%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP339-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:33:27 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 58
% Syntax : Number of formulae : 260 ( 13 unt; 29 def)
% Number of atoms : 824 ( 299 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1058 ( 494 ~; 535 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 30 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 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_c8,sk_c9) = sk_c7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
! [X3,X4,X1,X2,X5,X6] :
( multiply(X5,sk_c9) != X6
| inverse(X6) != sk_c9
| inverse(X5) != X6
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f43,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f44,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f45,plain,
multiply(sk_c8,sk_c9) = sk_c7,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f46,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f49,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f50,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f56,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f57,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f58,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f64,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f65,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f66,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f67,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f68,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f74,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f75,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f76,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f77,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f82,plain,
! [X5,X6] :
( multiply(X5,sk_c9) != X6
| inverse(X6) != sk_c9
| inverse(X5) != X6
| ! [X2] :
( multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| ! [X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4,X5] :
( multiply(X4,sk_c9) != X5
| inverse(X5) != sk_c9
| inverse(X4) != X5
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f84,f87]) ).
fof(f91,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f84,f91]) ).
fof(f95,definition,
( sQ3_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ3_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f97,plain,
( sQ3_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f84,f95]) ).
fof(f99,definition,
( sQ4_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ4_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f84,f99]) ).
fof(f103,definition,
( sQ5_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f84,f103]) ).
fof(f107,definition,
( sQ6_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ6_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f84,f107]) ).
fof(f123,definition,
( sQ10_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ10_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f55,f123,f87]) ).
fof(f127,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f56,f123,f91]) ).
fof(f128,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f57,f123,f95]) ).
fof(f129,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f58,f123,f99]) ).
fof(f130,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f123,f103]) ).
fof(f131,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f60,f123,f107]) ).
fof(f135,definition,
( sQ11_spl
<=> multiply(sk_c2,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f64,f135,f87]) ).
fof(f139,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f65,f135,f91]) ).
fof(f140,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f66,f135,f95]) ).
fof(f141,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f67,f135,f99]) ).
fof(f142,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f135,f103]) ).
fof(f143,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f135,f107]) ).
fof(f147,definition,
( sQ12_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ12_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f73,f147,f87]) ).
fof(f151,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f74,f147,f91]) ).
fof(f152,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f75,f147,f95]) ).
fof(f153,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f76,f147,f99]) ).
fof(f154,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f77,f147,f103]) ).
fof(f155,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f78,f147,f107]) ).
fof(f159,definition,
( sQ13_spl
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ13_spl
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,definition,
! [X0] :
( sQ14_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f163,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
! [X1] :
( sQ15_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f166,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
! [X2] :
( sQ16_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f169,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
! [X3] :
( sQ17_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f172,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
! [X4,X5] :
( sQ18_spl
<=> ( multiply(X4,sk_c9) != X5
| inverse(X5) != sk_c9
| inverse(X4) != X5 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X0,sk_c9) != X1
| inverse(X1) != sk_c9
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ18_spl
| sQ17_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f83,f159,f162,f165,f168,f95,f99,f171,f174]) ).
fof(f189,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f43,f44]) ).
fof(f190,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f42,f189]) ).
fof(f195,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f88,f44]) ).
fof(f203,plain,
( ~ sQ18_spl
| inverse(sk_c7) != sk_c9
| inverse(sk_c8) != sk_c7 ),
inference(resolution,[status(thm)],[f175,f45]) ).
fof(f215,definition,
( sQ20_spl
<=> inverse(sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ20_spl
| inverse(sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f227,definition,
( sQ23_spl
<=> inverse(sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f231,definition,
( sQ24_spl
<=> inverse(sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ24_spl
| inverse(sk_c7) != sk_c9 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f203,f95,f231,f174]) ).
fof(f241,plain,
( sQ13_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f45,f161]) ).
fof(f242,plain,
( sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f241]) ).
fof(f243,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f242]) ).
fof(f244,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f172,f108]) ).
fof(f246,plain,
( ~ sQ17_spl
| identity != sk_c8
| inverse(inverse(sk_c7)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f43,f172]) ).
fof(f249,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f104,f244]) ).
fof(f250,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f249]) ).
fof(f251,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f255,plain,
( ~ sQ16_spl
| inverse(sk_c8) != sk_c9
| sk_c7 != sk_c8 ),
inference(paramodulation,[status(thm)],[f45,f169]) ).
fof(f256,definition,
( sQ25_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ25_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f263,definition,
( sQ27_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ27_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f267,definition,
( sQ28_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ28_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f255,f267,f215,f168]) ).
fof(f272,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| inverse(sk_c2) != sk_c8 ),
inference(resolution,[status(thm)],[f166,f136]) ).
fof(f275,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c9 ),
inference(paramodulation,[status(thm)],[f42,f166]) ).
fof(f277,plain,
! [X0,X1] :
( ~ sQ15_spl
| inverse(multiply(X0,X1)) != sk_c8
| multiply(X0,multiply(X1,sk_c8)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f44,f166]) ).
fof(f279,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ12_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f148,f272]) ).
fof(f280,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f279]) ).
fof(f281,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f282,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f163,f124]) ).
fof(f284,plain,
( ~ sQ14_spl
| identity != sk_c9
| inverse(inverse(sk_c8)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f43,f163]) ).
fof(f287,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f85,f282]) ).
fof(f288,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f287]) ).
fof(f289,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,definition,
( sQ29_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ29_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f294,definition,
( sQ30_spl
<=> inverse(inverse(sk_c8)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ30_spl
| inverse(inverse(sk_c8)) != sk_c9 ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
( sQ31_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ31_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,plain,
( ~ sQ14_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f284,f294,f297,f162]) ).
fof(f308,plain,
( sQ20_spl
| ~ sQ3_spl
| sk_c7 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f96,f217]) ).
fof(f312,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c9 ),
inference(resolution,[status(thm)],[f169,f88]) ).
fof(f319,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f92,f312]) ).
fof(f320,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f319]) ).
fof(f321,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f348,plain,
( ~ sQ1_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f88,f190]) ).
fof(f349,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f108,f190]) ).
fof(f361,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f92,f348]) ).
fof(f362,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f104,f349]) ).
fof(f385,plain,
( sQ30_spl
| ~ sQ3_spl
| inverse(sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f96,f296]) ).
fof(f470,definition,
( sQ43_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ15_spl
| ~ sQ43_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f275,f263,f470,f165]) ).
fof(f494,plain,
! [X0] :
( ~ sQ15_spl
| inverse(multiply(inverse(X0),X0)) != sk_c8
| sk_c8 != sk_c9 ),
inference(paramodulation,[status(thm)],[f190,f277]) ).
fof(f519,definition,
! [X0] :
( sQ49_spl
<=> inverse(multiply(inverse(X0),X0)) != sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f520,plain,
! [X0] :
( ~ sQ49_spl
| inverse(multiply(inverse(X0),X0)) != sk_c8 ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,plain,
( ~ sQ15_spl
| sQ49_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f494,f263,f519,f165]) ).
fof(f535,plain,
( ~ sQ49_spl
| inverse(identity) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f43,f520]) ).
fof(f540,plain,
( ~ sQ11_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f136,f190]) ).
fof(f542,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f148,f540]) ).
fof(f576,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f542,f45]) ).
fof(f579,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f542,f190]) ).
fof(f581,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f269]) ).
fof(f582,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f631,definition,
( sQ53_spl
<=> sk_c7 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f633,plain,
( sQ53_spl
| sk_c7 != sk_c9 ),
inference(component_clause,[status(thm)],[f631]) ).
fof(f657,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c8) = multiply(sk_c3,sk_c9) ),
inference(paramodulation,[status(thm)],[f361,f195]) ).
fof(f660,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| sk_c9 != sk_c9
| inverse(sk_c9) != sk_c9 ),
inference(paramodulation,[status(thm)],[f361,f163]) ).
fof(f661,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f361,f190]) ).
fof(f663,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c3,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f362,f657]) ).
fof(f664,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f88,f663]) ).
fof(f666,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ29_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f660,f227,f290,f162,f91,f87]) ).
fof(f667,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f43,f661]) ).
fof(f672,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f664,f96]) ).
fof(f673,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f664,f45]) ).
fof(f689,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f673,f190]) ).
fof(f691,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f43,f689]) ).
fof(f692,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f691,f299]) ).
fof(f693,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f692]) ).
fof(f694,plain,
( sQ24_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f664,f233]) ).
fof(f695,plain,
( sQ24_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f672,f694]) ).
fof(f698,plain,
( sQ30_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f664,f385]) ).
fof(f699,plain,
( sQ30_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f672,f698]) ).
fof(f701,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f667,f672]) ).
fof(f711,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 != identity ),
inference(backward_demodulation,[status(thm)],[f667,f265]) ).
fof(f718,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f667,f701]) ).
fof(f721,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f711,f297,f91,f87,f263]) ).
fof(f724,plain,
( sQ30_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f699,f263,f103,f107,f91,f87,f95,f294]) ).
fof(f726,plain,
( sQ24_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f695,f263,f95,f103,f107,f91,f87,f231]) ).
fof(f729,plain,
( sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f292]) ).
fof(f730,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f731,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f43,f579]) ).
fof(f740,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f731,f124]) ).
fof(f741,plain,
( sQ53_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c7 != identity ),
inference(backward_demodulation,[status(thm)],[f731,f633]) ).
fof(f742,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f731,f85]) ).
fof(f756,plain,
( sQ31_spl
| ~ sQ11_spl
| ~ sQ12_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f731,f299]) ).
fof(f757,plain,
( sQ31_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f756]) ).
fof(f758,plain,
( sQ31_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f757]) ).
fof(f773,plain,
( sQ53_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c8 != identity ),
inference(forward_demodulation,[status(thm)],[f576,f741]) ).
fof(f779,plain,
( sQ3_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f576,f97]) ).
fof(f798,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(identity,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f742,f43]) ).
fof(f800,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f798]) ).
fof(f804,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(identity) = identity ),
inference(backward_demodulation,[status(thm)],[f800,f742]) ).
fof(f805,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(identity,sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f800,f740]) ).
fof(f808,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f805]) ).
fof(f809,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f808,f258]) ).
fof(f810,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f809]) ).
fof(f813,plain,
( sQ53_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f773,f256,f147,f135,f631]) ).
fof(f820,plain,
( sQ3_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c8) != identity ),
inference(backward_demodulation,[status(thm)],[f808,f779]) ).
fof(f825,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f808,f576]) ).
fof(f826,plain,
( sQ3_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f808,f820]) ).
fof(f843,plain,
( sQ3_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f804,f826]) ).
fof(f844,plain,
( sQ3_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f843]) ).
fof(f845,plain,
( sQ3_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f844]) ).
fof(f873,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f308,f631,f95,f215]) ).
fof(f875,plain,
( sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(identity,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f731,f101]) ).
fof(f876,plain,
( sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f42,f875]) ).
fof(f877,plain,
( sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f825,f876]) ).
fof(f878,plain,
( sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f808,f877]) ).
fof(f879,plain,
( sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f878]) ).
fof(f880,plain,
( sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f879]) ).
fof(f972,plain,
( sQ24_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(identity) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f825,f233]) ).
fof(f973,plain,
( sQ24_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f804,f972]) ).
fof(f974,plain,
( sQ24_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f731,f973]) ).
fof(f975,plain,
( sQ24_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f974]) ).
fof(f976,plain,
( sQ24_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f975]) ).
fof(f990,definition,
( sQ55_spl
<=> inverse(inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f992,plain,
( sQ55_spl
| inverse(inverse(sk_c7)) != sk_c8 ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f993,plain,
( ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f246,f990,f256,f171]) ).
fof(f998,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(inverse(identity)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f825,f992]) ).
fof(f999,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(identity) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f804,f998]) ).
fof(f1000,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f804,f999]) ).
fof(f1001,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f808,f1000]) ).
fof(f1002,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1001]) ).
fof(f1003,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1002]) ).
fof(f1060,plain,
( ~ sQ49_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f718,f535]) ).
fof(f1061,plain,
( ~ sQ49_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f667,f1060]) ).
fof(f1062,plain,
( ~ sQ49_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1061]) ).
fof(f1063,plain,
( ~ sQ49_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1062]) ).
fof(f1064,plain,
$false,
inference(sat_refutation,[status(thm)],[f90,f94,f98,f102,f106,f110,f126,f127,f128,f129,f130,f131,f138,f139,f140,f141,f142,f143,f150,f151,f152,f153,f154,f155,f177,f234,f243,f251,f270,f281,f289,f300,f321,f473,f522,f582,f666,f693,f721,f724,f726,f730,f758,f810,f813,f845,f873,f880,f976,f993,f1003,f1063]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP339-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:10:10 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.056094 seconds
% 0.14/0.44 % CPU time: 0.277100 seconds
% 0.14/0.44 % Total memory used: 70.026 MB
% 0.14/0.44 % Net memory used: 69.788 MB
%------------------------------------------------------------------------------