%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:33:14 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 62
% Syntax : Number of formulae : 324 ( 14 unt; 26 def)
% Number of atoms : 1323 ( 373 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1914 ( 915 ~; 973 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 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,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f41,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f48,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f51,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f71,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f73,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f74,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f75,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f76,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f77,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f78,plain,
! [X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| ! [X5] :
( inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ1_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f80,f83]) ).
fof(f87,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f80,f87]) ).
fof(f91,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f80,f91]) ).
fof(f95,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f80,f95]) ).
fof(f99,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f80,f99]) ).
fof(f103,definition,
( sQ6_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ6_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f48,f103,f83]) ).
fof(f107,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f49,f103,f87]) ).
fof(f108,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f50,f103,f91]) ).
fof(f109,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f51,f103,f95]) ).
fof(f110,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f52,f103,f99]) ).
fof(f111,definition,
( sQ7_spl
<=> multiply(sk_c2,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f115,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f111,f87]) ).
fof(f116,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f111,f91]) ).
fof(f119,definition,
( sQ8_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ8_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f119,f83]) ).
fof(f123,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f119,f87]) ).
fof(f124,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f119,f91]) ).
fof(f125,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f119,f95]) ).
fof(f126,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f119,f99]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( sQ9_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f127,f83]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f127,f87]) ).
fof(f132,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f91]) ).
fof(f133,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f127,f95]) ).
fof(f134,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f127,f99]) ).
fof(f135,definition,
( sQ10_spl
<=> multiply(sk_c3,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ10_spl
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f135,f83]) ).
fof(f139,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f135,f87]) ).
fof(f140,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f135,f91]) ).
fof(f141,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f135,f95]) ).
fof(f142,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f135,f99]) ).
fof(f143,definition,
( sQ11_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f143,f83]) ).
fof(f147,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f143,f87]) ).
fof(f148,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f143,f91]) ).
fof(f149,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f143,f95]) ).
fof(f150,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f143,f99]) ).
fof(f151,definition,
! [X0] :
( sQ12_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
! [X1] :
( sQ13_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X2] :
( sQ14_spl
<=> ( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3] :
( sQ15_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
! [X4] :
( sQ16_spl
<=> ( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ16_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ16_spl
| sQ15_spl
| ~ sQ1_spl
| sQ14_spl
| ~ sQ9_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f79,f151,f154,f127,f157,f83,f160,f163]) ).
fof(f167,plain,
( ~ sQ5_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f164,f100]) ).
fof(f168,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| sk_c8 != sk_c7
| inverse(sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f136,f164]) ).
fof(f170,plain,
( ~ sQ5_spl
| ~ sQ16_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f96,f167]) ).
fof(f171,plain,
( ~ sQ5_spl
| ~ sQ16_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f170]) ).
fof(f172,plain,
( ~ sQ5_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f161,f92]) ).
fof(f174,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| sk_c6 != sk_c8
| inverse(sk_c2) != sk_c8 ),
inference(paramodulation,[status(thm)],[f112,f161]) ).
fof(f176,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f88,f173]) ).
fof(f177,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f176]) ).
fof(f178,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f188,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f158,f136]) ).
fof(f191,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c6
| sk_c7 != sk_c8 ),
inference(paramodulation,[status(thm)],[f100,f158]) ).
fof(f192,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f144,f188]) ).
fof(f193,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f192]) ).
fof(f194,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f197,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f120,f41]) ).
fof(f198,plain,
( ~ sQ11_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f144,f41]) ).
fof(f199,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f41,f42]) ).
fof(f200,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f40,f199]) ).
fof(f214,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f40,f200]) ).
fof(f218,plain,
( ~ sQ0_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f81,f200]) ).
fof(f220,plain,
( ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f136,f200]) ).
fof(f224,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f104,f218]) ).
fof(f226,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c6 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f144,f220]) ).
fof(f227,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f128,f226]) ).
fof(f229,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f227,f197]) ).
fof(f230,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f227,f128]) ).
fof(f236,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f227,f120]) ).
fof(f245,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f227,f224]) ).
fof(f246,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f245,f200]) ).
fof(f248,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f246]) ).
fof(f250,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f248,f198]) ).
fof(f252,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f248,f41]) ).
fof(f253,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f248,f40]) ).
fof(f258,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f253,f229]) ).
fof(f259,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f267,f253]) ).
fof(f262,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f267,f236]) ).
fof(f264,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f267,f227]) ).
fof(f266,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c3) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f267,f144]) ).
fof(f267,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f248,f258]) ).
fof(f268,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f267,f155]) ).
fof(f271,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f267,f230]) ).
fof(f272,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c8) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f267,f271]) ).
fof(f273,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c8
| sk_c2 != sk_c7 ),
inference(paramodulation,[status(thm)],[f272,f152]) ).
fof(f276,definition,
( sQ17_spl
<=> sk_c2 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ17_spl
| sk_c2 != sk_c7 ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ18_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ18_spl
| inverse(sk_c2) != sk_c8 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f273,f276,f279,f151,f103,f80,f119,f143,f135,f127]) ).
fof(f283,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c7) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f264,f268]) ).
fof(f284,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f264,f283]) ).
fof(f285,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f264,f278]) ).
fof(f286,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f285]) ).
fof(f287,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f288,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c8 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f259,f272]) ).
fof(f301,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f266,f200]) ).
fof(f302,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f259,f301]) ).
fof(f303,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f262,f281]) ).
fof(f304,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f288,f303]) ).
fof(f305,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f304]) ).
fof(f306,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f339,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c3) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f267,f250]) ).
fof(f340,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c3 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f259,f339]) ).
fof(f343,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f351,f266]) ).
fof(f346,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c8 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f351,f288]) ).
fof(f348,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f351,f264]) ).
fof(f350,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f351,f267]) ).
fof(f351,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f267,f340]) ).
fof(f362,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f350,f252]) ).
fof(f369,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c3) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f351,f284]) ).
fof(f370,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f351,f369]) ).
fof(f371,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f351,f370]) ).
fof(f372,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ13_spl
| inverse(inverse(sk_c3)) != sk_c3 ),
inference(resolution,[status(thm)],[f371,f362]) ).
fof(f381,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f343,f372]) ).
fof(f382,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f343,f381]) ).
fof(f383,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f382]) ).
fof(f384,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f391,definition,
( sQ19_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ19_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f391]) ).
fof(f394,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f174,f279,f391,f160,f111]) ).
fof(f400,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f350,f393]) ).
fof(f401,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f346,f400]) ).
fof(f402,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f401]) ).
fof(f403,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f402]) ).
fof(f404,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c3,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f348,f85]) ).
fof(f405,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f302,f404]) ).
fof(f406,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f346,f405]) ).
fof(f407,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f350,f406]) ).
fof(f408,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f407]) ).
fof(f409,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f414,definition,
( sQ21_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( sQ21_spl
| inverse(sk_c3) != sk_c7 ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,definition,
( sQ22_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( sQ22_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f168,f414,f417,f163,f135]) ).
fof(f426,plain,
( sQ21_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f343,f416]) ).
fof(f427,plain,
( sQ21_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f348,f426]) ).
fof(f428,plain,
( sQ21_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f427]) ).
fof(f429,plain,
( sQ21_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f428]) ).
fof(f430,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f346,f419]) ).
fof(f431,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f348,f430]) ).
fof(f432,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f431]) ).
fof(f433,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f436,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f84,f200]) ).
fof(f440,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f92,f200]) ).
fof(f442,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f88,f440]) ).
fof(f443,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f100,f200]) ).
fof(f445,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f96,f443]) ).
fof(f446,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f200,f214]) ).
fof(f452,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f442,f200]) ).
fof(f454,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f445,f200]) ).
fof(f521,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c7) ),
inference(backward_demodulation,[status(thm)],[f531,f452]) ).
fof(f525,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f531,f442]) ).
fof(f526,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f531,f129]) ).
fof(f531,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f436,f454]) ).
fof(f532,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(forward_demodulation,[status(thm)],[f531,f521]) ).
fof(f533,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f532]) ).
fof(f534,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f531,f525]) ).
fof(f535,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f445,f534]) ).
fof(f540,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f533,f41]) ).
fof(f542,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f533,f446]) ).
fof(f547,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c7) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f535,f526]) ).
fof(f548,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f535,f531]) ).
fof(f556,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f535,f96]) ).
fof(f558,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f535,f547]) ).
fof(f562,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f535,f540]) ).
fof(f565,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f562,f42]) ).
fof(f566,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f200,f565]) ).
fof(f571,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f535,f542]) ).
fof(f575,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(paramodulation,[status(thm)],[f556,f562]) ).
fof(f577,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f571,f575]) ).
fof(f579,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f577,f556]) ).
fof(f582,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f577,f562]) ).
fof(f584,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f577,f548]) ).
fof(f586,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f577,f535]) ).
fof(f588,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f577,f566]) ).
fof(f614,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f577,f558]) ).
fof(f615,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f588,f614]) ).
fof(f616,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f577,f615]) ).
fof(f617,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f577,f616]) ).
fof(f618,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f617]) ).
fof(f619,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f644,definition,
( sQ24_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( sQ24_spl
| inverse(sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f647,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f191,f417,f644,f157,f99]) ).
fof(f648,plain,
( sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f579,f646]) ).
fof(f649,plain,
( sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f577,f648]) ).
fof(f650,plain,
( sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f649]) ).
fof(f651,plain,
( sQ24_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f652,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f584,f152]) ).
fof(f653,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f586,f652]) ).
fof(f654,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f584,f653]) ).
fof(f704,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f584,f419]) ).
fof(f705,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f586,f704]) ).
fof(f706,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f705]) ).
fof(f707,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f706]) ).
fof(f739,definition,
( sQ25_spl
<=> sk_c2 = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( sQ25_spl
| sk_c2 != sk_c2 ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f750,plain,
( sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f741]) ).
fof(f751,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f811,definition,
( sQ29_spl
<=> sk_c3 = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f813,plain,
( sQ29_spl
| sk_c3 != sk_c3 ),
inference(component_clause,[status(thm)],[f811]) ).
fof(f822,plain,
( sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f813]) ).
fof(f823,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f822]) ).
fof(f878,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(resolution,[status(thm)],[f654,f582]) ).
fof(f891,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f586,f155]) ).
fof(f892,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f577,f891]) ).
fof(f893,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f586,f892]) ).
fof(f894,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ13_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(resolution,[status(thm)],[f893,f582]) ).
fof(f911,definition,
( sQ32_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( sQ32_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f918,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f913]) ).
fof(f919,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f918]) ).
fof(f928,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f579,f878]) ).
fof(f929,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f579,f928]) ).
fof(f930,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f929]) ).
fof(f931,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f930]) ).
fof(f933,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f579,f894]) ).
fof(f934,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ13_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f579,f933]) ).
fof(f935,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f934]) ).
fof(f936,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f935]) ).
fof(f937,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f90,f94,f98,f102,f106,f107,f108,f109,f110,f115,f116,f122,f123,f124,f125,f126,f130,f131,f132,f133,f134,f138,f139,f140,f141,f142,f146,f147,f148,f149,f150,f166,f172,f178,f194,f282,f287,f306,f384,f394,f403,f409,f420,f429,f433,f619,f647,f651,f707,f751,f823,f919,f931,f936]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 20:09:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.052407 seconds
% 0.14/0.42 % CPU time: 0.132789 seconds
% 0.14/0.42 % Total memory used: 27.947 MB
% 0.14/0.42 % Net memory used: 27.790 MB
%------------------------------------------------------------------------------