%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP237-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:10 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.52s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 52
% Syntax : Number of formulae : 325 ( 9 unt; 18 def)
% Number of atoms : 1385 ( 394 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 2051 ( 991 ~;1042 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 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,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X4,X5,X6,X2,X1,X3,X7] :
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X2) != X1
| multiply(X2,X1) != sk_c9
| inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c9) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f42,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f47,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f49,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f59,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f61,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f65,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f71,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f77,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f78,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f79,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f80,plain,
! [X7] :
( inverse(X7) != sk_c9
| ! [X3] :
( multiply(X7,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| ! [X1] :
( multiply(X1,sk_c8) != sk_c9
| ! [X2] :
( inverse(X2) != X1
| multiply(X2,X1) != sk_c9
| ! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| ! [X4] :
( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c9) != sk_c8 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,definition,
( sQ0_spl
<=> inverse(sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| inverse(sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| inverse(sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f82,f85]) ).
fof(f89,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f82,f89]) ).
fof(f93,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f97,definition,
( sQ4_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f82,f97]) ).
fof(f101,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f82,f101]) ).
fof(f105,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f82,f105]) ).
fof(f109,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f109,f85]) ).
fof(f113,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f109,f89]) ).
fof(f114,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f109,f93]) ).
fof(f115,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f53,f109,f97]) ).
fof(f116,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f109,f101]) ).
fof(f117,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f109,f105]) ).
fof(f118,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( sQ8_spl
| multiply(sk_c1,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f118,f85]) ).
fof(f122,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f118,f89]) ).
fof(f124,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f118,f97]) ).
fof(f126,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f118,f105]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c9,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f127,f85]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f127,f89]) ).
fof(f133,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f97]) ).
fof(f134,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f127,f101]) ).
fof(f135,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f127,f105]) ).
fof(f136,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c9) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f136,f85]) ).
fof(f140,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f136,f89]) ).
fof(f142,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f136,f97]) ).
fof(f143,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f136,f101]) ).
fof(f144,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f136,f105]) ).
fof(f145,definition,
( sQ11_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f145,f85]) ).
fof(f149,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f145,f89]) ).
fof(f151,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f145,f97]) ).
fof(f152,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f145,f101]) ).
fof(f153,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f145,f105]) ).
fof(f154,definition,
! [X0] :
( sQ12_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X1,X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3,X4] :
( sQ14_spl
<=> ( multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sQ14_spl
| multiply(X1,sk_c8) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f157,f160]) ).
fof(f164,plain,
! [X0] :
( ~ sQ14_spl
| multiply(inverse(X0),sk_c8) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f161]) ).
fof(f179,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| multiply(sk_c5,sk_c8) != sk_c9
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f90,f164]) ).
fof(f181,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f110,f164]) ).
fof(f183,definition,
( sQ15_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ15_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f179,f183,f93,f160,f89]) ).
fof(f190,definition,
( sQ17_spl
<=> multiply(sk_c9,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ17_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f194,definition,
( sQ18_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ18_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f181,f194,f190,f160,f109]) ).
fof(f204,plain,
( sQ18_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f110,f196]) ).
fof(f205,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f158]) ).
fof(f207,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f102,f205]) ).
fof(f208,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c9
| multiply(sk_c9,sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f137,f205]) ).
fof(f209,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f207,f97,f105,f157,f101]) ).
fof(f210,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f208,f127,f145,f157,f136]) ).
fof(f212,plain,
( ~ sQ2_spl
| multiply(sk_c5,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f90,f42]) ).
fof(f213,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c9) = identity ),
inference(paramodulation,[status(thm)],[f83,f42]) ).
fof(f214,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f110,f42]) ).
fof(f215,plain,
( ~ sQ11_spl
| multiply(sk_c9,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f146,f42]) ).
fof(f216,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f217,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f216]) ).
fof(f241,plain,
( ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f86,f217]) ).
fof(f243,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f119,f217]) ).
fof(f244,plain,
( ~ sQ11_spl
| sk_c2 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f215,f217]) ).
fof(f245,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f214,f217]) ).
fof(f248,plain,
( ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f137,f217]) ).
fof(f251,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c5,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f90,f241]) ).
fof(f252,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f110,f243]) ).
fof(f253,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f83,f244]) ).
fof(f254,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f83,f245]) ).
fof(f257,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c9,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f146,f248]) ).
fof(f258,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f128,f257]) ).
fof(f261,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f258,f214]) ).
fof(f262,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f258,f213]) ).
fof(f265,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f258,f83]) ).
fof(f270,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f258,f119]) ).
fof(f271,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f258,f128]) ).
fof(f274,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f258,f146]) ).
fof(f285,plain,
( sQ15_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f90,f185]) ).
fof(f291,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c9) = identity ),
inference(paramodulation,[status(thm)],[f83,f42]) ).
fof(f294,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f251,f217]) ).
fof(f296,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f294]) ).
fof(f300,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f296,f212]) ).
fof(f301,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f296,f42]) ).
fof(f302,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f296,f41]) ).
fof(f303,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(inverse(sk_c9),X0) ),
inference(paramodulation,[status(thm)],[f302,f217]) ).
fof(f305,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f83,f303]) ).
fof(f311,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 = identity ),
inference(backward_demodulation,[status(thm)],[f319,f296]) ).
fof(f315,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c1) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f319,f110]) ).
fof(f316,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f319,f83]) ).
fof(f319,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f302,f252]) ).
fof(f320,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f315,f217]) ).
fof(f321,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f305,f320]) ).
fof(f322,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f319,f98]) ).
fof(f325,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f328,f311]) ).
fof(f326,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c7 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f328,f319]) ).
fof(f327,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| X0 = multiply(sk_c7,X0) ),
inference(backward_demodulation,[status(thm)],[f328,f305]) ).
fof(f328,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f305,f322]) ).
fof(f332,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f328,f316]) ).
fof(f333,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f328,f332]) ).
fof(f344,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f328,f254]) ).
fof(f345,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f327,f344]) ).
fof(f350,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f354,f333]) ).
fof(f351,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c1 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f354,f326]) ).
fof(f352,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f354,f325]) ).
fof(f353,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c1 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f354,f328]) ).
fof(f354,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f325,f345]) ).
fof(f355,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f354,f350]) ).
fof(f502,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f351,f155]) ).
fof(f503,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c1) != sk_c9
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f353,f502]) ).
fof(f504,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c1) != sk_c1
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f351,f503]) ).
fof(f506,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c1) != sk_c1 ),
inference(resolution,[status(thm)],[f504,f355]) ).
fof(f510,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ12_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f321,f506]) ).
fof(f511,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f510]) ).
fof(f512,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f563,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c8) = identity ),
inference(forward_demodulation,[status(thm)],[f258,f291]) ).
fof(f572,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f258,f192]) ).
fof(f573,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f563,f572]) ).
fof(f574,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f258,f573]) ).
fof(f578,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f258,f204]) ).
fof(f579,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f258,f578]) ).
fof(f584,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ18_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f579]) ).
fof(f585,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ18_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f258,f155]) ).
fof(f587,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(X0,sk_c8) != sk_c8
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f258,f586]) ).
fof(f590,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c3 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f271,f217]) ).
fof(f592,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c3 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f265,f590]) ).
fof(f593,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f563,f592]) ).
fof(f595,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c3 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f593,f574]) ).
fof(f598,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f593,f41]) ).
fof(f604,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c1) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f593,f261]) ).
fof(f605,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c1 = multiply(inverse(sk_c8),sk_c3) ),
inference(paramodulation,[status(thm)],[f604,f217]) ).
fof(f607,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f265,f605]) ).
fof(f608,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c1 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f271,f607]) ).
fof(f616,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f608,f274]) ).
fof(f620,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c9 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f608,f258]) ).
fof(f628,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c8) = identity ),
inference(forward_demodulation,[status(thm)],[f608,f262]) ).
fof(f629,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f608,f628]) ).
fof(f630,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c1) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f593,f629]) ).
fof(f645,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c1) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f608,f119]) ).
fof(f646,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f630,f645]) ).
fof(f647,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c3 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f620,f646]) ).
fof(f650,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c3 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f608,f595]) ).
fof(f662,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f647,f616]) ).
fof(f665,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f647,f608]) ).
fof(f669,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f647,f650]) ).
fof(f670,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f669]) ).
fof(f671,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f670]) ).
fof(f677,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| X0 = multiply(sk_c3,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f662,f217]) ).
fof(f678,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f598,f677]) ).
fof(f684,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c2 = multiply(sk_c3,identity) ),
inference(forward_demodulation,[status(thm)],[f665,f253]) ).
fof(f685,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f598,f684]) ).
fof(f686,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f695,f662]) ).
fof(f688,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f695,f665]) ).
fof(f695,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f593,f685]) ).
fof(f698,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(X0,sk_c8) != sk_c8
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f688,f587]) ).
fof(f699,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(X0,sk_c2) != sk_c8
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f688,f698]) ).
fof(f700,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f688,f699]) ).
fof(f704,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f686,f700]) ).
fof(f707,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f678,f704]) ).
fof(f708,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f707]) ).
fof(f709,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f708]) ).
fof(f712,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f352,f42]) ).
fof(f729,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c1) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f351,f83]) ).
fof(f730,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f353,f729]) ).
fof(f748,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c8) != sk_c9
| multiply(X0,inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f351,f164]) ).
fof(f749,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c1) != sk_c9
| multiply(X0,inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f353,f748]) ).
fof(f750,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c1) != sk_c1
| multiply(X0,inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f351,f749]) ).
fof(f751,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ14_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c1 ),
inference(resolution,[status(thm)],[f750,f712]) ).
fof(f756,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f321,f751]) ).
fof(f757,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f730,f756]) ).
fof(f758,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f757]) ).
fof(f759,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f758]) ).
fof(f761,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f296,f41]) ).
fof(f767,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c9,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f110,f217]) ).
fof(f768,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f761,f767]) ).
fof(f771,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f106,f217]) ).
fof(f772,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f761,f771]) ).
fof(f779,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(paramodulation,[status(thm)],[f106,f301]) ).
fof(f781,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c1) = sk_c9 ),
inference(paramodulation,[status(thm)],[f110,f301]) ).
fof(f785,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f761,f779]) ).
fof(f786,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f761,f781]) ).
fof(f788,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f792,f83]) ).
fof(f792,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f761,f98]) ).
fof(f799,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f785,f106]) ).
fof(f803,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c1 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f805,f785]) ).
fof(f805,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| sk_c1 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f785,f786]) ).
fof(f815,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f803,f788]) ).
fof(f820,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f805,f799]) ).
fof(f821,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f815,f820]) ).
fof(f826,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f827,f792]) ).
fof(f827,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c7 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f805,f821]) ).
fof(f879,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f768,f120]) ).
fof(f880,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f826,f879]) ).
fof(f881,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f803,f880]) ).
fof(f882,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f881]) ).
fof(f883,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f882]) ).
fof(f895,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| inverse(sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f785,f788]) ).
fof(f897,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f900,f792]) ).
fof(f900,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f799,f895]) ).
fof(f904,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c6) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f897,f94]) ).
fof(f905,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f785,f904]) ).
fof(f907,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f905,f43]) ).
fof(f908,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f772,f907]) ).
fof(f909,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f772,f908]) ).
fof(f910,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f772,f102]) ).
fof(f911,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f785,f910]) ).
fof(f919,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f909,f300]) ).
fof(f921,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f922,f90]) ).
fof(f922,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f785,f919]) ).
fof(f926,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f799,f921]) ).
fof(f929,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f922,f285]) ).
fof(f930,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c5 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f772,f929]) ).
fof(f931,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f926,f930]) ).
fof(f932,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f785,f931]) ).
fof(f933,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f932]) ).
fof(f934,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f933]) ).
fof(f935,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f785,f155]) ).
fof(f936,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c6) != sk_c9
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f897,f935]) ).
fof(f937,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c6) != sk_c6
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f785,f936]) ).
fof(f946,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f937,f799]) ).
fof(f948,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f772,f946]) ).
fof(f949,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f948]) ).
fof(f950,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f949]) ).
fof(f961,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f785,f84]) ).
fof(f962,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f799,f961]) ).
fof(f966,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f911,f792]) ).
fof(f971,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f966,f962]) ).
fof(f972,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f971]) ).
fof(f973,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f972]) ).
fof(f974,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f92,f100,f104,f108,f112,f113,f114,f115,f116,f117,f121,f122,f124,f126,f130,f131,f133,f134,f135,f139,f140,f142,f143,f144,f148,f149,f151,f152,f153,f163,f186,f197,f209,f210,f512,f585,f671,f709,f759,f883,f934,f950,f973]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP237-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.48 % Computer : n013.cluster.edu
% 0.08/0.48 % Model : x86_64 x86_64
% 0.08/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.48 % Memory : 8046.5625MB
% 0.08/0.48 % OS : Linux 6.8.0-71-generic
% 0.08/0.49 % CPULimit : 300
% 0.08/0.49 % WCLimit : 300
% 0.08/0.49 % DateTime : Sun Sep 20 20:06:36 UTC 2026
% 0.08/0.49 % CPUTime :
% 0.08/0.50 % Drodi V4.1.1
% 0.08/0.52 % Refutation found
% 0.08/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.56 % Elapsed time: 0.058739 seconds
% 0.08/0.56 % CPU time: 0.184047 seconds
% 0.08/0.56 % Total memory used: 104.363 MB
% 0.08/0.56 % Net memory used: 104.186 MB
%------------------------------------------------------------------------------