%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP382-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:33:34 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.49s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 83
% Syntax : Number of formulae : 382 ( 12 unt; 42 def)
% Number of atoms : 1222 ( 460 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1578 ( 738 ~; 798 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 43 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 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_c12) = sk_c11
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c11,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| multiply(X6,sk_c12) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| inverse(X4) != sk_c12
| multiply(sk_c11,sk_c10) != sk_c12
| inverse(sk_c12) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f76,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f77,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c11,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f90,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f93,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f102,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f103,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f108,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f109,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f111,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f113,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f118,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f119,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f120,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f121,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f122,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c2,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f123,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f128,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f129,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f130,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f131,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f132,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f133,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f140,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f141,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f143,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f148,plain,
! [X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| ! [X2] :
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| ! [X1] :
( inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| ! [X6] :
( multiply(X6,sk_c12) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X4] :
( multiply(X4,sk_c11) != sk_c12
| inverse(X4) != sk_c12
| multiply(sk_c11,sk_c10) != sk_c12
| inverse(sk_c12) != sk_c11 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| multiply(X2,sk_c12) != sk_c11
| inverse(X1) != X2
| multiply(X1,X2) != sk_c11
| multiply(X0,sk_c11) != sk_c12
| inverse(X0) != sk_c12
| multiply(sk_c11,sk_c10) != sk_c12
| inverse(sk_c12) != sk_c11 ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,definition,
( sQ0_spl
<=> inverse(sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ0_spl
| inverse(sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f152,plain,
( sQ0_spl
| inverse(sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f150,f153]) ).
fof(f157,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c12 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f150,f157]) ).
fof(f161,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f80,f150,f161]) ).
fof(f165,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c11 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f150,f165]) ).
fof(f169,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c9) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c12 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f82,f150,f169]) ).
fof(f173,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f83,f150,f173]) ).
fof(f193,definition,
( sQ11_spl
<=> multiply(sk_c11,sk_c10) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ11_spl
| multiply(sk_c11,sk_c10) = sk_c12 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( sQ11_spl
| multiply(sk_c11,sk_c10) != sk_c12 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f88,f193,f153]) ).
fof(f197,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f89,f193,f157]) ).
fof(f198,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f90,f193,f161]) ).
fof(f199,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f91,f193,f165]) ).
fof(f200,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f92,f193,f169]) ).
fof(f201,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f93,f193,f173]) ).
fof(f206,definition,
( sQ12_spl
<=> inverse(sk_c1) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ12_spl
| inverse(sk_c1) = sk_c12 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f98,f206,f153]) ).
fof(f210,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f99,f206,f157]) ).
fof(f212,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f101,f206,f165]) ).
fof(f213,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f102,f206,f169]) ).
fof(f214,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f103,f206,f173]) ).
fof(f219,definition,
( sQ13_spl
<=> multiply(sk_c1,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ13_spl
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f221,plain,
( sQ13_spl
| multiply(sk_c1,sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f108,f219,f153]) ).
fof(f223,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f109,f219,f157]) ).
fof(f225,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f111,f219,f165]) ).
fof(f226,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f112,f219,f169]) ).
fof(f227,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f113,f219,f173]) ).
fof(f232,definition,
( sQ14_spl
<=> multiply(sk_c2,sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ14_spl
| multiply(sk_c2,sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f118,f232,f153]) ).
fof(f236,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f119,f232,f157]) ).
fof(f237,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f120,f232,f161]) ).
fof(f238,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f121,f232,f165]) ).
fof(f239,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f122,f232,f169]) ).
fof(f240,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f123,f232,f173]) ).
fof(f245,definition,
( sQ15_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ15_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f128,f245,f153]) ).
fof(f249,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f129,f245,f157]) ).
fof(f250,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f130,f245,f161]) ).
fof(f251,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f131,f245,f165]) ).
fof(f252,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f132,f245,f169]) ).
fof(f253,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f133,f245,f173]) ).
fof(f258,definition,
( sQ16_spl
<=> multiply(sk_c3,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ16_spl
| multiply(sk_c3,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f263,plain,
( sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f140,f258,f161]) ).
fof(f264,plain,
( sQ4_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f141,f258,f165]) ).
fof(f266,plain,
( sQ6_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f143,f258,f173]) ).
fof(f271,definition,
! [X0] :
( sQ17_spl
<=> ( multiply(X0,sk_c11) != sk_c12
| inverse(X0) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f272,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c11) != sk_c12
| inverse(X0) != sk_c12 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
! [X1,X2] :
( sQ18_spl
<=> ( multiply(X2,sk_c12) != sk_c11
| inverse(X1) != X2
| multiply(X1,X2) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f275,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,sk_c12) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
! [X3] :
( sQ19_spl
<=> ( inverse(X3) != sk_c12
| multiply(X3,sk_c12) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f278,plain,
! [X0] :
( ~ sQ19_spl
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
! [X4] :
( sQ20_spl
<=> ( inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f281,plain,
! [X0] :
( ~ sQ20_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,definition,
! [X5,X6,X7,X8] :
( sQ21_spl
<=> ( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f284,plain,
! [X0,X1,X2,X3] :
( ~ sQ21_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c11) != sk_c12
| inverse(X0) != X1
| multiply(X0,X1) != sk_c12 ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,plain,
( sQ21_spl
| sQ20_spl
| sQ19_spl
| sQ18_spl
| sQ17_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f149,f150,f193,f271,f274,f277,f280,f283]) ).
fof(f298,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f76,f77]) ).
fof(f299,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f75,f298]) ).
fof(f302,plain,
( ~ sQ4_spl
| multiply(sk_c11,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f166,f76]) ).
fof(f305,plain,
( ~ sQ0_spl
| multiply(sk_c11,sk_c12) = identity ),
inference(paramodulation,[status(thm)],[f151,f76]) ).
fof(f318,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| multiply(X1,identity) != X2
| inverse(X2) != identity
| inverse(X1) != X2
| sk_c11 != sk_c12
| inverse(X0) != identity
| multiply(X0,identity) != sk_c12 ),
inference(paramodulation,[status(thm)],[f75,f284]) ).
fof(f337,definition,
( sQ27_spl
<=> sk_c10 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ27_spl
| sk_c10 != sk_c12 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f344,definition,
( sQ29_spl
<=> sk_c12 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ29_spl
| sk_c12 != sk_c12 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f352,definition,
( sQ31_spl
<=> identity = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( sQ31_spl
| identity != sk_c12 ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f359,definition,
! [X0] :
( sQ33_spl
<=> ( inverse(X0) != identity
| multiply(X0,identity) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f360,plain,
! [X0] :
( ~ sQ33_spl
| inverse(X0) != identity
| multiply(X0,identity) != sk_c12 ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,definition,
( sQ34_spl
<=> sk_c11 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( ~ sQ34_spl
| sk_c11 = sk_c12 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f364,plain,
( sQ34_spl
| sk_c11 != sk_c12 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,definition,
! [X1,X2] :
( sQ35_spl
<=> ( multiply(X1,identity) != X2
| inverse(X2) != identity
| inverse(X1) != X2 ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f366,plain,
! [X0,X1] :
( ~ sQ35_spl
| multiply(X0,identity) != X1
| inverse(X1) != identity
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ sQ21_spl
| sQ35_spl
| ~ sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f318,f359,f362,f365,f283]) ).
fof(f369,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| inverse(sk_c1) != sk_c11
| sk_c12 != sk_c10 ),
inference(paramodulation,[status(thm)],[f220,f281]) ).
fof(f370,plain,
( ~ sQ20_spl
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10 ),
inference(paramodulation,[status(thm)],[f76,f281]) ).
fof(f371,plain,
( ~ sQ20_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramodulation,[status(thm)],[f75,f281]) ).
fof(f373,definition,
( sQ36_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( sQ36_spl
| inverse(sk_c1) != sk_c11 ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ36_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f369,f337,f373,f280,f219]) ).
fof(f377,definition,
( sQ37_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( sQ37_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,definition,
( sQ38_spl
<=> inverse(inverse(sk_c11)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ20_spl
| ~ sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f370,f377,f380,f280]) ).
fof(f384,definition,
( sQ39_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ39_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,definition,
( sQ40_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ40_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,plain,
( ~ sQ20_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f371,f384,f387,f280]) ).
fof(f391,plain,
( sQ36_spl
| ~ sQ12_spl
| sk_c12 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f207,f375]) ).
fof(f392,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| inverse(sk_c4) != sk_c12 ),
inference(resolution,[status(thm)],[f278,f154]) ).
fof(f396,plain,
( ~ sQ19_spl
| inverse(identity) != sk_c12
| sk_c12 != sk_c11 ),
inference(paramodulation,[status(thm)],[f75,f278]) ).
fof(f399,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ2_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f158,f392]) ).
fof(f400,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f399]) ).
fof(f401,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f404,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ18_spl
| sk_c11 != sk_c11
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c11 ),
inference(paramodulation,[status(thm)],[f154,f275]) ).
fof(f405,plain,
! [X0] :
( ~ sQ18_spl
| identity != sk_c11
| inverse(X0) != inverse(sk_c12)
| multiply(X0,inverse(sk_c12)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f76,f275]) ).
fof(f406,plain,
! [X0] :
( ~ sQ18_spl
| sk_c12 != sk_c11
| inverse(X0) != identity
| multiply(X0,identity) != sk_c11 ),
inference(paramodulation,[status(thm)],[f75,f275]) ).
fof(f408,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| sk_c11 != sk_c11
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c11 ),
inference(paramodulation,[status(thm)],[f259,f275]) ).
fof(f409,definition,
! [X0] :
( sQ41_spl
<=> ( inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f412,definition,
( sQ42_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( sQ42_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f415,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f404,f409,f412,f274,f153]) ).
fof(f416,definition,
! [X0] :
( sQ43_spl
<=> ( inverse(X0) != inverse(sk_c12)
| multiply(X0,inverse(sk_c12)) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f417,plain,
! [X0] :
( ~ sQ43_spl
| inverse(X0) != inverse(sk_c12)
| multiply(X0,inverse(sk_c12)) != sk_c11 ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,definition,
( sQ44_spl
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( sQ44_spl
| identity != sk_c11 ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( ~ sQ18_spl
| ~ sQ44_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f405,f416,f419,f274]) ).
fof(f423,definition,
! [X0] :
( sQ45_spl
<=> ( inverse(X0) != identity
| multiply(X0,identity) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f424,plain,
! [X0] :
( ~ sQ45_spl
| inverse(X0) != identity
| multiply(X0,identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ18_spl
| ~ sQ34_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f406,f423,f362,f274]) ).
fof(f427,definition,
! [X0] :
( sQ46_spl
<=> ( inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ42_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f408,f427,f412,f274,f258]) ).
fof(f431,plain,
( sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f414]) ).
fof(f432,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ0_spl
| inverse(X0) != inverse(sk_c12)
| multiply(X0,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f151,f417]) ).
fof(f434,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ0_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f151,f433]) ).
fof(f435,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| inverse(sk_c1) != sk_c12 ),
inference(resolution,[status(thm)],[f272,f220]) ).
fof(f437,plain,
( ~ sQ17_spl
| identity != sk_c12
| inverse(inverse(sk_c11)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f76,f272]) ).
fof(f438,plain,
( ~ sQ17_spl
| sk_c11 != sk_c12
| inverse(identity) != sk_c12 ),
inference(paramodulation,[status(thm)],[f75,f272]) ).
fof(f440,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ12_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f207,f435]) ).
fof(f441,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f440]) ).
fof(f442,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f449,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| inverse(sk_c5) != sk_c11 ),
inference(resolution,[status(thm)],[f281,f162]) ).
fof(f456,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| ~ sQ4_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f166,f449]) ).
fof(f457,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f456]) ).
fof(f458,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f497,plain,
( ~ sQ1_spl
| sk_c12 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f154,f299]) ).
fof(f498,plain,
( ~ sQ3_spl
| sk_c11 = multiply(inverse(sk_c5),sk_c10) ),
inference(paramodulation,[status(thm)],[f162,f299]) ).
fof(f501,plain,
( ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c12) ),
inference(paramodulation,[status(thm)],[f170,f299]) ).
fof(f511,plain,
( ~ sQ14_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c11) ),
inference(paramodulation,[status(thm)],[f233,f299]) ).
fof(f518,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f158,f497]) ).
fof(f519,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f166,f498]) ).
fof(f520,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c11 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f194,f519]) ).
fof(f521,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f364]) ).
fof(f522,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c12) ),
inference(forward_demodulation,[status(thm)],[f174,f501]) ).
fof(f526,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sk_c3 = multiply(sk_c3,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f246,f511]) ).
fof(f550,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(inverse(sk_c12),sk_c12) ),
inference(paramodulation,[status(thm)],[f518,f299]) ).
fof(f553,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f550]) ).
fof(f554,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f421]) ).
fof(f555,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ44_spl ),
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f558,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(identity,sk_c10) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f553,f195]) ).
fof(f562,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(identity,sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f553,f302]) ).
fof(f565,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f553,f389]) ).
fof(f567,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,identity) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f553,f162]) ).
fof(f568,plain,
( sQ39_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f553,f386]) ).
fof(f569,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f553,f166]) ).
fof(f570,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c1,identity) = sk_c12 ),
inference(backward_demodulation,[status(thm)],[f553,f220]) ).
fof(f574,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f75,f558]) ).
fof(f578,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f562]) ).
fof(f595,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) = identity ),
inference(backward_demodulation,[status(thm)],[f578,f569]) ).
fof(f596,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(identity,identity) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f578,f567]) ).
fof(f597,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| identity = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f75,f596]) ).
fof(f598,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f379]) ).
fof(f599,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f598]) ).
fof(f600,plain,
( sQ39_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f568,f377,f157,f153,f384]) ).
fof(f624,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f595,f565]) ).
fof(f625,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f624]) ).
fof(f626,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f636,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ35_spl
| inverse(sk_c12) != identity
| inverse(sk_c1) != sk_c12 ),
inference(resolution,[status(thm)],[f366,f570]) ).
fof(f640,plain,
( ~ sQ35_spl
| inverse(identity) != identity
| inverse(identity) != identity ),
inference(resolution,[status(thm)],[f366,f75]) ).
fof(f650,definition,
( sQ47_spl
<=> inverse(sk_c12) = identity ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f652,plain,
( sQ47_spl
| inverse(sk_c12) != identity ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ35_spl
| ~ sQ47_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f636,f206,f650,f365,f157,f153,f219]) ).
fof(f665,definition,
( sQ51_spl
<=> inverse(inverse(identity)) = identity ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( sQ51_spl
| inverse(inverse(identity)) != identity ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,definition,
( sQ52_spl
<=> inverse(identity) = identity ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f670,plain,
( sQ52_spl
| inverse(identity) != identity ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f672,plain,
( ~ sQ35_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f640,f668,f365]) ).
fof(f682,plain,
( sQ52_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f595,f670]) ).
fof(f683,plain,
( sQ52_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f682]) ).
fof(f684,plain,
( sQ52_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f683]) ).
fof(f686,plain,
( sQ51_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f595,f667]) ).
fof(f687,plain,
( sQ51_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f595,f686]) ).
fof(f688,plain,
( sQ51_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f687]) ).
fof(f689,plain,
( sQ51_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f697,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ33_spl
| inverse(sk_c1) != identity
| sk_c12 != sk_c12 ),
inference(paramodulation,[status(thm)],[f570,f360]) ).
fof(f699,plain,
( ~ sQ33_spl
| inverse(inverse(identity)) != identity
| identity != sk_c12 ),
inference(paramodulation,[status(thm)],[f76,f360]) ).
fof(f700,plain,
( ~ sQ33_spl
| inverse(identity) != identity
| identity != sk_c12 ),
inference(paramodulation,[status(thm)],[f75,f360]) ).
fof(f702,definition,
( sQ53_spl
<=> inverse(sk_c1) = identity ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f704,plain,
( sQ53_spl
| inverse(sk_c1) != identity ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f705,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ33_spl
| ~ sQ53_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f697,f344,f702,f359,f157,f153,f219]) ).
fof(f710,plain,
( ~ sQ33_spl
| ~ sQ51_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f699,f352,f665,f359]) ).
fof(f711,plain,
( ~ sQ33_spl
| ~ sQ52_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f700,f352,f668,f359]) ).
fof(f712,plain,
( sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f346]) ).
fof(f713,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f714,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| identity != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f597,f574]) ).
fof(f721,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c12 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f523,f299]) ).
fof(f724,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c12 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f721]) ).
fof(f725,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f724,f714]) ).
fof(f726,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f725]) ).
fof(f735,definition,
( sQ56_spl
<=> inverse(inverse(sk_c11)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f738,plain,
( ~ sQ17_spl
| ~ sQ31_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f437,f735,f352,f271]) ).
fof(f739,definition,
( sQ57_spl
<=> inverse(identity) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( sQ57_spl
| inverse(identity) != sk_c12 ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f742,plain,
( ~ sQ17_spl
| ~ sQ34_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f438,f739,f362,f271]) ).
fof(f753,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f724,f207]) ).
fof(f755,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(identity,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f753,f76]) ).
fof(f757,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f755]) ).
fof(f781,plain,
( ~ sQ34_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f553,f363]) ).
fof(f794,plain,
( sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c1,identity) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f553,f221]) ).
fof(f795,plain,
( sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c1,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f724,f794]) ).
fof(f796,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c4) = identity ),
inference(forward_demodulation,[status(thm)],[f724,f158]) ).
fof(f798,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(identity,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f796,f76]) ).
fof(f800,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f798]) ).
fof(f802,plain,
( sQ31_spl
| ~ sQ5_spl
| ~ sQ6_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f724,f354]) ).
fof(f803,plain,
( sQ31_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f802]) ).
fof(f804,plain,
( sQ31_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f803]) ).
fof(f809,plain,
( sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl
| multiply(identity,identity) != identity ),
inference(backward_demodulation,[status(thm)],[f757,f795]) ).
fof(f811,plain,
( sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f75,f809]) ).
fof(f812,plain,
( sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f811]) ).
fof(f813,plain,
( sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f812]) ).
fof(f814,plain,
( sQ36_spl
| ~ sQ12_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f391,f362,f206,f373]) ).
fof(f838,plain,
( sQ53_spl
| ~ sQ12_spl
| sk_c12 != identity ),
inference(backward_demodulation,[status(thm)],[f207,f704]) ).
fof(f843,plain,
( sQ47_spl
| ~ sQ0_spl
| sk_c11 != identity ),
inference(backward_demodulation,[status(thm)],[f151,f652]) ).
fof(f867,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f526,f299]) ).
fof(f869,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f867]) ).
fof(f870,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sQ47_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f869,f843]) ).
fof(f871,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sQ47_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f870]) ).
fof(f878,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| multiply(identity,sk_c10) = sk_c12 ),
inference(backward_demodulation,[status(thm)],[f869,f194]) ).
fof(f880,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sk_c10 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f75,f878]) ).
fof(f890,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(identity) = identity ),
inference(backward_demodulation,[status(thm)],[f800,f796]) ).
fof(f935,plain,
( ~ sQ34_spl
| ~ sQ14_spl
| ~ sQ15_spl
| identity = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f869,f363]) ).
fof(f936,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(identity) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f800,f158]) ).
fof(f962,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f578,f166]) ).
fof(f963,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f595,f962]) ).
fof(f972,plain,
( sQ53_spl
| ~ sQ12_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f838,f352,f206,f702]) ).
fof(f974,plain,
! [X0] :
( ~ sQ45_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(X0) != identity
| multiply(X0,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f869,f424]) ).
fof(f986,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| multiply(identity,sk_c12) = identity ),
inference(forward_demodulation,[status(thm)],[f869,f305]) ).
fof(f987,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sk_c12 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f986]) ).
fof(f994,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(sk_c12) = identity ),
inference(forward_demodulation,[status(thm)],[f869,f151]) ).
fof(f1008,plain,
( sQ34_spl
| ~ sQ14_spl
| ~ sQ15_spl
| identity != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f869,f364]) ).
fof(f1025,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(identity) = identity ),
inference(backward_demodulation,[status(thm)],[f987,f994]) ).
fof(f1026,plain,
( sQ27_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sk_c10 != identity ),
inference(backward_demodulation,[status(thm)],[f987,f339]) ).
fof(f1037,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f987,f880]) ).
fof(f1038,plain,
( sQ34_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f987,f1008]) ).
fof(f1039,plain,
( sQ34_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1038]) ).
fof(f1040,plain,
( sQ34_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1039]) ).
fof(f1053,plain,
( ~ sQ34_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f935,f352,f245,f232,f362]) ).
fof(f1061,plain,
( sQ37_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f1037,f379]) ).
fof(f1062,plain,
( sQ37_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1061]) ).
fof(f1063,plain,
( sQ37_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1062]) ).
fof(f1068,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f987,f741]) ).
fof(f1075,plain,
( sQ27_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f1037,f1026]) ).
fof(f1076,plain,
( sQ27_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1075]) ).
fof(f1077,plain,
( sQ27_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1076]) ).
fof(f1079,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f987,f207]) ).
fof(f1081,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| multiply(identity,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f1079,f76]) ).
fof(f1083,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f1081]) ).
fof(f1091,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(identity) = identity ),
inference(backward_demodulation,[status(thm)],[f1083,f1079]) ).
fof(f1092,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f1091,f668,f245,f232,f150,f206]) ).
fof(f1102,plain,
( ~ sQ19_spl
| ~ sQ57_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f396,f362,f739,f277]) ).
fof(f1111,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f1068,f668,f245,f232,f150,f739]) ).
fof(f1144,definition,
( sQ63_spl
<=> identity = identity ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1146,plain,
( sQ63_spl
| identity != identity ),
inference(component_clause,[status(thm)],[f1144]) ).
fof(f1160,plain,
( sQ63_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1146]) ).
fof(f1161,plain,
sQ63_spl,
inference(contradiction_clause,[status(thm)],[f1160]) ).
fof(f1268,plain,
( ~ sQ45_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(inverse(identity)) != identity ),
inference(resolution,[status(thm)],[f974,f76]) ).
fof(f1275,plain,
( ~ sQ45_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f1025,f1268]) ).
fof(f1276,plain,
( ~ sQ45_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f1025,f1275]) ).
fof(f1277,plain,
( ~ sQ45_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1276]) ).
fof(f1278,plain,
( ~ sQ45_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1277]) ).
fof(f1279,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f936,f739,f173,f169,f157]) ).
fof(f1377,plain,
( sQ0_spl
| ~ sQ34_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f781,f152]) ).
fof(f1378,plain,
( sQ0_spl
| ~ sQ34_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| identity != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f890,f1377]) ).
fof(f1379,plain,
( sQ0_spl
| ~ sQ34_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f963,f1378]) ).
fof(f1380,plain,
( sQ0_spl
| ~ sQ34_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1379]) ).
fof(f1381,plain,
( sQ0_spl
| ~ sQ34_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1380]) ).
fof(f1382,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c11
| multiply(X0,identity) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f963,f434]) ).
fof(f1383,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c11
| multiply(X0,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f963,f1382]) ).
fof(f1384,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != identity
| multiply(X0,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f963,f1383]) ).
fof(f1605,plain,
( ~ sQ43_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(inverse(identity)) != identity ),
inference(resolution,[status(thm)],[f1384,f76]) ).
fof(f1606,plain,
( ~ sQ43_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != identity ),
inference(resolution,[status(thm)],[f1384,f75]) ).
fof(f1612,plain,
( ~ sQ43_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1605,f665,f157,f153,f165,f150,f416]) ).
fof(f1613,plain,
( ~ sQ43_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f1606,f668,f157,f153,f165,f150,f416]) ).
fof(f1619,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f160,f164,f168,f172,f176,f196,f197,f198,f199,f200,f201,f209,f210,f212,f213,f214,f222,f223,f225,f226,f227,f235,f236,f237,f238,f239,f240,f248,f249,f250,f251,f252,f253,f263,f264,f266,f286,f368,f376,f383,f390,f401,f415,f422,f426,f430,f432,f442,f458,f522,f555,f599,f600,f626,f653,f672,f684,f689,f705,f710,f711,f713,f726,f738,f742,f804,f813,f814,f871,f972,f1040,f1053,f1063,f1077,f1092,f1102,f1111,f1161,f1278,f1279,f1381,f1612,f1613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP382-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:10:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.49 % Refutation found
% 0.09/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.52 % Elapsed time: 0.140186 seconds
% 0.09/0.52 % CPU time: 0.814921 seconds
% 0.09/0.52 % Total memory used: 117.233 MB
% 0.09/0.52 % Net memory used: 116.787 MB
%------------------------------------------------------------------------------