f242]) ).
fof(f398,definition,
( sQ48_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( ~ sQ48_spl
| identity = sk_c10 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f400,plain,
( sQ48_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f405,definition,
( sQ50_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ50_spl
| sk_c11 = sk_c10 ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f407,plain,
( sQ50_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f416,definition,
( sQ53_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( sQ53_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f397,f416,f137,f241,f133]) ).
fof(f420,plain,
( sQ53_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f418]) ).
fof(f421,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f424,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c11,inverse(sk_c11)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f131,f391]) ).
fof(f425,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| multiply(sk_c2,sk_c9) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f213,f391]) ).
fof(f430,definition,
( sQ55_spl
<=> multiply(sk_c11,inverse(sk_c11)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( sQ55_spl
| multiply(sk_c11,inverse(sk_c11)) != sk_c10 ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,definition,
( sQ56_spl
<=> multiply(sk_c10,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( sQ56_spl
| multiply(sk_c10,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ56_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f424,f430,f433,f238,f130]) ).
fof(f437,definition,
( sQ57_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ57_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f425,f437,f225,f238,f212]) ).
fof(f441,plain,
( sQ57_spl
| ~ sQ14_spl
| multiply(sk_c1,sk_c2) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f213,f439]) ).
fof(f442,plain,
( sQ57_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f200,f441]) ).
fof(f443,plain,
( sQ57_spl
| ~ sQ14_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f442]) ).
fof(f444,plain,
( sQ57_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f500,plain,
( sQ24_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f287]) ).
fof(f514,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f134,f353]) ).
fof(f515,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f142,f353]) ).
fof(f521,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f65,f353]) ).
fof(f523,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c9,X0) = multiply(inverse(sk_c11),multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f254,f353]) ).
fof(f527,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c11) ),
inference(paramodulation,[status(thm)],[f150,f353]) ).
fof(f535,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f138,f514]) ).
fof(f536,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f500]) ).
fof(f537,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f538,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f146,f515]) ).
fof(f539,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f435]) ).
fof(f540,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f154,f527]) ).
fof(f560,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f542,f353]) ).
fof(f564,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f560]) ).
fof(f574,plain,
( sQ48_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f564,f400]) ).
fof(f577,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f564,f66]) ).
fof(f578,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f564,f65]) ).
fof(f593,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f578,f187]) ).
fof(f596,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f593,f373]) ).
fof(f597,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f598,plain,
( sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f578,f188]) ).
fof(f600,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c3) = sk_c11 ),
inference(paramodulation,[status(thm)],[f138,f577]) ).
fof(f605,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f578,f600]) ).
fof(f610,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f605,f578]) ).
fof(f613,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f605,f138]) ).
fof(f623,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f605,f535]) ).
fof(f624,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = multiply(sk_c3,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f605,f623]) ).
fof(f625,plain,
( sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f631,f598]) ).
fof(f631,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f610,f624]) ).
fof(f641,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f631,f538]) ).
fof(f642,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = multiply(sk_c3,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f631,f641]) ).
fof(f643,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f610,f642]) ).
fof(f644,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f643,f625]) ).
fof(f645,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f644]) ).
fof(f646,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c9,X0) = multiply(inverse(sk_c3),multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f605,f523]) ).
fof(f647,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c9,X0) = multiply(sk_c3,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f613,f646]) ).
fof(f648,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c9,X0) = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f610,f647]) ).
fof(f649,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c9,X0) = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f631,f648]) ).
fof(f650,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f610,f649]) ).
fof(f658,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c3,sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f631,f175]) ).
fof(f659,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f610,f658]) ).
fof(f660,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f605,f659]) ).
fof(f663,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f643,f631]) ).
fof(f664,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f643,f613]) ).
fof(f667,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f643,f605]) ).
fof(f668,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f643,f664]) ).
fof(f678,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f643,f660]) ).
fof(f679,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f678]) ).
fof(f680,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f702,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f667,f132]) ).
fof(f703,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f668,f702]) ).
fof(f704,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f663,f703]) ).
fof(f705,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f704]) ).
fof(f706,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f705]) ).
fof(f707,plain,
( sQ48_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f667,f574]) ).
fof(f708,plain,
( sQ48_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f663,f707]) ).
fof(f709,plain,
( sQ48_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f708]) ).
fof(f710,plain,
( sQ48_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f718,plain,
( sQ55_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c9,inverse(sk_c11)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f667,f432]) ).
fof(f719,plain,
( sQ55_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f650,f718]) ).
fof(f720,plain,
( sQ55_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f667,f719]) ).
fof(f721,plain,
( sQ55_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f668,f720]) ).
fof(f722,plain,
( sQ55_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f663,f721]) ).
fof(f723,plain,
( sQ55_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f722]) ).
fof(f724,plain,
( sQ55_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f723]) ).
fof(f740,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f667,f407]) ).
fof(f741,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f663,f740]) ).
fof(f742,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f741]) ).
fof(f743,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f742]) ).
fof(f766,plain,
( ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c11),sk_c10) ),
inference(paramodulation,[status(thm)],[f187,f353]) ).
fof(f768,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f131,f766]) ).
fof(f796,plain,
( ~ sQ13_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f200,f353]) ).
fof(f798,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c2 = multiply(sk_c2,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f213,f796]) ).
fof(f803,plain,
( ~ sQ17_spl
| inverse(inverse(identity)) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramodulation,[status(thm)],[f521,f242]) ).
fof(f808,definition,
( sQ58_spl
<=> inverse(inverse(identity)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f810,plain,
( sQ58_spl
| inverse(inverse(identity)) != sk_c11 ),
inference(component_clause,[status(thm)],[f808]) ).
fof(f811,plain,
( ~ sQ17_spl
| ~ sQ58_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f803,f405,f808,f241]) ).
fof(f835,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f798,f353]) ).
fof(f837,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f835]) ).
fof(f838,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f837,f400]) ).
fof(f839,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f838]) ).
fof(f847,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f837,f65]) ).
fof(f848,plain,
( sQ44_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c10) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f837,f376]) ).
fof(f850,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f847,f768]) ).
fof(f851,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f847,f174]) ).
fof(f867,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c9 = identity ),
inference(backward_demodulation,[status(thm)],[f850,f837]) ).
fof(f880,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c11) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f850,f131]) ).
fof(f919,plain,
( sQ44_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| inverse(sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f850,f848]) ).
fof(f920,plain,
( sQ44_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f850,f919]) ).
fof(f923,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f851,f880]) ).
fof(f924,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f923,f920]) ).
fof(f925,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sQ44_spl ),
inference(contradiction_clause,[status(thm)],[f924]) ).
fof(f931,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| inverse(inverse(sk_c9)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f867,f810]) ).
fof(f932,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f923,f931]) ).
fof(f933,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f923,f932]) ).
fof(f934,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f851,f933]) ).
fof(f935,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f934]) ).
fof(f936,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f935]) ).
fof(f995,plain,
( sQ50_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f851,f407]) ).
fof(f996,plain,
( sQ50_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f850,f995]) ).
fof(f997,plain,
( sQ50_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f996]) ).
fof(f998,plain,
( sQ50_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f997]) ).
fof(f1024,plain,
( sQ43_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f850,f373]) ).
fof(f1025,plain,
( sQ43_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1024]) ).
fof(f1026,plain,
( sQ43_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1025]) ).
fof(f1220,plain,
( ~ sQ50_spl
| ~ sQ43_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f406]) ).
fof(f1221,plain,
( ~ sQ48_spl
| ~ sQ43_spl
| identity = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f399]) ).
fof(f1230,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ50_spl
| ~ sQ43_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1220,f251]) ).
fof(f1231,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ50_spl
| ~ sQ43_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c9) != sk_c11
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f1230]) ).
fof(f1232,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ50_spl
| ~ sQ43_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1220,f1231]) ).
fof(f1248,plain,
( ~ sQ12_spl
| ~ sQ50_spl
| ~ sQ43_spl
| multiply(sk_c9,sk_c9) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1220,f187]) ).
fof(f1249,plain,
( ~ sQ12_spl
| ~ sQ50_spl
| ~ sQ43_spl
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f1248]) ).
fof(f1262,plain,
( ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| inverse(sk_c9) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1220,f131]) ).
fof(f1263,plain,
( ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f1262]) ).
fof(f1266,definition,
( sQ83_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1268,plain,
( sQ83_spl
| multiply(sk_c9,inverse(sk_c9)) != sk_c9 ),
inference(component_clause,[status(thm)],[f1266]) ).
fof(f1269,definition,
( sQ84_spl
<=> multiply(inverse(sk_c9),sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1271,plain,
( sQ84_spl
| multiply(inverse(sk_c9),sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f1269]) ).
fof(f1277,plain,
( sQ84_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1263,f1271]) ).
fof(f1278,plain,
( sQ84_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1249,f1277]) ).
fof(f1279,plain,
( sQ84_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1278]) ).
fof(f1280,plain,
( sQ84_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1279]) ).
fof(f1281,plain,
( sQ83_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1263,f1268]) ).
fof(f1282,plain,
( sQ83_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1249,f1281]) ).
fof(f1283,plain,
( sQ83_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1282]) ).
fof(f1284,plain,
( sQ83_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1283]) ).
fof(f1288,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ43_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1221,f65]) ).
fof(f1289,plain,
( ~ sQ19_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ48_spl
| inverse(inverse(sk_c9)) != inverse(sk_c9)
| multiply(inverse(sk_c9),sk_c9) != sk_c9
| multiply(sk_c9,inverse(sk_c9)) != sk_c9 ),
inference(resolution,[status(thm)],[f1288,f1232]) ).
fof(f1293,definition,
( sQ86_spl
<=> inverse(inverse(sk_c9)) = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1295,plain,
( sQ86_spl
| inverse(inverse(sk_c9)) != inverse(sk_c9) ),
inference(component_clause,[status(thm)],[f1293]) ).
fof(f1296,plain,
( ~ sQ19_spl
| ~ sQ50_spl
| ~ sQ43_spl
| ~ sQ48_spl
| ~ sQ86_spl
| ~ sQ84_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f1289,f1266,f1269,f1293,f398,f371,f405,f247]) ).
fof(f1302,plain,
( sQ86_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| inverse(sk_c9) != inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f1263,f1295]) ).
fof(f1303,plain,
( sQ86_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| sk_c9 != inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f1263,f1302]) ).
fof(f1304,plain,
( sQ86_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1263,f1303]) ).
fof(f1305,plain,
( sQ86_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1304]) ).
fof(f1306,plain,
( sQ86_spl
| ~ sQ0_spl
| ~ sQ50_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f1305]) ).
fof(f1307,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f140,f144,f148,f152,f156,f176,f177,f178,f179,f180,f181,f189,f190,f191,f192,f193,f194,f202,f203,f204,f205,f206,f207,f215,f216,f217,f218,f219,f220,f228,f229,f230,f231,f232,f233,f250,f377,f381,f390,f419,f421,f436,f440,f444,f537,f540,f597,f645,f680,f706,f710,f724,f743,f811,f839,f925,f936,f998,f1026,f1280,f1284,f1296,f1306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP384-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:13:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.059089 seconds
% 0.09/0.43 % CPU time: 0.235521 seconds
% 0.09/0.43 % Total memory used: 107.634 MB
% 0.09/0.43 % Net memory used: 107.494 MB
%------------------------------------------------------------------------------