%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP238-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:33:11 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 79
% Syntax : Number of formulae : 461 ( 13 unt; 39 def)
% Number of atoms : 2042 ( 528 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 3070 (1489 ~;1542 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 41 ( 39 usr; 40 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 107 ( 107 !; 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_c4,sk_c5) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
! [X4,X5,X6,X2,X1,X3,X7,X8,X9] :
( multiply(X9,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| multiply(X8,sk_c11) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| inverse(X2) != X1
| multiply(X2,X1) != sk_c11
| inverse(X6) != sk_c11
| multiply(X6,sk_c11) != X5
| multiply(sk_c11,X5) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| inverse(X4) != sk_c11
| inverse(sk_c11) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f66,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f67,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f68,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f71,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f76,plain,
( inverse(sk_c9) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f81,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f84,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f85,plain,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
( inverse(sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f96,plain,
( inverse(sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f97,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f101,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f102,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f106,plain,
( inverse(sk_c9) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f107,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f108,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f109,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f111,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f116,plain,
( inverse(sk_c9) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f117,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f118,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f119,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f121,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f122,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f126,plain,
( inverse(sk_c9) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f127,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f128,plain,
! [X9] :
( multiply(X9,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| ! [X8] :
( multiply(X8,sk_c11) != sk_c10
| ! [X7] :
( inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| ! [X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| ! [X1] :
( multiply(X1,sk_c10) != sk_c11
| ! [X2] :
( inverse(X2) != X1
| multiply(X2,X1) != sk_c11
| ! [X6] :
( inverse(X6) != sk_c11
| ! [X5] :
( multiply(X6,sk_c11) != X5
| multiply(sk_c11,X5) != sk_c10
| ! [X4] :
( multiply(X4,sk_c10) != sk_c11
| inverse(X4) != sk_c11
| inverse(sk_c11) != sk_c10 ) ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( multiply(X8,sk_c11) != sk_c10
| inverse(X8) != sk_c10
| multiply(X7,sk_c11) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != X1
| multiply(sk_c11,X1) != sk_c10
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11
| inverse(sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,definition,
( sQ0_spl
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ0_spl
| inverse(sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( sQ0_spl
| inverse(sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f130,f133]) ).
fof(f137,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f130,f137]) ).
fof(f145,definition,
( sQ4_spl
<=> inverse(sk_c6) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ4_spl
| inverse(sk_c6) = sk_c11 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f130,f145]) ).
fof(f149,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f130,f149]) ).
fof(f157,definition,
( sQ7_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ7_spl
| inverse(sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f161,definition,
( sQ8_spl
<=> multiply(sk_c8,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f165,definition,
( sQ9_spl
<=> inverse(sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ9_spl
| inverse(sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f130,f165]) ).
fof(f169,definition,
( sQ10_spl
<=> multiply(sk_c9,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f171,plain,
( sQ10_spl
| multiply(sk_c9,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f173,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f173,f133]) ).
fof(f177,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f173,f137]) ).
fof(f179,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f173,f145]) ).
fof(f180,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f173,f149]) ).
fof(f182,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f173,f157]) ).
fof(f183,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f173,f161]) ).
fof(f184,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f86,f173,f165]) ).
fof(f186,definition,
( sQ12_spl
<=> multiply(sk_c1,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ12_spl
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f188,plain,
( sQ12_spl
| multiply(sk_c1,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f186,f133]) ).
fof(f190,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f186,f137]) ).
fof(f192,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f186,f145]) ).
fof(f193,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f186,f149]) ).
fof(f197,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f186,f165]) ).
fof(f198,plain,
( sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f97,f186,f169]) ).
fof(f199,definition,
( sQ13_spl
<=> multiply(sk_c11,sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ13_spl
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f199,f133]) ).
fof(f203,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f199,f137]) ).
fof(f205,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f199,f145]) ).
fof(f206,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f199,f149]) ).
fof(f210,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f106,f199,f165]) ).
fof(f211,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f107,f199,f169]) ).
fof(f212,definition,
( sQ14_spl
<=> multiply(sk_c2,sk_c11) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ14_spl
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f108,f212,f133]) ).
fof(f216,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f109,f212,f137]) ).
fof(f218,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f212,f145]) ).
fof(f219,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f212,f149]) ).
fof(f223,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f116,f212,f165]) ).
fof(f224,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f117,f212,f169]) ).
fof(f225,definition,
( sQ15_spl
<=> inverse(sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ15_spl
| inverse(sk_c2) = sk_c11 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f118,f225,f133]) ).
fof(f229,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f119,f225,f137]) ).
fof(f231,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f121,f225,f145]) ).
fof(f232,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f122,f225,f149]) ).
fof(f236,plain,
( sQ9_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f126,f225,f165]) ).
fof(f237,plain,
( sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f127,f225,f169]) ).
fof(f238,definition,
! [X0] :
( sQ16_spl
<=> ( multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0] :
( ~ sQ16_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
! [X1,X2] :
( sQ17_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != X1
| multiply(sk_c11,X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f242,plain,
! [X0,X1] :
( ~ sQ17_spl
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != X0
| multiply(sk_c11,X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
! [X3,X4] :
( sQ18_spl
<=> ( multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f245,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
! [X6,X7] :
( sQ19_spl
<=> ( multiply(X7,sk_c11) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0,X1] :
( ~ sQ19_spl
| multiply(X1,sk_c11) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
! [X8] :
( sQ20_spl
<=> ( multiply(X8,sk_c11) != sk_c10
| inverse(X8) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f251,plain,
! [X0] :
( ~ sQ20_spl
| multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f130,f238,f241,f244,f247,f250]) ).
fof(f267,plain,
( ~ sQ10_spl
| ~ sQ20_spl
| inverse(sk_c9) != sk_c10 ),
inference(resolution,[status(thm)],[f251,f170]) ).
fof(f269,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| sk_c10 != sk_c10
| inverse(sk_c8) != sk_c10 ),
inference(paramodulation,[status(thm)],[f162,f251]) ).
fof(f271,plain,
( ~ sQ14_spl
| ~ sQ20_spl
| sk_c3 != sk_c10
| inverse(sk_c2) != sk_c10 ),
inference(paramodulation,[status(thm)],[f213,f251]) ).
fof(f272,plain,
( ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ9_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f166,f267]) ).
fof(f273,plain,
( ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f272]) ).
fof(f274,plain,
( ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0] :
( ~ sQ19_spl
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f248]) ).
fof(f276,plain,
! [X0] :
( ~ sQ18_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f245]) ).
fof(f277,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c11
| multiply(sk_c11,multiply(X0,sk_c11)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f242]) ).
fof(f283,plain,
( ~ sQ11_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f174,f66]) ).
fof(f284,plain,
( ~ sQ15_spl
| multiply(sk_c11,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f226,f66]) ).
fof(f285,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f66,f67]) ).
fof(f286,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f65,f285]) ).
fof(f308,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f65,f286]) ).
fof(f310,plain,
( ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f134,f286]) ).
fof(f318,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f187,f286]) ).
fof(f319,plain,
( ~ sQ15_spl
| sk_c2 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f284,f286]) ).
fof(f320,plain,
( ~ sQ11_spl
| sk_c1 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f283,f286]) ).
fof(f322,plain,
( ~ sQ13_spl
| sk_c3 = multiply(inverse(sk_c11),sk_c10) ),
inference(paramodulation,[status(thm)],[f200,f286]) ).
fof(f323,plain,
( ~ sQ14_spl
| sk_c11 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f213,f286]) ).
fof(f325,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c5,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f138,f310]) ).
fof(f328,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f174,f318]) ).
fof(f329,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| sk_c2 = multiply(sk_c10,identity) ),
inference(forward_demodulation,[status(thm)],[f131,f319]) ).
fof(f330,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c10,identity) ),
inference(forward_demodulation,[status(thm)],[f131,f320]) ).
fof(f332,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| sk_c3 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f131,f322]) ).
fof(f333,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sk_c11 = multiply(sk_c11,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f226,f323]) ).
fof(f334,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f200,f333]) ).
fof(f340,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c5) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f334,f134]) ).
fof(f347,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f334,f131]) ).
fof(f351,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c2) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f334,f226]) ).
fof(f360,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f334,f275]) ).
fof(f365,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ19_spl
| multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f347,f360]) ).
fof(f368,definition,
( sQ21_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ21_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,definition,
( sQ22_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( sQ22_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f378,definition,
( sQ24_spl
<=> multiply(sk_c10,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ19_spl
| ~ sQ24_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f365,f368,f378,f247,f199,f225,f212,f130]) ).
fof(f405,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f347,f370]) ).
fof(f414,plain,
( sQ10_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c9,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f334,f171]) ).
fof(f415,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(X0) != sk_c11
| multiply(sk_c10,multiply(X0,sk_c11)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f334,f277]) ).
fof(f416,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(X0) != sk_c11
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f334,f415]) ).
fof(f417,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f334,f416]) ).
fof(f420,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f334,f276]) ).
fof(f421,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f334,f420]) ).
fof(f422,plain,
( ~ sQ18_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| identity != sk_c10
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f66,f421]) ).
fof(f426,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ18_spl
| multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f347,f421]) ).
fof(f428,plain,
( ~ sQ18_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f422,f368,f371,f199,f225,f212,f244]) ).
fof(f432,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ24_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f426,f368,f378,f244,f199,f225,f212,f130]) ).
fof(f439,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c5 = multiply(sk_c5,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f334,f325]) ).
fof(f440,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f439,f286]) ).
fof(f442,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f440]) ).
fof(f443,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f373]) ).
fof(f444,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f455,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c10,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f334,f328]) ).
fof(f456,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f334,f455]) ).
fof(f457,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f456,f286]) ).
fof(f459,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f457]) ).
fof(f460,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| X0 = multiply(inverse(sk_c10),X0) ),
inference(backward_demodulation,[status(thm)],[f459,f308]) ).
fof(f463,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f347,f460]) ).
fof(f468,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f463,f329]) ).
fof(f469,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f479,f463]) ).
fof(f470,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f479,f459]) ).
fof(f472,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c9) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f479,f166]) ).
fof(f473,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c5) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f479,f340]) ).
fof(f474,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f479,f351]) ).
fof(f477,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f479,f334]) ).
fof(f479,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f459,f468]) ).
fof(f484,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| X0 = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f472,f286]) ).
fof(f485,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f469,f484]) ).
fof(f536,plain,
( sQ10_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f485,f414]) ).
fof(f537,plain,
( sQ10_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f479,f536]) ).
fof(f538,plain,
( sQ10_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f479,f537]) ).
fof(f539,plain,
( sQ10_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ10_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f550,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(X0) != sk_c10
| multiply(sk_c2,multiply(X0,sk_c10)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f479,f417]) ).
fof(f551,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f469,f550]) ).
fof(f552,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c2) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f479,f551]) ).
fof(f553,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f479,f552]) ).
fof(f554,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f479,f553]) ).
fof(f557,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl
| inverse(sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f554,f469]) ).
fof(f562,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f474,f557]) ).
fof(f563,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f562]) ).
fof(f564,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f579,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f286,f308]) ).
fof(f585,plain,
( ~ sQ16_spl
| sk_c10 != sk_c11
| inverse(identity) != sk_c11 ),
inference(paramodulation,[status(thm)],[f579,f239]) ).
fof(f586,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ16_spl
| sk_c3 != sk_c11
| inverse(sk_c10) != sk_c11 ),
inference(paramodulation,[status(thm)],[f332,f239]) ).
fof(f587,plain,
( ~ sQ16_spl
| sk_c10 != sk_c11
| inverse(inverse(identity)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f308,f239]) ).
fof(f589,definition,
( sQ31_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ31_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f589]) ).
fof(f592,definition,
( sQ32_spl
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( sQ32_spl
| sk_c10 != sk_c11 ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f595,plain,
( ~ sQ16_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f585,f589,f592,f238]) ).
fof(f596,definition,
( sQ33_spl
<=> inverse(sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ33_spl
| inverse(sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f596]) ).
fof(f599,definition,
( sQ34_spl
<=> sk_c3 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( sQ34_spl
| sk_c3 != sk_c11 ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f602,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f586,f596,f599,f238,f130,f199]) ).
fof(f603,definition,
( sQ35_spl
<=> inverse(inverse(identity)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f605,plain,
( sQ35_spl
| inverse(inverse(identity)) != sk_c11 ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f606,plain,
( ~ sQ16_spl
| ~ sQ32_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f587,f603,f592,f238]) ).
fof(f618,plain,
( ~ sQ16_spl
| identity != sk_c11
| inverse(inverse(sk_c10)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f66,f239]) ).
fof(f621,definition,
( sQ36_spl
<=> inverse(inverse(sk_c10)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f624,definition,
( sQ37_spl
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( sQ37_spl
| identity != sk_c11 ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,plain,
( ~ sQ16_spl
| ~ sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f618,f621,f624,f238]) ).
fof(f629,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 = multiply(inverse(sk_c11),sk_c10) ),
inference(paramodulation,[status(thm)],[f328,f286]) ).
fof(f631,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c11 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f131,f629]) ).
fof(f632,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sk_c11 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f332,f631]) ).
fof(f633,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f632,f601]) ).
fof(f634,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f633]) ).
fof(f635,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f325,f286]) ).
fof(f637,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f635]) ).
fof(f638,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f637,f626]) ).
fof(f639,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f638]) ).
fof(f641,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f134,f473]) ).
fof(f646,plain,
( sQ33_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c10) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f632,f598]) ).
fof(f650,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| inverse(sk_c3) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f632,f131]) ).
fof(f664,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f632,f641]) ).
fof(f714,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f477,f200]) ).
fof(f715,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f469,f714]) ).
fof(f726,plain,
( sQ33_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f479,f646]) ).
fof(f727,plain,
( sQ33_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sk_c2 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f474,f726]) ).
fof(f728,plain,
( sQ33_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ1_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f664,f727]) ).
fof(f729,plain,
( sQ33_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f728]) ).
fof(f730,plain,
( sQ33_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f731,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f637,f579]) ).
fof(f734,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(sk_c11,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f174,f286]) ).
fof(f735,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f731,f734]) ).
fof(f736,plain,
! [X0] :
( ~ sQ0_spl
| X0 = multiply(sk_c10,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f131,f286]) ).
fof(f737,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f731,f736]) ).
fof(f738,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c11,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f146,f286]) ).
fof(f739,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f731,f738]) ).
fof(f742,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f187,f286]) ).
fof(f744,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f174,f742]) ).
fof(f745,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f731,f744]) ).
fof(f749,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f146,f276]) ).
fof(f750,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| multiply(sk_c10,sk_c10) != sk_c11
| multiply(sk_c11,inverse(sk_c11)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f131,f276]) ).
fof(f751,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c1,inverse(sk_c1)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f174,f276]) ).
fof(f755,definition,
( sQ39_spl
<=> multiply(sk_c10,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f757,plain,
( sQ39_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f755]) ).
fof(f766,definition,
( sQ42_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f769,definition,
( sQ43_spl
<=> multiply(sk_c11,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f771,plain,
( sQ43_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f769]) ).
fof(f772,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| ~ sQ43_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f749,f766,f769,f244,f145]) ).
fof(f773,definition,
( sQ44_spl
<=> multiply(sk_c11,inverse(sk_c11)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f775,plain,
( sQ44_spl
| multiply(sk_c11,inverse(sk_c11)) != sk_c11 ),
inference(component_clause,[status(thm)],[f773]) ).
fof(f776,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ39_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f750,f773,f755,f244,f130]) ).
fof(f777,definition,
( sQ45_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f780,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ43_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f751,f777,f769,f244,f173]) ).
fof(f781,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f731,f771]) ).
fof(f783,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f731,f775]) ).
fof(f784,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f131,f783]) ).
fof(f796,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c1) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f745,f174]) ).
fof(f798,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 = identity ),
inference(backward_demodulation,[status(thm)],[f745,f637]) ).
fof(f799,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f745,f781]) ).
fof(f800,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f799]) ).
fof(f801,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f800]) ).
fof(f820,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f745,f283]) ).
fof(f821,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f737,f820]) ).
fof(f822,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f830,f796]) ).
fof(f827,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f830,f798]) ).
fof(f828,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c1 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f830,f745]) ).
fof(f830,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c1 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f798,f821]) ).
fof(f835,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f739,f150]) ).
fof(f869,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f827,f66]) ).
fof(f894,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f830,f275]) ).
fof(f895,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c1) != sk_c10
| multiply(X0,inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f828,f894]) ).
fof(f896,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c1) != sk_c1
| multiply(X0,inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f830,f895]) ).
fof(f897,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ19_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c1 ),
inference(resolution,[status(thm)],[f896,f869]) ).
fof(f901,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ19_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f735,f897]) ).
fof(f902,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ19_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f822,f901]) ).
fof(f903,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f902]) ).
fof(f904,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f903]) ).
fof(f905,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f830,f757]) ).
fof(f906,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f735,f905]) ).
fof(f907,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c1 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f830,f906]) ).
fof(f908,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f828,f907]) ).
fof(f909,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f908]) ).
fof(f910,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f909]) ).
fof(f911,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f405,f378,f199,f225,f212,f130,f368]) ).
fof(f912,definition,
( sQ46_spl
<=> inverse(sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f914,plain,
( sQ46_spl
| inverse(sk_c8) != sk_c10 ),
inference(component_clause,[status(thm)],[f912]) ).
fof(f915,definition,
( sQ47_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f917,plain,
( sQ47_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f918,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ47_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f269,f912,f915,f250,f161]) ).
fof(f919,definition,
( sQ48_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f921,plain,
( sQ48_spl
| inverse(sk_c2) != sk_c10 ),
inference(component_clause,[status(thm)],[f919]) ).
fof(f922,definition,
( sQ49_spl
<=> sk_c3 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( sQ49_spl
| sk_c3 != sk_c10 ),
inference(component_clause,[status(thm)],[f922]) ).
fof(f925,plain,
( ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f271,f919,f922,f250,f212]) ).
fof(f926,plain,
( sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f917]) ).
fof(f927,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f926]) ).
fof(f930,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f477,f632]) ).
fof(f973,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f835,f637]) ).
fof(f974,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f835,f784]) ).
fof(f975,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f974]) ).
fof(f976,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f975]) ).
fof(f986,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f973,f66]) ).
fof(f1002,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f973,f579]) ).
fof(f1006,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c7) = sk_c10 ),
inference(paramodulation,[status(thm)],[f158,f986]) ).
fof(f1008,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(paramodulation,[status(thm)],[f166,f986]) ).
fof(f1010,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1002,f1008]) ).
fof(f1012,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1010,f166]) ).
fof(f1018,plain,
( sQ46_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c8) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1010,f914]) ).
fof(f1019,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1010,f986]) ).
fof(f1022,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c9 = identity ),
inference(backward_demodulation,[status(thm)],[f1010,f973]) ).
fof(f1023,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| sk_c9 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1010,f835]) ).
fof(f1029,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f1010,f737]) ).
fof(f1056,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f1010,f330]) ).
fof(f1057,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f1029,f1056]) ).
fof(f1064,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1067,f1023]) ).
fof(f1067,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1022,f1057]) ).
fof(f1084,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1067,f170]) ).
fof(f1085,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f735,f1084]) ).
fof(f1086,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1064,f1085]) ).
fof(f1101,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f735,f188]) ).
fof(f1102,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1086,f1101]) ).
fof(f1103,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f1064,f1102]) ).
fof(f1104,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1103]) ).
fof(f1105,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1104]) ).
fof(f1144,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f735,f187]) ).
fof(f1201,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c9,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1019,f67]) ).
fof(f1202,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f286,f1201]) ).
fof(f1325,definition,
( sQ52_spl
<=> sk_c1 = sk_c1 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1327,plain,
( sQ52_spl
| sk_c1 != sk_c1 ),
inference(component_clause,[status(thm)],[f1325]) ).
fof(f1333,plain,
( sQ52_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1327]) ).
fof(f1334,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f1333]) ).
fof(f1413,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1023,f162]) ).
fof(f1414,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1010,f1413]) ).
fof(f1416,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| multiply(sk_c9,X0) = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f1414,f67]) ).
fof(f1417,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| X0 = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f1202,f1416]) ).
fof(f1418,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f1202,f1417]) ).
fof(f1432,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1418,f1006]) ).
fof(f1433,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c9) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1435,f158]) ).
fof(f1435,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1010,f1432]) ).
fof(f1436,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1012,f1433]) ).
fof(f1439,plain,
( sQ46_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1436,f1018]) ).
fof(f1441,plain,
( sQ46_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1012,f1439]) ).
fof(f1442,plain,
( sQ46_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1441]) ).
fof(f1443,plain,
( sQ46_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1442]) ).
fof(f1455,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1010,f275]) ).
fof(f1456,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1023,f1455]) ).
fof(f1457,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1010,f1456]) ).
fof(f1458,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ19_spl
| multiply(sk_c9,inverse(sk_c9)) != sk_c9 ),
inference(resolution,[status(thm)],[f1457,f1019]) ).
fof(f1461,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ19_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1202,f1458]) ).
fof(f1462,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ19_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1012,f1461]) ).
fof(f1463,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1462]) ).
fof(f1464,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f1463]) ).
fof(f1468,plain,
( sQ39_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1010,f757]) ).
fof(f1469,plain,
( sQ39_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1202,f1468]) ).
fof(f1470,plain,
( sQ39_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1010,f1469]) ).
fof(f1471,plain,
( sQ39_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1023,f1470]) ).
fof(f1472,plain,
( sQ39_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1471]) ).
fof(f1473,plain,
( sQ39_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1472]) ).
fof(f1474,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| inverse(X0) != sk_c11
| multiply(sk_c9,multiply(X0,sk_c11)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1023,f277]) ).
fof(f1475,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1202,f1474]) ).
fof(f1476,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1023,f1475]) ).
fof(f1477,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1010,f1476]) ).
fof(f1478,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1023,f1477]) ).
fof(f1497,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ17_spl
| inverse(sk_c9) != sk_c9 ),
inference(resolution,[status(thm)],[f1478,f1202]) ).
fof(f1502,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ17_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1012,f1497]) ).
fof(f1503,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1502]) ).
fof(f1504,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f1503]) ).
fof(f1523,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| inverse(sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1023,f132]) ).
fof(f1524,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1012,f1523]) ).
fof(f1525,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1010,f1524]) ).
fof(f1526,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1525]) ).
fof(f1527,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1526]) ).
fof(f1624,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1144,f592,f137,f133,f173,f186]) ).
fof(f1679,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1010,f594]) ).
fof(f1680,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1023,f1679]) ).
fof(f1681,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1680]) ).
fof(f1682,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1681]) ).
fof(f1691,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| inverse(inverse(sk_c9)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1022,f605]) ).
fof(f1692,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| inverse(sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1012,f1691]) ).
fof(f1693,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1012,f1692]) ).
fof(f1694,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1023,f1693]) ).
fof(f1695,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1694]) ).
fof(f1696,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1695]) ).
fof(f1697,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f456,f378,f199,f225,f212,f173,f186]) ).
fof(f1699,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f930,f715]) ).
fof(f1713,plain,
( sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1699,f594]) ).
fof(f1714,plain,
( sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f477,f1713]) ).
fof(f1715,plain,
( sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1714]) ).
fof(f1716,plain,
( sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1715]) ).
fof(f1726,plain,
( sQ48_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1699,f921]) ).
fof(f1735,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f930,f650]) ).
fof(f1736,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1699,f1735]) ).
fof(f1777,plain,
( sQ48_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1736,f1726]) ).
fof(f1778,plain,
( sQ48_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1777]) ).
fof(f1779,plain,
( sQ48_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1778]) ).
fof(f1790,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f470,f591]) ).
fof(f1791,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1736,f1790]) ).
fof(f1792,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f477,f1791]) ).
fof(f1793,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1792]) ).
fof(f1794,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1793]) ).
fof(f1798,plain,
( sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sk_c2 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f930,f924]) ).
fof(f1799,plain,
( sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1699,f1798]) ).
fof(f1800,plain,
( sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1799]) ).
fof(f1801,plain,
( sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1800]) ).
fof(f1802,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f140,f148,f152,f168,f176,f177,f179,f180,f182,f183,f184,f189,f190,f192,f193,f197,f198,f202,f203,f205,f206,f210,f211,f215,f216,f218,f219,f223,f224,f228,f229,f231,f232,f236,f237,f253,f274,f390,f428,f432,f444,f540,f564,f595,f602,f606,f627,f634,f639,f730,f772,f776,f780,f801,f904,f910,f911,f918,f925,f927,f976,f1105,f1334,f1443,f1464,f1473,f1504,f1527,f1624,f1682,f1696,f1697,f1716,f1779,f1794,f1801]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP238-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:06:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.055238 seconds
% 0.14/0.42 % CPU time: 0.249174 seconds
% 0.14/0.42 % Total memory used: 57.133 MB
% 0.14/0.42 % Net memory used: 56.884 MB
%------------------------------------------------------------------------------