%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP357-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:33:30 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 60
% Syntax : Number of formulae : 283 ( 11 unt; 26 def)
% Number of atoms : 1028 ( 337 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1406 ( 661 ~; 719 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X4,sk_c7) != sk_c8
| inverse(X3) != X4
| multiply(X3,X4) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != 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,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X5] :
( inverse(X5) != sk_c8
| ! [X2] :
( multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| ! [X4] :
( multiply(X4,sk_c7) != sk_c8
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
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
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
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
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f83,plain,
( sQ3_spl
| inverse(sk_c3) != 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_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = 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_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
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_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c4) = 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_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| inverse(sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ7_spl
| inverse(sk_c8) != sk_c6 ),
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_c1,sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c2) = 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_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c2 ),
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_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| multiply(sk_c2,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
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3,X4] :
( sQ13_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != 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
| sQ12_spl
| ~ sQ1_spl
| sQ11_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f97,f133,f73,f136,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(f146,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f78,f37]) ).
fof(f147,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f86,f37]) ).
fof(f171,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f147,f143]) ).
fof(f173,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f143]) ).
fof(f174,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f143]) ).
fof(f175,definition,
( sQ14_spl
<=> multiply(sk_c7,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( sQ14_spl
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ15_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f171,f175,f178,f139,f85]) ).
fof(f182,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f173,f182,f81,f139,f77]) ).
fof(f186,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f174,f85,f93,f139,f89]) ).
fof(f187,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(f189,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8
| sk_c5 != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f137]) ).
fof(f190,definition,
( sQ17_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ17_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f189,f190,f93,f136,f89]) ).
fof(f199,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f200,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f199]) ).
fof(f216,plain,
( ~ sQ11_spl
| identity != sk_c8
| multiply(sk_c7,inverse(sk_c7)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f36,f187]) ).
fof(f217,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| multiply(sk_c8,sk_c7) != sk_c8
| multiply(sk_c3,inverse(sk_c3)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f82,f187]) ).
fof(f218,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| multiply(sk_c6,sk_c7) != sk_c8
| multiply(sk_c8,inverse(sk_c8)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f98,f187]) ).
fof(f219,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| multiply(sk_c8,sk_c7) != sk_c8
| multiply(sk_c4,inverse(sk_c4)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f94,f187]) ).
fof(f220,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c7) != sk_c8
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f116,f187]) ).
fof(f221,definition,
( sQ18_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f224,definition,
( sQ19_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f216,f221,f224,f133]) ).
fof(f228,definition,
( sQ20_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ20_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c8 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,definition,
( sQ21_spl
<=> multiply(sk_c8,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ21_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f217,f228,f231,f133,f81]) ).
fof(f235,definition,
( sQ22_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f238,definition,
( sQ23_spl
<=> multiply(sk_c6,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ23_spl
| multiply(sk_c6,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f218,f235,f238,f133,f97]) ).
fof(f242,definition,
( sQ24_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ21_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f219,f242,f231,f133,f93]) ).
fof(f246,definition,
( sQ25_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ25_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f220,f246,f124,f133,f115]) ).
fof(f250,plain,
( sQ21_spl
| ~ sQ1_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f74,f233]) ).
fof(f251,plain,
( sQ25_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c2) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f116,f248]) ).
fof(f252,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f107,f251]) ).
fof(f253,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f252]) ).
fof(f254,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f255,plain,
( sQ20_spl
| ~ sQ3_spl
| multiply(sk_c3,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f82,f230]) ).
fof(f256,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f255]) ).
fof(f270,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f200]) ).
fof(f273,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f200]) ).
fof(f278,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f90,f200]) ).
fof(f282,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f82,f270]) ).
fof(f283,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f74,f282]) ).
fof(f284,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f250]) ).
fof(f285,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f287,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f94,f278]) ).
fof(f288,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f287]) ).
fof(f289,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ20_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f256]) ).
fof(f290,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ20_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f295,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f283,f240]) ).
fof(f296,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f283,f99]) ).
fof(f298,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f283,f74]) ).
fof(f301,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f295,f231,f73,f81,f77,f238]) ).
fof(f303,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f288,f86]) ).
fof(f306,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c5 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f288,f192]) ).
fof(f314,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f288,f298]) ).
fof(f316,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f314,f200]) ).
fof(f319,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f316]) ).
fof(f326,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f319,f36]) ).
fof(f327,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f319,f35]) ).
fof(f338,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f327,f303]) ).
fof(f339,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f306]) ).
fof(f340,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f341,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f288,f72]) ).
fof(f342,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f327,f341]) ).
fof(f343,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f283,f342]) ).
fof(f344,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f343]) ).
fof(f345,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f357,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f338,f327]) ).
fof(f363,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f338,f82]) ).
fof(f365,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c5) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f338,f296]) ).
fof(f366,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f338,f365]) ).
fof(f386,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f338,f326]) ).
fof(f387,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c3) = sk_c5 ),
inference(paramodulation,[status(thm)],[f363,f386]) ).
fof(f392,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f357,f387]) ).
fof(f396,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f392,f363]) ).
fof(f397,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f366]) ).
fof(f398,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f401,plain,
( ~ sQ8_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f107,f200]) ).
fof(f403,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = multiply(sk_c2,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f116,f401]) ).
fof(f406,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f200,f273]) ).
fof(f431,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f403,f200]) ).
fof(f433,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f431]) ).
fof(f434,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f433,f36]) ).
fof(f436,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f433,f406]) ).
fof(f437,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(inverse(sk_c8),X0) ),
inference(backward_demodulation,[status(thm)],[f433,f273]) ).
fof(f439,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f98,f437]) ).
fof(f440,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f436,f75]) ).
fof(f445,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(inverse(sk_c6),X0) ),
inference(paramodulation,[status(thm)],[f439,f200]) ).
fof(f456,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 = sk_c8 ),
inference(paramodulation,[status(thm)],[f434,f445]) ).
fof(f463,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f456,f440]) ).
fof(f464,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f456,f71]) ).
fof(f465,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f456,f98]) ).
fof(f466,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f464,f177]) ).
fof(f468,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f464,f37]) ).
fof(f469,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f436,f468]) ).
fof(f470,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f436,f469]) ).
fof(f475,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(inverse(sk_c7),X0) ),
inference(paramodulation,[status(thm)],[f470,f200]) ).
fof(f479,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 = sk_c8 ),
inference(paramodulation,[status(thm)],[f434,f475]) ).
fof(f481,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 = sk_c8 ),
inference(paramodulation,[status(thm)],[f475,f434]) ).
fof(f484,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f463]) ).
fof(f485,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f494,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f436,f143]) ).
fof(f498,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f481,f125]) ).
fof(f501,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c2 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f403,f498]) ).
fof(f502,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f481,f466]) ).
fof(f503,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f502]) ).
fof(f504,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f509,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f501,f481]) ).
fof(f510,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c8) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f501,f465]) ).
fof(f513,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f501,f434]) ).
fof(f514,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f501,f436]) ).
fof(f520,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c3) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f501,f83]) ).
fof(f522,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f501,f510]) ).
fof(f528,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f501,f494]) ).
fof(f529,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f509,f528]) ).
fof(f530,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f501,f529]) ).
fof(f531,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f530,f514]) ).
fof(f534,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f522,f531]) ).
fof(f535,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f509,f146]) ).
fof(f538,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f514,f537]) ).
fof(f539,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(sk_c3,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f501,f538]) ).
fof(f540,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f514,f539]) ).
fof(f549,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f501,f137]) ).
fof(f550,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f509,f549]) ).
fof(f551,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f501,f550]) ).
fof(f562,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(inverse(sk_c3),X0) ),
inference(paramodulation,[status(thm)],[f540,f200]) ).
fof(f567,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c3 = sk_c2 ),
inference(paramodulation,[status(thm)],[f513,f562]) ).
fof(f574,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ2_spl
| inverse(sk_c2) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f567,f520]) ).
fof(f576,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f522,f574]) ).
fof(f577,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f576]) ).
fof(f578,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f673,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ12_spl
| inverse(inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f551,f513]) ).
fof(f678,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f522,f673]) ).
fof(f679,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ12_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f522,f678]) ).
fof(f680,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f679]) ).
fof(f681,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f680]) ).
fof(f682,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,f181,f185,f186,f193,f227,f234,f241,f245,f249,f254,f285,f290,f301,f340,f345,f398,f485,f504,f536,f578,f681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP357-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:10:18 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.45 % Elapsed time: 0.075903 seconds
% 0.15/0.45 % CPU time: 0.212638 seconds
% 0.15/0.45 % Total memory used: 103.452 MB
% 0.15/0.45 % Net memory used: 103.227 MB
%------------------------------------------------------------------------------