%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP331-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:33:26 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 61
% Syntax : Number of formulae : 302 ( 14 unt; 27 def)
% Number of atoms : 1026 ( 346 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1377 ( 653 ~; 697 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( multiply(X5,sk_c8) != sk_c6
| inverse(X5) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/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,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X5] :
( multiply(X5,sk_c8) != sk_c6
| inverse(X5) != sk_c6
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| ! [X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c8) != sk_c6
| inverse(X4) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c3,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_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c3) = 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_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c6 ),
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
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c4) = 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
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| inverse(sk_c5) = 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
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
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
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
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
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
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_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
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_c2,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c6) = sk_c7 ),
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] :
( sQ11_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
! [X4] :
( sQ15_spl
<=> ( multiply(X4,sk_c8) != sk_c6
| inverse(X4) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f146,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c8) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f139,f142,f145]) ).
fof(f150,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f146,f94]) ).
fof(f151,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| sk_c6 != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f71,f146]) ).
fof(f154,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f90,f150]) ).
fof(f155,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f143,f82]) ).
fof(f159,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramodulation,[status(thm)],[f98,f143]) ).
fof(f160,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f157]) ).
fof(f161,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f160]) ).
fof(f162,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f74]) ).
fof(f164,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c7) != sk_c8
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f167,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f163]) ).
fof(f168,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f167]) ).
fof(f169,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f176,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f125,f37]) ).
fof(f179,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f125]) ).
fof(f182,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f116,f179]) ).
fof(f183,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f182]) ).
fof(f184,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f183]) ).
fof(f189,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f107,f36]) ).
fof(f190,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f191,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f190]) ).
fof(f198,plain,
! [X0] :
( ~ sQ8_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f189,f37]) ).
fof(f199,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f198]) ).
fof(f210,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f191]) ).
fof(f212,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f191]) ).
fof(f213,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f82,f191]) ).
fof(f214,plain,
( ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f94,f191]) ).
fof(f215,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f98,f191]) ).
fof(f218,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f78,f212]) ).
fof(f219,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f213]) ).
fof(f220,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f90,f214]) ).
fof(f221,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f107,f215]) ).
fof(f227,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f210,f191]) ).
fof(f229,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f218,f191]) ).
fof(f231,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f229]) ).
fof(f237,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f231,f36]) ).
fof(f238,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f231,f35]) ).
fof(f241,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f98]) ).
fof(f246,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c7
| sk_c6 != sk_c8 ),
inference(paramodulation,[status(thm)],[f82,f134]) ).
fof(f248,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f107,f241]) ).
fof(f249,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f248]) ).
fof(f250,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f258,definition,
( sQ18_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ18_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f265,definition,
( sQ20_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f246,f265,f85,f133,f81]) ).
fof(f270,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f238,f71]) ).
fof(f272,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f238,f72]) ).
fof(f274,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c4) = sk_c7 ),
inference(paramodulation,[status(thm)],[f86,f237]) ).
fof(f278,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f238,f274]) ).
fof(f280,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f278,f237]) ).
fof(f281,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f278,f238]) ).
fof(f299,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f278,f219]) ).
fof(f300,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c4,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f278,f299]) ).
fof(f301,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f304,f272]) ).
fof(f302,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f304,f90]) ).
fof(f304,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f281,f300]) ).
fof(f305,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(paramodulation,[status(thm)],[f302,f280]) ).
fof(f306,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f302,f191]) ).
fof(f307,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f281,f305]) ).
fof(f308,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f281,f306]) ).
fof(f309,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f307,f302]) ).
fof(f310,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f307,f301]) ).
fof(f311,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c5 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f307,f304]) ).
fof(f312,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f307,f280]) ).
fof(f317,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f307,f278]) ).
fof(f331,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f311,f220]) ).
fof(f332,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f308,f331]) ).
fof(f333,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f311,f332]) ).
fof(f334,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f310]) ).
fof(f335,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f260]) ).
fof(f337,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f353,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f317,f137]) ).
fof(f354,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(X0,sk_c5) != sk_c7
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f311,f353]) ).
fof(f355,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f317,f354]) ).
fof(f359,definition,
( sQ21_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( sQ21_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f403,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ12_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(resolution,[status(thm)],[f355,f312]) ).
fof(f410,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f309,f403]) ).
fof(f411,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ12_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f309,f410]) ).
fof(f412,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f411]) ).
fof(f413,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,definition,
( sQ22_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( sQ22_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,definition,
( sQ23_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f164,f414,f417,f139,f70]) ).
fof(f425,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f159,f265,f106,f142,f97]) ).
fof(f428,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f98,f191]) ).
fof(f430,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f107,f428]) ).
fof(f434,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f191]) ).
fof(f440,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f221,f71]) ).
fof(f441,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f416]) ).
fof(f442,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f445,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f440,f125]) ).
fof(f449,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f440,f107]) ).
fof(f450,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f440,f116]) ).
fof(f461,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f440,f189]) ).
fof(f466,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f450,f36]) ).
fof(f477,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f440,f430]) ).
fof(f478,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f440,f477]) ).
fof(f479,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f478,f191]) ).
fof(f481,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f479]) ).
fof(f483,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f481,f36]) ).
fof(f484,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c1) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f481,f461]) ).
fof(f486,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f481,f35]) ).
fof(f493,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f440,f143]) ).
fof(f494,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f440,f493]) ).
fof(f497,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c8) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramodulation,[status(thm)],[f486,f494]) ).
fof(f500,definition,
( sQ25_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ25_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
( sQ26_spl
<=> inverse(sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f497,f500,f503,f142,f70,f106,f97]) ).
fof(f511,plain,
( sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f502]) ).
fof(f512,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f528,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f270,f265,f77,f73,f70]) ).
fof(f537,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c8),X0) ),
inference(forward_demodulation,[status(thm)],[f481,f434]) ).
fof(f541,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(inverse(sk_c8)) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramodulation,[status(thm)],[f537,f494]) ).
fof(f544,definition,
( sQ28_spl
<=> inverse(inverse(sk_c8)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ28_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f541,f500,f544,f142,f70,f106,f97]) ).
fof(f548,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f445,f494]) ).
fof(f552,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f450,f548]) ).
fof(f553,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f552]) ).
fof(f554,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f556,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f440,f140]) ).
fof(f558,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f440,f361]) ).
fof(f559,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f440,f558]) ).
fof(f560,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f559]) ).
fof(f561,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f566,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c2) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f481,f466]) ).
fof(f597,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(inverse(inverse(sk_c8)),X0) ),
inference(forward_demodulation,[status(thm)],[f481,f227]) ).
fof(f600,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c8) = sk_c8 ),
inference(paramodulation,[status(thm)],[f483,f597]) ).
fof(f618,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| X0 = multiply(sk_c6,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f440,f199]) ).
fof(f636,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramodulation,[status(thm)],[f486,f556]) ).
fof(f637,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c6) != sk_c8
| sk_c6 != sk_c6 ),
inference(paramodulation,[status(thm)],[f478,f556]) ).
fof(f643,definition,
( sQ29_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f645,plain,
( sQ29_spl
| inverse(sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ29_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f636,f265,f643,f139,f70,f106,f97]) ).
fof(f647,definition,
( sQ30_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ30_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f637,f500,f647,f139,f70,f106,f97]) ).
fof(f676,definition,
( sQ34_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( sQ34_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f679,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ25_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f151,f676,f500,f145,f70]) ).
fof(f698,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f440,f176]) ).
fof(f699,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c6,multiply(sk_c1,X0)) = multiply(sk_c2,X0) ),
inference(paramodulation,[status(thm)],[f618,f698]) ).
fof(f706,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f618,f699]) ).
fof(f717,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(inverse(sk_c2),X0) ),
inference(paramodulation,[status(thm)],[f706,f191]) ).
fof(f723,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f450,f717]) ).
fof(f725,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f723,f484]) ).
fof(f726,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c2 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f723,f566]) ).
fof(f728,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f723,f478]) ).
fof(f732,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f728,f265,f115,f124,f70,f106,f97]) ).
fof(f734,plain,
( sQ29_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f600,f645]) ).
fof(f735,plain,
( sQ29_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f734]) ).
fof(f736,plain,
( sQ29_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f737,plain,
( sQ34_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f440,f678]) ).
fof(f740,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c8) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f725,f600]) ).
fof(f746,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f725,f740]) ).
fof(f747,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f449,f746]) ).
fof(f750,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f725,f726]) ).
fof(f753,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f755,f450]) ).
fof(f755,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f750,f747]) ).
fof(f772,plain,
( sQ34_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f755,f737]) ).
fof(f773,plain,
( sQ34_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f755,f772]) ).
fof(f777,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f753,f773]) ).
fof(f778,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f777]) ).
fof(f779,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,f148,f156,f162,f169,f184,f250,f268,f335,f337,f413,f420,f425,f442,f506,f512,f528,f547,f554,f561,f646,f650,f679,f732,f736,f778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP331-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:14:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.049047 seconds
% 0.14/0.42 % CPU time: 0.203387 seconds
% 0.14/0.42 % Total memory used: 70.895 MB
% 0.14/0.42 % Net memory used: 70.761 MB
%------------------------------------------------------------------------------