%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP228-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:33:09 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.44s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 52
% Syntax : Number of formulae : 258 ( 9 unt; 23 def)
% Number of atoms : 973 ( 326 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1351 ( 636 ~; 692 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
! [X4,X5,X6,X1,X3,X2,X7,X8] :
( multiply(X7,X2) != X8
| inverse(X8) != X2
| inverse(X7) != X8
| multiply(X2,sk_c9) != sk_c10
| inverse(X3) != X2
| multiply(X3,X2) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X6) != sk_c10
| multiply(X6,sk_c10) != X5
| multiply(sk_c10,X5) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f51,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f52,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f53,plain,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f56,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f57,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f62,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f65,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f71,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f73,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f74,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f75,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f80,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f82,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f83,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f84,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f89,plain,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f90,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f91,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f98,plain,
! [X2,X7,X8] :
( multiply(X7,X2) != X8
| inverse(X8) != X2
| inverse(X7) != X8
| multiply(X2,sk_c9) != sk_c10
| ! [X3] :
( inverse(X3) != X2
| multiply(X3,X2) != sk_c10
| ! [X1] :
( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(sk_c10) != sk_c9
| ! [X6] :
( inverse(X6) != sk_c10
| ! [X5] :
( multiply(X6,sk_c10) != X5
| multiply(sk_c10,X5) != sk_c9
| ! [X4] :
( multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != X5
| multiply(X4,X5) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
( sQ1_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ1_spl
| inverse(sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f105,plain,
( sQ1_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f100,f103]) ).
fof(f107,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f100,f107]) ).
fof(f111,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f100,f111]) ).
fof(f115,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f100,f115]) ).
fof(f119,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f100,f119]) ).
fof(f139,definition,
( sQ10_spl
<=> multiply(sk_c1,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ10_spl
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f139,f103]) ).
fof(f143,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f139,f107]) ).
fof(f144,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f139,f111]) ).
fof(f145,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f139,f115]) ).
fof(f146,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f139,f119]) ).
fof(f151,definition,
( sQ11_spl
<=> multiply(sk_c10,sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f151,f103]) ).
fof(f155,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f151,f107]) ).
fof(f156,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f151,f111]) ).
fof(f157,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f151,f115]) ).
fof(f158,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f151,f119]) ).
fof(f163,definition,
( sQ12_spl
<=> multiply(sk_c2,sk_c10) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ12_spl
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f80,f163,f103]) ).
fof(f167,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f163,f107]) ).
fof(f168,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f163,f111]) ).
fof(f169,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f163,f115]) ).
fof(f170,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f163,f119]) ).
fof(f175,definition,
( sQ13_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f175,f103]) ).
fof(f179,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f90,f175,f107]) ).
fof(f180,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f175,f111]) ).
fof(f181,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f175,f115]) ).
fof(f182,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f175,f119]) ).
fof(f187,definition,
! [X0] :
( sQ14_spl
<=> ( multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,definition,
! [X1,X2] :
( sQ15_spl
<=> ( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f191,plain,
! [X0,X1] :
( ~ sQ15_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
! [X4,X5,X6,X7] :
( sQ16_spl
<=> ( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != X5
| multiply(X4,X5) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f194,plain,
! [X0,X1,X2,X3] :
( ~ sQ16_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ16_spl
| ~ sQ1_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f187,f190,f103,f193]) ).
fof(f197,plain,
! [X0,X1] :
( ~ sQ16_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f194]) ).
fof(f200,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f116,f52]) ).
fof(f205,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c3,X0) = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f164,f52]) ).
fof(f289,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f191]) ).
fof(f291,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c2) != sk_c10
| multiply(sk_c10,sk_c3) != sk_c9 ),
inference(paramodulation,[status(thm)],[f164,f289]) ).
fof(f292,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f291,f151,f175,f190,f163]) ).
fof(f300,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f51,f52]) ).
fof(f301,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f50,f300]) ).
fof(f315,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f188,f112]) ).
fof(f317,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f188,f140]) ).
fof(f324,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f108,f315]) ).
fof(f325,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f324]) ).
fof(f326,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f325]) ).
fof(f327,plain,
( ~ sQ16_spl
| inverse(inverse(identity)) != inverse(identity)
| multiply(inverse(identity),sk_c9) != sk_c10
| multiply(identity,inverse(identity)) != sk_c10 ),
inference(resolution,[status(thm)],[f197,f50]) ).
fof(f337,definition,
( sQ35_spl
<=> multiply(identity,inverse(identity)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ35_spl
| multiply(identity,inverse(identity)) != sk_c10 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,definition,
( sQ36_spl
<=> multiply(inverse(identity),sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ36_spl
| multiply(inverse(identity),sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,definition,
( sQ37_spl
<=> inverse(inverse(identity)) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( sQ37_spl
| inverse(inverse(identity)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( ~ sQ16_spl
| ~ sQ37_spl
| ~ sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f327,f337,f340,f343,f193]) ).
fof(f365,plain,
( sQ35_spl
| inverse(identity) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f50,f339]) ).
fof(f413,plain,
( ~ sQ3_spl
| sk_c9 = multiply(inverse(sk_c4),sk_c10) ),
inference(paramodulation,[status(thm)],[f112,f301]) ).
fof(f415,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c10) ),
inference(paramodulation,[status(thm)],[f116,f301]) ).
fof(f422,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f164,f301]) ).
fof(f428,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f108,f413]) ).
fof(f430,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f120,f415]) ).
fof(f433,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c10,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f176,f422]) ).
fof(f463,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f50,f289]) ).
fof(f480,definition,
( sQ45_spl
<=> multiply(sk_c10,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ45_spl
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f491,definition,
( sQ48_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( sQ48_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,plain,
( ~ sQ15_spl
| ~ sQ48_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f463,f480,f491,f190]) ).
fof(f496,plain,
( sQ45_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f428,f482]) ).
fof(f497,plain,
( sQ45_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f496]) ).
fof(f498,plain,
( sQ45_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f503,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c10,sk_c10) = multiply(sk_c5,sk_c8) ),
inference(paramodulation,[status(thm)],[f430,f200]) ).
fof(f505,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c10 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f430,f301]) ).
fof(f508,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f428,f503]) ).
fof(f509,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f116,f508]) ).
fof(f517,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f51,f505]) ).
fof(f519,plain,
( sQ48_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(identity) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f509,f493]) ).
fof(f527,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f509,f104]) ).
fof(f544,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f509,f517]) ).
fof(f545,plain,
( sQ48_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f544,f519]) ).
fof(f546,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f545]) ).
fof(f547,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f561,plain,
( sQ37_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(inverse(sk_c9)) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f544,f345]) ).
fof(f562,plain,
( sQ37_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(inverse(sk_c9)) != inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f544,f561]) ).
fof(f563,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(inverse(sk_c9),sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f544,f342]) ).
fof(f564,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(inverse(sk_c9),sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f509,f563]) ).
fof(f565,plain,
( sQ35_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f365,f491,f337]) ).
fof(f602,plain,
( ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f140,f301]) ).
fof(f604,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f101,f602]) ).
fof(f609,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(sk_c2) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f620,f176]) ).
fof(f612,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f620,f152]) ).
fof(f613,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(identity) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f620,f493]) ).
fof(f617,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f620,f105]) ).
fof(f618,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c1) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f620,f101]) ).
fof(f620,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f152,f433]) ).
fof(f632,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f620,f164]) ).
fof(f657,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c9,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f618,f51]) ).
fof(f658,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c9,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f609,f51]) ).
fof(f668,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f620,f604]) ).
fof(f669,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f620,f668]) ).
fof(f679,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f612,f301]) ).
fof(f681,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f51,f679]) ).
fof(f688,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f681,f613]) ).
fof(f689,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f681,f50]) ).
fof(f697,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c9,sk_c1) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f681,f657]) ).
fof(f704,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c9,sk_c2) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f681,f658]) ).
fof(f735,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| X0 = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f689,f205]) ).
fof(f736,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| X0 = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f620,f735]) ).
fof(f737,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c2,sk_c9) ),
inference(paramodulation,[status(thm)],[f669,f736]) ).
fof(f743,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c9 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f632,f737]) ).
fof(f781,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c2) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f743,f704]) ).
fof(f783,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c1) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f743,f697]) ).
fof(f784,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c3) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f743,f688]) ).
fof(f791,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f743,f618]) ).
fof(f797,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c10 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f743,f620]) ).
fof(f801,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f689,f781]) ).
fof(f803,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f689,f783]) ).
fof(f811,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c9 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f801,f743]) ).
fof(f815,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f801,f681]) ).
fof(f816,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f801,f803]) ).
fof(f818,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c10 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f801,f797]) ).
fof(f822,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f801,f784]) ).
fof(f823,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f801,f822]) ).
fof(f824,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f816,f791]) ).
fof(f825,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f801,f824]) ).
fof(f826,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f823]) ).
fof(f827,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f831,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f544,f51]) ).
fof(f899,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f509,f104]) ).
fof(f906,definition,
( sQ66_spl
<=> multiply(inverse(sk_c9),sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f908,plain,
( sQ66_spl
| multiply(inverse(sk_c9),sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f906]) ).
fof(f914,plain,
( sQ66_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f831,f908]) ).
fof(f915,plain,
( sQ66_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f914]) ).
fof(f916,plain,
( sQ66_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f915]) ).
fof(f924,definition,
( sQ68_spl
<=> inverse(inverse(sk_c9)) = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f926,plain,
( sQ68_spl
| inverse(inverse(sk_c9)) != inverse(sk_c9) ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f933,plain,
( sQ68_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c9) != inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f899,f926]) ).
fof(f934,plain,
( sQ68_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 != inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f899,f933]) ).
fof(f935,plain,
( sQ68_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f899,f934]) ).
fof(f936,plain,
( sQ68_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f935]) ).
fof(f937,plain,
( sQ68_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f936]) ).
fof(f950,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f815,f50]) ).
fof(f980,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f815,f51]) ).
fof(f985,plain,
! [X0,X1] :
( ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f818,f197]) ).
fof(f986,plain,
! [X0,X1] :
( ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f811,f985]) ).
fof(f987,plain,
! [X0,X1] :
( ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f818,f986]) ).
fof(f988,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ16_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2)
| multiply(inverse(sk_c2),sk_c2) != sk_c2
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f987,f950]) ).
fof(f993,definition,
( sQ69_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f995,plain,
( sQ69_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(component_clause,[status(thm)],[f993]) ).
fof(f996,definition,
( sQ70_spl
<=> multiply(inverse(sk_c2),sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f998,plain,
( sQ70_spl
| multiply(inverse(sk_c2),sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f996]) ).
fof(f999,definition,
( sQ71_spl
<=> inverse(inverse(sk_c2)) = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1001,plain,
( sQ71_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2) ),
inference(component_clause,[status(thm)],[f999]) ).
fof(f1002,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ71_spl
| ~ sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f988,f993,f996,f999,f193,f100,f139,f175,f163,f151]) ).
fof(f1011,plain,
( sQ70_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f980,f998]) ).
fof(f1012,plain,
( sQ70_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1011]) ).
fof(f1013,plain,
( sQ70_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1012]) ).
fof(f1014,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f950,f995]) ).
fof(f1024,plain,
( sQ37_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f562,f924,f107,f111,f119,f115,f343]) ).
fof(f1025,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f564,f906,f107,f111,f119,f115,f340]) ).
fof(f1039,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f818,f176]) ).
fof(f1052,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1039,f1014]) ).
fof(f1053,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1052]) ).
fof(f1054,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1053]) ).
fof(f1055,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f811,f617]) ).
fof(f1056,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1039,f1055]) ).
fof(f1057,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f811,f1056]) ).
fof(f1058,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1057]) ).
fof(f1059,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1058]) ).
fof(f1114,plain,
( sQ71_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1039,f1001]) ).
fof(f1115,plain,
( sQ71_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1039,f1114]) ).
fof(f1116,plain,
( sQ71_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1039,f1115]) ).
fof(f1117,plain,
( sQ71_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1116]) ).
fof(f1118,plain,
( sQ71_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1117]) ).
fof(f1123,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f816,f317]) ).
fof(f1124,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c2 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1039,f1123]) ).
fof(f1125,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f818,f1124]) ).
fof(f1126,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1125]) ).
fof(f1127,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1126]) ).
fof(f1128,plain,
$false,
inference(sat_refutation,[status(thm)],[f106,f110,f114,f118,f122,f142,f143,f144,f145,f146,f154,f155,f156,f157,f158,f166,f167,f168,f169,f170,f178,f179,f180,f181,f182,f196,f292,f326,f346,f494,f498,f547,f565,f827,f916,f937,f1002,f1013,f1024,f1025,f1054,f1059,f1118,f1127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP228-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:10:05 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.44 % Refutation found
% 0.08/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.46 % Elapsed time: 0.086963 seconds
% 0.08/0.46 % CPU time: 0.372986 seconds
% 0.08/0.46 % Total memory used: 110.444 MB
% 0.08/0.46 % Net memory used: 110.088 MB
%------------------------------------------------------------------------------