%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP385-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 69
% Syntax : Number of formulae : 306 ( 13 unt; 31 def)
% Number of atoms : 989 ( 366 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1258 ( 575 ~; 652 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 32 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 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,
inverse(sk_c10) = sk_c9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7] :
( multiply(X7,sk_c8) != sk_c10
| inverse(X7) != sk_c10
| multiply(X6,sk_c9) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != X3
| multiply(sk_c10,X3) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f48,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f49,plain,
inverse(sk_c10) = sk_c9,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f50,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f56,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f59,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f60,plain,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f64,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f65,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f66,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f67,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f68,plain,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f69,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f70,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f71,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f72,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f73,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
( inverse(sk_c3) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f77,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f78,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f79,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f80,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f81,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f82,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f83,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f84,plain,
( inverse(sk_c3) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f85,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f86,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f87,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f88,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f89,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f90,plain,
! [X7] :
( multiply(X7,sk_c8) != sk_c10
| inverse(X7) != sk_c10
| ! [X6] :
( multiply(X6,sk_c9) != sk_c8
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c10
| ! [X1] :
( multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9
| ! [X4] :
( inverse(X4) != sk_c10
| ! [X3] :
( multiply(X4,sk_c10) != X3
| multiply(sk_c10,X3) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| inverse(sk_c10) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X6,sk_c8) != sk_c10
| inverse(X6) != sk_c10
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| inverse(sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,definition,
( sQ0_spl
<=> multiply(sk_c9,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ0_spl
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f94,plain,
( sQ0_spl
| multiply(sk_c9,sk_c8) != sk_c10 ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ1_spl
<=> multiply(sk_c10,sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ1_spl
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f92,f95]) ).
fof(f99,definition,
( sQ2_spl
<=> multiply(sk_c3,sk_c10) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f92,f99]) ).
fof(f103,definition,
( sQ3_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f92,f103]) ).
fof(f107,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f111,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f115,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f119,definition,
( sQ7_spl
<=> inverse(sk_c7) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ7_spl
| inverse(sk_c7) = sk_c10 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f92,f119]) ).
fof(f123,definition,
( sQ8_spl
<=> multiply(sk_c7,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( sQ9_spl
| multiply(sk_c10,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f127,f95]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f127,f99]) ).
fof(f132,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f127,f103]) ).
fof(f136,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f127,f119]) ).
fof(f137,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f123]) ).
fof(f138,definition,
( sQ10_spl
<=> multiply(sk_c10,sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ10_spl
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f138,f95]) ).
fof(f142,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f138,f99]) ).
fof(f143,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f138,f103]) ).
fof(f144,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f138,f107]) ).
fof(f145,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f138,f111]) ).
fof(f146,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f138,f115]) ).
fof(f147,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f138,f119]) ).
fof(f148,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f138,f123]) ).
fof(f149,definition,
( sQ11_spl
<=> multiply(sk_c1,sk_c10) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ11_spl
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f149,f95]) ).
fof(f153,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f149,f99]) ).
fof(f154,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f149,f103]) ).
fof(f155,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f149,f107]) ).
fof(f156,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f149,f111]) ).
fof(f157,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f149,f115]) ).
fof(f158,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f149,f119]) ).
fof(f159,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f149,f123]) ).
fof(f160,definition,
( sQ12_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( ~ sQ12_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f160,f95]) ).
fof(f164,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f160,f99]) ).
fof(f165,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f160,f103]) ).
fof(f166,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f160,f107]) ).
fof(f167,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f160,f111]) ).
fof(f168,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f160,f115]) ).
fof(f169,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f160,f119]) ).
fof(f170,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f160,f123]) ).
fof(f171,definition,
( sQ13_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ13_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
! [X0,X1] :
( sQ14_spl
<=> ( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,definition,
! [X4,X5] :
( sQ15_spl
<=> ( multiply(X5,sk_c9) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f178,plain,
! [X0,X1] :
( ~ sQ15_spl
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
! [X6] :
( sQ16_spl
<=> ( multiply(X6,sk_c8) != sk_c10
| inverse(X6) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f181,plain,
! [X0] :
( ~ sQ16_spl
| multiply(X0,sk_c8) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,plain,
( sQ16_spl
| sQ15_spl
| sQ14_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f171,f92,f127,f174,f177,f180]) ).
fof(f185,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| inverse(sk_c7) != sk_c10 ),
inference(resolution,[status(thm)],[f181,f124]) ).
fof(f186,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| sk_c10 != sk_c10
| inverse(sk_c9) != sk_c10 ),
inference(paramodulation,[status(thm)],[f93,f181]) ).
fof(f189,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ7_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f120,f185]) ).
fof(f190,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f189]) ).
fof(f191,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f192,plain,
! [X0] :
( ~ sQ15_spl
| multiply(inverse(X0),sk_c9) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f178]) ).
fof(f193,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f175]) ).
fof(f194,plain,
( sQ13_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f49,f173]) ).
fof(f195,plain,
( sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f194]) ).
fof(f196,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f209,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c3,inverse(sk_c3)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f104,f192]) ).
fof(f210,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| multiply(sk_c6,sk_c9) != sk_c8
| multiply(sk_c5,inverse(sk_c5)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f112,f192]) ).
fof(f211,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f161,f192]) ).
fof(f212,plain,
( ~ sQ15_spl
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c10,inverse(sk_c10)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f49,f192]) ).
fof(f213,definition,
( sQ17_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f216,definition,
( sQ18_spl
<=> multiply(sk_c10,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f209,f213,f216,f177,f103]) ).
fof(f220,definition,
( sQ19_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ19_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c8 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f210,f220,f115,f177,f111]) ).
fof(f224,definition,
( sQ20_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ20_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f211,f224,f216,f177,f160]) ).
fof(f228,definition,
( sQ21_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f231,definition,
( sQ22_spl
<=> multiply(sk_c9,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( ~ sQ22_spl
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f233,plain,
( sQ22_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f212,f228,f231,f177]) ).
fof(f236,plain,
( sQ20_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c10) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f161,f226]) ).
fof(f237,plain,
( sQ20_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f150,f236]) ).
fof(f238,plain,
( sQ19_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f112,f222]) ).
fof(f239,plain,
( sQ19_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f108,f238]) ).
fof(f240,plain,
( sQ19_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f239]) ).
fof(f241,plain,
( sQ19_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f245,plain,
( ~ sQ3_spl
| multiply(sk_c10,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f104,f47]) ).
fof(f248,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f47,f48]) ).
fof(f249,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f46,f248]) ).
fof(f265,plain,
( ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c3),sk_c4) ),
inference(paramodulation,[status(thm)],[f100,f249]) ).
fof(f270,plain,
( ~ sQ3_spl
| sk_c3 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f245,f249]) ).
fof(f271,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f128,f249]) ).
fof(f272,plain,
( ~ sQ1_spl
| sk_c4 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f96,f249]) ).
fof(f276,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c10 = multiply(sk_c10,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f104,f265]) ).
fof(f277,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f96,f276]) ).
fof(f279,plain,
( ~ sQ3_spl
| sk_c3 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f49,f270]) ).
fof(f280,plain,
( ~ sQ9_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f49,f271]) ).
fof(f281,plain,
( ~ sQ9_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f233]) ).
fof(f282,plain,
( ~ sQ9_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f283,plain,
( ~ sQ1_spl
| sk_c4 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f49,f272]) ).
fof(f287,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f277,f96]) ).
fof(f289,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f277,f124]) ).
fof(f291,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f277,f49]) ).
fof(f292,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f277,f120]) ).
fof(f294,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c9,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f292,f47]) ).
fof(f297,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f277,f129]) ).
fof(f298,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f287,f249]) ).
fof(f300,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f47,f298]) ).
fof(f309,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 = multiply(sk_c9,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f300,f279]) ).
fof(f310,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c9) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f318,f291]) ).
fof(f313,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f318,f287]) ).
fof(f314,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c9,sk_c8) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f318,f297]) ).
fof(f315,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f318,f292]) ).
fof(f316,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c10 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f318,f277]) ).
fof(f318,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f287,f309]) ).
fof(f319,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f318,f310]) ).
fof(f320,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c3,sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f318,f313]) ).
fof(f321,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c8) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f318,f314]) ).
fof(f322,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c8) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f318,f289]) ).
fof(f343,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c7) = identity ),
inference(forward_demodulation,[status(thm)],[f318,f294]) ).
fof(f344,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f300,f343]) ).
fof(f345,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c4) ),
inference(paramodulation,[status(thm)],[f344,f249]) ).
fof(f347,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c3,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f319,f345]) ).
fof(f366,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c3,sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f375,f321]) ).
fof(f370,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f375,f315]) ).
fof(f372,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| sk_c10 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f375,f316]) ).
fof(f373,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f375,f322]) ).
fof(f374,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f375,f318]) ).
fof(f375,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f320,f347]) ).
fof(f376,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f375,f366]) ).
fof(f390,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f373,f376]) ).
fof(f391,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f398,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c10
| multiply(sk_c10,sk_c2) != sk_c9 ),
inference(paramodulation,[status(thm)],[f150,f193]) ).
fof(f400,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f398,f138,f160,f174,f149]) ).
fof(f401,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| inverse(X0) != sk_c7
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f372,f193]) ).
fof(f403,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c2) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f372,f139]) ).
fof(f404,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c10)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f401]) ).
fof(f405,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f404]) ).
fof(f414,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f128]) ).
fof(f415,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f414]) ).
fof(f424,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f374,f280]) ).
fof(f425,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f374,f424]) ).
fof(f429,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c4 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f374,f283]) ).
fof(f430,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c4 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f374,f429]) ).
fof(f431,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c4 = multiply(sk_c7,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f434,f425]) ).
fof(f432,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f434,f415]) ).
fof(f434,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f425,f430]) ).
fof(f486,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c2) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f403]) ).
fof(f511,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f405]) ).
fof(f523,definition,
( sQ25_spl
<=> multiply(sk_c7,sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ25_spl
| multiply(sk_c7,sk_c2) != sk_c7 ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,definition,
( sQ26_spl
<=> inverse(sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( sQ26_spl
| inverse(sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f535,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f486,f525]) ).
fof(f536,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f535]) ).
fof(f537,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f538,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f370,f528]) ).
fof(f539,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f553,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c4) != sk_c7 ),
inference(paramodulation,[status(thm)],[f431,f511]) ).
fof(f556,definition,
( sQ29_spl
<=> multiply(sk_c7,sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( sQ29_spl
| multiply(sk_c7,sk_c4) != sk_c7 ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f553,f556,f526,f174,f119,f99,f95,f103,f127]) ).
fof(f562,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f432,f558]) ).
fof(f563,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f562]) ).
fof(f564,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f565,definition,
( sQ30_spl
<=> inverse(sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( sQ30_spl
| inverse(sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f568,definition,
( sQ31_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ31_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f571,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f186,f565,f568,f180,f92]) ).
fof(f575,definition,
( sQ33_spl
<=> sk_c9 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( sQ33_spl
| sk_c9 != sk_c10 ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f579,plain,
( sQ31_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f570]) ).
fof(f580,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
( sQ33_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f318,f577]) ).
fof(f582,plain,
( sQ33_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f316,f581]) ).
fof(f583,plain,
( sQ33_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f582]) ).
fof(f584,plain,
( sQ33_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f587,plain,
( ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f150,f249]) ).
fof(f589,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = multiply(sk_c10,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f161,f587]) ).
fof(f608,plain,
( ~ sQ10_spl
| sk_c2 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f139,f249]) ).
fof(f610,plain,
( ~ sQ10_spl
| sk_c2 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f49,f608]) ).
fof(f611,plain,
( ~ sQ10_spl
| ~ sQ22_spl
| sk_c2 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f232,f610]) ).
fof(f612,plain,
( ~ sQ10_spl
| ~ sQ22_spl
| sQ20_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f611,f237]) ).
fof(f613,plain,
( ~ sQ10_spl
| ~ sQ22_spl
| sQ20_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f612]) ).
fof(f620,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| multiply(sk_c9,sk_c9) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f611,f232]) ).
fof(f647,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f139,f589]) ).
fof(f656,plain,
( sQ30_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| inverse(sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f647,f567]) ).
fof(f659,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f647,f49]) ).
fof(f666,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ22_spl
| multiply(inverse(X0),sk_c9) != sk_c8
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f611,f192]) ).
fof(f667,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ22_spl
| multiply(inverse(X0),sk_c9) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f611,f666]) ).
fof(f673,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f656]) ).
fof(f674,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f673]) ).
fof(f681,definition,
( sQ35_spl
<=> multiply(sk_c9,sk_c9) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ22_spl
| multiply(sk_c9,sk_c9) != sk_c2
| multiply(sk_c9,inverse(sk_c9)) != sk_c2 ),
inference(paramodulation,[status(thm)],[f659,f667]) ).
fof(f693,definition,
( sQ36_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( sQ36_spl
| multiply(sk_c9,inverse(sk_c9)) != sk_c2 ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f696,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ22_spl
| ~ sQ35_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f691,f693,f681,f231,f177,f138,f160,f149]) ).
fof(f697,plain,
( sQ36_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(sk_c9,sk_c9) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f659,f695]) ).
fof(f701,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c8) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f318,f94]) ).
fof(f738,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f375,f320]) ).
fof(f739,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f375,f738]) ).
fof(f790,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f375,f701]) ).
fof(f791,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c4) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f434,f790]) ).
fof(f792,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c7 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f739,f791]) ).
fof(f793,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f372,f792]) ).
fof(f794,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f793]) ).
fof(f795,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f794]) ).
fof(f796,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f620,f681,f138,f231]) ).
fof(f797,plain,
( sQ36_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f697,f681,f138,f160,f149,f693]) ).
fof(f798,plain,
$false,
inference(sat_refutation,[status(thm)],[f98,f102,f106,f122,f130,f131,f132,f136,f137,f141,f142,f143,f144,f145,f146,f147,f148,f152,f153,f154,f155,f156,f157,f158,f159,f163,f164,f165,f166,f167,f168,f169,f170,f183,f191,f196,f219,f223,f227,f234,f241,f282,f391,f400,f537,f540,f559,f564,f571,f580,f584,f613,f674,f696,f795,f796,f797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP385-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:11:11 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.074716 seconds
% 0.13/0.44 % CPU time: 0.249276 seconds
% 0.13/0.44 % Total memory used: 106.670 MB
% 0.13/0.44 % Net memory used: 106.409 MB
%------------------------------------------------------------------------------