%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP388-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:35 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.61s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 62
% Syntax : Number of formulae : 285 ( 18 unt; 27 def)
% Number of atoms : 867 ( 340 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1070 ( 488 ~; 555 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 28 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
inverse(sk_c10) = sk_c9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7] :
( multiply(X7,sk_c8) != sk_c10
| inverse(X7) != sk_c10
| multiply(X6,sk_c9) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != X3
| multiply(sk_c10,X3) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f39,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
inverse(sk_c10) = sk_c9,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f43,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f49,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f50,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f54,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f55,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f56,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f57,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f59,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f60,plain,
( inverse(sk_c3) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f62,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f63,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f64,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f65,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f66,plain,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f67,plain,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f68,plain,
( inverse(sk_c3) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f69,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f70,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f71,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f72,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f73,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f74,plain,
! [X7] :
( multiply(X7,sk_c8) != sk_c10
| inverse(X7) != sk_c10
| ! [X6] :
( multiply(X6,sk_c9) != sk_c8
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c10
| ! [X1] :
( multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9
| ! [X4] :
( inverse(X4) != sk_c10
| ! [X3] :
( multiply(X4,sk_c10) != X3
| multiply(sk_c10,X3) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X6,sk_c8) != sk_c10
| inverse(X6) != sk_c10
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( sQ0_spl
| multiply(sk_c8,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ1_spl
<=> multiply(sk_c10,sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ1_spl
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f76,f79]) ).
fof(f83,definition,
( sQ2_spl
<=> multiply(sk_c3,sk_c10) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f76,f83]) ).
fof(f87,definition,
( sQ3_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f76,f87]) ).
fof(f91,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f95,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f99,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f76,f99]) ).
fof(f103,definition,
( sQ7_spl
<=> inverse(sk_c7) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ7_spl
| inverse(sk_c7) = sk_c10 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f76,f103]) ).
fof(f107,definition,
( sQ8_spl
<=> multiply(sk_c7,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f76,f107]) ).
fof(f111,definition,
( sQ9_spl
<=> multiply(sk_c10,sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ9_spl
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f113,plain,
( sQ9_spl
| multiply(sk_c10,sk_c2) != sk_c9 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f111,f79]) ).
fof(f115,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f111,f83]) ).
fof(f116,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f111,f87]) ).
fof(f117,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f111,f91]) ).
fof(f118,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f111,f95]) ).
fof(f119,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f111,f99]) ).
fof(f120,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f111,f103]) ).
fof(f121,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f111,f107]) ).
fof(f122,definition,
( sQ10_spl
<=> multiply(sk_c1,sk_c10) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ10_spl
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f58,f122,f79]) ).
fof(f126,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f122,f83]) ).
fof(f127,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f60,f122,f87]) ).
fof(f128,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f61,f122,f91]) ).
fof(f129,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f122,f95]) ).
fof(f130,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f122,f99]) ).
fof(f131,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f122,f103]) ).
fof(f132,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f122,f107]) ).
fof(f133,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f66,f133,f79]) ).
fof(f137,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f67,f133,f83]) ).
fof(f138,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f133,f87]) ).
fof(f139,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f133,f91]) ).
fof(f140,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f133,f95]) ).
fof(f141,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f133,f99]) ).
fof(f142,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f133,f103]) ).
fof(f143,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f133,f107]) ).
fof(f144,definition,
( sQ12_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ12_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
! [X0,X1] :
( sQ13_spl
<=> ( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f148,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
! [X4,X5] :
( sQ14_spl
<=> ( multiply(X5,sk_c9) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f151,plain,
! [X0,X1] :
( ~ sQ14_spl
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
! [X6] :
( sQ15_spl
<=> ( multiply(X6,sk_c8) != sk_c10
| inverse(X6) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f154,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c8) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f75,f144,f76,f147,f150,f153]) ).
fof(f160,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c2,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f123,f40]) ).
fof(f162,plain,
( ~ sQ3_spl
| multiply(sk_c10,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f88,f39]) ).
fof(f164,plain,
( ~ sQ7_spl
| multiply(sk_c10,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f104,f39]) ).
fof(f165,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f134,f39]) ).
fof(f166,plain,
multiply(sk_c9,sk_c10) = identity,
inference(paramodulation,[status(thm)],[f41,f39]) ).
fof(f167,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f39,f40]) ).
fof(f168,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f38,f167]) ).
fof(f171,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c8,X0) = multiply(sk_c6,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f100,f40]) ).
fof(f173,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c4,X0) = multiply(sk_c3,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f84,f40]) ).
fof(f174,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f80,f40]) ).
fof(f175,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c10,X0) = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f77,f40]) ).
fof(f176,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| inverse(sk_c7) != sk_c10 ),
inference(resolution,[status(thm)],[f154,f108]) ).
fof(f181,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f104,f176]) ).
fof(f182,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f181]) ).
fof(f183,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,plain,
! [X0] :
( ~ sQ14_spl
| multiply(inverse(X0),sk_c9) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f151]) ).
fof(f185,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f148]) ).
fof(f186,plain,
( sQ12_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f41,f146]) ).
fof(f187,plain,
( sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f186]) ).
fof(f188,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
( ~ sQ14_spl
| multiply(inverse(identity),sk_c9) != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f38,f184]) ).
fof(f191,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| multiply(inverse(sk_c3),sk_c9) != sk_c8
| multiply(sk_c3,sk_c10) != sk_c8 ),
inference(paramodulation,[status(thm)],[f88,f184]) ).
fof(f192,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| multiply(inverse(sk_c5),sk_c9) != sk_c8
| multiply(sk_c5,sk_c6) != sk_c8 ),
inference(paramodulation,[status(thm)],[f96,f184]) ).
fof(f193,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| multiply(inverse(sk_c1),sk_c9) != sk_c8
| multiply(sk_c1,sk_c10) != sk_c8 ),
inference(paramodulation,[status(thm)],[f134,f184]) ).
fof(f194,plain,
( ~ sQ14_spl
| multiply(inverse(sk_c10),sk_c9) != sk_c8
| multiply(sk_c10,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f41,f184]) ).
fof(f195,definition,
( sQ16_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f198,definition,
( sQ17_spl
<=> multiply(inverse(identity),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f189,f195,f198,f150]) ).
fof(f202,definition,
( sQ18_spl
<=> multiply(sk_c3,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f205,definition,
( sQ19_spl
<=> multiply(inverse(sk_c3),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ19_spl
| multiply(inverse(sk_c3),sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f191,f202,f205,f150,f87]) ).
fof(f209,definition,
( sQ20_spl
<=> multiply(inverse(sk_c5),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ20_spl
| multiply(inverse(sk_c5),sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f192,f91,f209,f150,f95]) ).
fof(f213,definition,
( sQ21_spl
<=> multiply(sk_c1,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( sQ21_spl
| multiply(sk_c1,sk_c10) != sk_c8 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
( sQ22_spl
<=> multiply(inverse(sk_c1),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ22_spl
| multiply(inverse(sk_c1),sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f193,f213,f216,f150,f133]) ).
fof(f220,definition,
( sQ23_spl
<=> multiply(sk_c10,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ23_spl
| multiply(sk_c10,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ24_spl
<=> multiply(inverse(sk_c10),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f194,f220,f223,f150]) ).
fof(f228,plain,
( sQ22_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f134,f218]) ).
fof(f229,plain,
( sQ21_spl
| ~ sQ10_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f123,f215]) ).
fof(f230,plain,
( sQ20_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f96,f211]) ).
fof(f231,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f100,f230]) ).
fof(f232,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f231]) ).
fof(f233,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f234,plain,
( sQ19_spl
| ~ sQ3_spl
| multiply(sk_c10,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f88,f207]) ).
fof(f236,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c10
| multiply(sk_c10,sk_c4) != sk_c9 ),
inference(paramodulation,[status(thm)],[f84,f185]) ).
fof(f239,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c10
| multiply(sk_c10,sk_c2) != sk_c9 ),
inference(paramodulation,[status(thm)],[f123,f185]) ).
fof(f241,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f236,f79,f87,f147,f83]) ).
fof(f256,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f239,f111,f133,f147,f122]) ).
fof(f260,plain,
! [X0] :
( ~ sQ3_spl
| multiply(identity,X0) = multiply(sk_c10,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f162,f40]) ).
fof(f261,plain,
! [X0] :
( ~ sQ3_spl
| X0 = multiply(sk_c10,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f38,f260]) ).
fof(f262,plain,
! [X0] :
( ~ sQ11_spl
| multiply(identity,X0) = multiply(sk_c10,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f165,f40]) ).
fof(f263,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(sk_c10,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f38,f262]) ).
fof(f264,plain,
! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c10,X0)),
inference(paramodulation,[status(thm)],[f166,f40]) ).
fof(f265,plain,
! [X0] : X0 = multiply(sk_c9,multiply(sk_c10,X0)),
inference(forward_demodulation,[status(thm)],[f38,f264]) ).
fof(f270,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c7) = multiply(sk_c1,identity) ),
inference(paramodulation,[status(thm)],[f164,f160]) ).
fof(f271,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c1) = multiply(sk_c1,identity) ),
inference(paramodulation,[status(thm)],[f165,f160]) ).
fof(f276,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c1) = multiply(sk_c2,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f270,f271]) ).
fof(f285,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c10) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f166,f171]) ).
fof(f312,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f173,f261]) ).
fof(f313,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c10 = multiply(sk_c10,sk_c4) ),
inference(paramodulation,[status(thm)],[f84,f261]) ).
fof(f317,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c10) = identity ),
inference(backward_demodulation,[status(thm)],[f324,f166]) ).
fof(f324,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c10,X0) = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f174,f312]) ).
fof(f325,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c10) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f334,f78]) ).
fof(f326,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c2) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f334,f113]) ).
fof(f334,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f80,f313]) ).
fof(f354,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c10 = multiply(sk_c10,sk_c2) ),
inference(paramodulation,[status(thm)],[f123,f263]) ).
fof(f358,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f354,f326]) ).
fof(f359,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f365,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c10) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f366,f222]) ).
fof(f366,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f354,f112]) ).
fof(f370,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c10,X0) = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f366,f175]) ).
fof(f371,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(inverse(X0),sk_c10) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f366,f184]) ).
fof(f373,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c10) = identity ),
inference(forward_demodulation,[status(thm)],[f366,f166]) ).
fof(f375,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| X0 = multiply(sk_c10,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f366,f265]) ).
fof(f380,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f366,f41]) ).
fof(f387,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f373,f365]) ).
fof(f434,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ14_spl
| multiply(inverse(sk_c10),sk_c10) != sk_c8
| multiply(sk_c10,sk_c10) != sk_c8 ),
inference(paramodulation,[status(thm)],[f380,f371]) ).
fof(f436,definition,
( sQ33_spl
<=> multiply(sk_c10,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ33_spl
| multiply(sk_c10,sk_c10) != sk_c8 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
( sQ34_spl
<=> multiply(inverse(sk_c10),sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ34_spl
| multiply(inverse(sk_c10),sk_c10) != sk_c8 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f434,f436,f439,f150,f133,f122,f111]) ).
fof(f443,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f373,f438]) ).
fof(f444,plain,
( sQ34_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f39,f441]) ).
fof(f472,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c10,multiply(sk_c1,X0)) = multiply(sk_c8,X0) ),
inference(paramodulation,[status(thm)],[f263,f370]) ).
fof(f482,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f263,f472]) ).
fof(f516,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c1,X0) = multiply(inverse(sk_c10),X0) ),
inference(paramodulation,[status(thm)],[f263,f168]) ).
fof(f517,plain,
( ~ sQ11_spl
| sk_c1 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f165,f168]) ).
fof(f518,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f168,f168]) ).
fof(f519,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f39,f168]) ).
fof(f552,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c2,X0) = multiply(sk_c10,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f557,f160]) ).
fof(f553,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c10,sk_c10) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f557,f123]) ).
fof(f557,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c1,X0) = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f380,f516]) ).
fof(f558,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c1 = multiply(sk_c10,identity) ),
inference(forward_demodulation,[status(thm)],[f380,f517]) ).
fof(f563,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f518,f519]) ).
fof(f587,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f375,f552]) ).
fof(f602,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c1 = multiply(sk_c2,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f587,f276]) ).
fof(f604,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f608,f164]) ).
fof(f608,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f587,f602]) ).
fof(f616,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c1 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f563,f558]) ).
fof(f617,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c10,sk_c10) = identity ),
inference(forward_demodulation,[status(thm)],[f616,f165]) ).
fof(f645,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c10,sk_c10) = identity ),
inference(forward_demodulation,[status(thm)],[f616,f604]) ).
fof(f654,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(X0,sk_c2) ),
inference(backward_demodulation,[status(thm)],[f660,f563]) ).
fof(f660,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| identity = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f645,f553]) ).
fof(f681,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c8 = sk_c2 ),
inference(paramodulation,[status(thm)],[f482,f654]) ).
fof(f688,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f681,f229]) ).
fof(f689,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f734,plain,
( sQ34_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f735,f444]) ).
fof(f735,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f553,f617]) ).
fof(f741,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(X0,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f735,f563]) ).
fof(f758,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c2 ),
inference(paramodulation,[status(thm)],[f482,f741]) ).
fof(f761,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 = sk_c8 ),
inference(paramodulation,[status(thm)],[f741,f482]) ).
fof(f765,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f734]) ).
fof(f766,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f765]) ).
fof(f767,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(X0,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f761,f741]) ).
fof(f771,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c8 = identity ),
inference(backward_demodulation,[status(thm)],[f761,f735]) ).
fof(f785,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f735,f387]) ).
fof(f786,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f761,f785]) ).
fof(f787,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f786]) ).
fof(f788,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f787]) ).
fof(f803,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 != sk_c10
| inverse(X0) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f767,f154]) ).
fof(f806,plain,
( sQ22_spl
| ~ sQ11_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f228,f220,f133,f216]) ).
fof(f808,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c10) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f803]) ).
fof(f809,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f808,f380]) ).
fof(f810,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f809]) ).
fof(f812,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f771,f443]) ).
fof(f813,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f812]) ).
fof(f814,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f813]) ).
fof(f821,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c10) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f334,f234]) ).
fof(f834,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c10) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f563,f285]) ).
fof(f847,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| sk_c6 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f834,f325]) ).
fof(f858,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f317,f821]) ).
fof(f862,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c10) ),
inference(paramodulation,[status(thm)],[f108,f168]) ).
fof(f864,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f104,f862]) ).
fof(f865,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f317,f864]) ).
fof(f873,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f865,f38]) ).
fof(f882,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f865,f858]) ).
fof(f883,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f882]) ).
fof(f884,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f883]) ).
fof(f888,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c10 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f873,f834]) ).
fof(f899,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f888,f847]) ).
fof(f900,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f899]) ).
fof(f901,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f86,f90,f102,f106,f110,f114,f115,f116,f117,f118,f119,f120,f121,f125,f126,f127,f128,f129,f130,f131,f132,f136,f137,f138,f139,f140,f141,f142,f143,f156,f183,f188,f201,f208,f212,f219,f226,f233,f241,f256,f359,f442,f689,f766,f788,f806,f810,f814,f884,f900]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP388-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.56 % Computer : n009.cluster.edu
% 0.12/0.56 % Model : x86_64 x86_64
% 0.12/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.56 % Memory : 8046.5625MB
% 0.12/0.56 % OS : Linux 6.8.0-71-generic
% 0.12/0.56 % CPULimit : 300
% 0.12/0.56 % WCLimit : 300
% 0.12/0.56 % DateTime : Sun Sep 20 20:10:59 UTC 2026
% 0.12/0.57 % CPUTime :
% 0.12/0.58 % Drodi V4.1.1
% 0.12/0.61 % Refutation found
% 0.12/0.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.63 % Elapsed time: 0.061824 seconds
% 0.15/0.63 % CPU time: 0.233115 seconds
% 0.15/0.63 % Total memory used: 105.924 MB
% 0.15/0.63 % Net memory used: 105.686 MB
%------------------------------------------------------------------------------