%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP212-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:06 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 61
% Syntax : Number of formulae : 269 ( 13 unt; 27 def)
% Number of atoms : 790 ( 316 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 949 ( 428 ~; 494 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 28 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 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_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(X6,sk_c7) != sk_c8
| inverse(X6) != sk_c8
| multiply(X5,sk_c7) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X3] :
( inverse(X3) != sk_c8
| ! [X2] :
( multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| ! [X6] :
( multiply(X6,sk_c7) != sk_c8
| inverse(X6) != sk_c8
| ! [X5] :
( multiply(X5,sk_c7) != sk_c8
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c8 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f70,f89]) ).
fof(f93,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f70,f93]) ).
fof(f97,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f106,f73]) ).
fof(f110,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f106,f77]) ).
fof(f111,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f106,f81]) ).
fof(f112,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f106,f85]) ).
fof(f113,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f106,f89]) ).
fof(f114,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f106,f93]) ).
fof(f115,definition,
( sQ9_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f115,f73]) ).
fof(f119,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f115,f77]) ).
fof(f120,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f115,f81]) ).
fof(f121,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f115,f85]) ).
fof(f122,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f115,f89]) ).
fof(f123,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f115,f93]) ).
fof(f124,definition,
( sQ10_spl
<=> multiply(sk_c3,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f124,f73]) ).
fof(f128,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f124,f77]) ).
fof(f129,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f124,f81]) ).
fof(f130,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f124,f85]) ).
fof(f131,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f124,f89]) ).
fof(f132,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f124,f93]) ).
fof(f133,definition,
! [X0,X1] :
( sQ11_spl
<=> ( multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0,X1] :
( ~ sQ11_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X4,X5] :
( sQ13_spl
<=> ( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f133,f136,f73,f139]) ).
fof(f143,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f145,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f125,f37]) ).
fof(f148,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f107,f37]) ).
fof(f150,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f151,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f94,f36]) ).
fof(f153,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f116,f36]) ).
fof(f154,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f155,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f154]) ).
fof(f156,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f71,f37]) ).
fof(f157,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f90,f37]) ).
fof(f158,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f86,f37]) ).
fof(f159,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f82,f37]) ).
fof(f160,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f150,f37]) ).
fof(f161,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f160]) ).
fof(f162,plain,
! [X0] :
( ~ sQ6_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f151,f37]) ).
fof(f163,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f162]) ).
fof(f166,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f143]) ).
fof(f167,plain,
( ~ sQ13_spl
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f36,f143]) ).
fof(f168,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f143]) ).
fof(f169,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(multiply(X0,X1)) != sk_c8
| multiply(sk_c8,multiply(X0,multiply(X1,sk_c8))) != sk_c7 ),
inference(paramodulation,[status(thm)],[f37,f143]) ).
fof(f170,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f166,f85,f93,f139,f89]) ).
fof(f171,definition,
( sQ14_spl
<=> multiply(sk_c8,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ14_spl
| multiply(sk_c8,identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ15_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ15_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f167,f171,f174,f139]) ).
fof(f178,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ16_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
( sQ17_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ17_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f168,f178,f181,f139]) ).
fof(f185,plain,
! [X0] :
( ~ sQ11_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f186,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f137,f82]) ).
fof(f188,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f137,f125]) ).
fof(f195,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f186]) ).
fof(f196,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f195]) ).
fof(f197,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f198,plain,
( ~ sQ11_spl
| multiply(inverse(identity),sk_c7) != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f35,f185]) ).
fof(f201,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c8
| multiply(sk_c1,sk_c2) != sk_c8 ),
inference(paramodulation,[status(thm)],[f98,f185]) ).
fof(f202,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| multiply(inverse(sk_c3),sk_c7) != sk_c8
| multiply(sk_c3,sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f116,f185]) ).
fof(f203,definition,
( sQ18_spl
<=> multiply(inverse(identity),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ18_spl
| multiply(inverse(identity),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f198,f181,f203,f133]) ).
fof(f214,definition,
( sQ21_spl
<=> multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( sQ21_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ21_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f201,f70,f214,f133,f97]) ).
fof(f218,definition,
( sQ22_spl
<=> multiply(sk_c3,sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ22_spl
| multiply(sk_c3,sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,definition,
( sQ23_spl
<=> multiply(inverse(sk_c3),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f202,f218,f221,f133,f115]) ).
fof(f226,plain,
( sQ21_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f216]) ).
fof(f227,plain,
( sQ21_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f107,f226]) ).
fof(f228,plain,
( sQ21_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f227]) ).
fof(f229,plain,
( sQ21_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f232,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f74,f36]) ).
fof(f241,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f74,f185]) ).
fof(f252,definition,
( sQ26_spl
<=> multiply(sk_c8,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ26_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ27_spl
<=> multiply(inverse(sk_c8),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ27_spl
| multiply(inverse(sk_c8),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f241,f252,f255,f133,f73]) ).
fof(f289,plain,
! [X0] :
( ~ sQ1_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f232,f37]) ).
fof(f290,plain,
! [X0] :
( ~ sQ1_spl
| X0 = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f289]) ).
fof(f291,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f159,f161]) ).
fof(f292,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(paramodulation,[status(thm)],[f82,f161]) ).
fof(f307,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f157,f163]) ).
fof(f308,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f163]) ).
fof(f311,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f319,f232]) ).
fof(f316,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| X0 = multiply(sk_c8,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f319,f290]) ).
fof(f319,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f158,f307]) ).
fof(f321,plain,
( sQ26_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f330,f254]) ).
fof(f323,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f330,f74]) ).
fof(f327,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f330,f125]) ).
fof(f330,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f308]) ).
fof(f332,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f292,f311]) ).
fof(f336,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f340,f183]) ).
fof(f340,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f330,f332]) ).
fof(f342,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f291,f316]) ).
fof(f350,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f319,f342]) ).
fof(f356,plain,
( sQ26_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f292,f321]) ).
fof(f357,plain,
( sQ26_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f330,f356]) ).
fof(f358,plain,
( sQ26_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ26_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f365,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f220]) ).
fof(f366,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f378,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f323,f336]) ).
fof(f379,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f378]) ).
fof(f380,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f398,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f323,f257]) ).
fof(f399,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f350,f398]) ).
fof(f400,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f330,f399]) ).
fof(f401,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f400]) ).
fof(f402,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f404,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f116,f188]) ).
fof(f405,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f404]) ).
fof(f406,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f427,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(multiply(sk_c3,sk_c7)) != sk_c8
| multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f145,f169]) ).
fof(f428,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| inverse(multiply(sk_c2,sk_c7)) != sk_c8
| multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f148,f169]) ).
fof(f432,definition,
( sQ28_spl
<=> multiply(sk_c8,multiply(sk_c8,sk_c8)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f435,definition,
( sQ29_spl
<=> inverse(multiply(sk_c3,sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f427,f432,f435,f139,f124]) ).
fof(f439,definition,
( sQ30_spl
<=> inverse(multiply(sk_c2,sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ30_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f428,f432,f439,f139,f106]) ).
fof(f453,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f155,f155]) ).
fof(f454,plain,
( ~ sQ9_spl
| sk_c3 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f153,f155]) ).
fof(f456,plain,
( ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f125,f155]) ).
fof(f461,plain,
( ~ sQ0_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f71,f155]) ).
fof(f467,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f116,f456]) ).
fof(f468,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f180]) ).
fof(f469,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c2,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f98,f461]) ).
fof(f492,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f155]) ).
fof(f494,plain,
( sQ18_spl
| sk_c7 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f492,f205]) ).
fof(f497,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f36,f155]) ).
fof(f499,plain,
( sQ14_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f501,f173]) ).
fof(f500,plain,
( ~ sQ9_spl
| sk_c3 = inverse(sk_c8) ),
inference(backward_demodulation,[status(thm)],[f501,f454]) ).
fof(f501,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f453,f497]) ).
fof(f503,plain,
( sQ1_spl
| ~ sQ9_spl
| sk_c3 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f500,f75]) ).
fof(f505,plain,
( sQ15_spl
| ~ sQ9_spl
| inverse(sk_c3) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f500,f176]) ).
fof(f506,plain,
( sQ15_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f116,f505]) ).
fof(f507,plain,
( sQ15_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f506]) ).
fof(f508,plain,
( sQ15_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f528,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c8) = multiply(sk_c1,sk_c2) ),
inference(paramodulation,[status(thm)],[f471,f156]) ).
fof(f529,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f471,f155]) ).
fof(f531,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c1,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f467,f528]) ).
fof(f532,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f71,f531]) ).
fof(f536,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f543,f35]) ).
fof(f537,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f543,f153]) ).
fof(f543,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f529]) ).
fof(f544,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c3 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f532,f503]) ).
fof(f556,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f532,f499]) ).
fof(f557,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f556]) ).
fof(f558,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f532,f494]) ).
fof(f560,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f559]) ).
fof(f561,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f571,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f536,f537]) ).
fof(f607,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ1_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f544]) ).
fof(f608,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ1_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f609,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f100,f101,f102,f103,f104,f105,f109,f110,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f142,f170,f177,f184,f197,f206,f217,f224,f229,f258,f359,f366,f380,f402,f406,f438,f442,f469,f508,f558,f561,f608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP212-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:07:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.059146 seconds
% 0.12/0.43 % CPU time: 0.198896 seconds
% 0.12/0.43 % Total memory used: 104.502 MB
% 0.12/0.43 % Net memory used: 104.285 MB
%------------------------------------------------------------------------------