%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP294-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:33:20 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 55
% Syntax : Number of formulae : 313 ( 12 unt; 21 def)
% Number of atoms : 1366 ( 368 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 2034 ( 981 ~;1032 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 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_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
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_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
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_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c6) = 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_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = 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_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c6 ),
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_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,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_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f93,f73]) ).
fof(f97,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f93,f77]) ).
fof(f98,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f45,f93,f81]) ).
fof(f99,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f46,f93,f85]) ).
fof(f100,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f47,f93,f89]) ).
fof(f101,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f101,f73]) ).
fof(f105,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f101,f77]) ).
fof(f106,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f101,f81]) ).
fof(f107,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f101,f85]) ).
fof(f108,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f101,f89]) ).
fof(f109,definition,
( sQ8_spl
<=> multiply(sk_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f111,plain,
( sQ8_spl
| multiply(sk_c7,sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f109,f73]) ).
fof(f113,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f109,f77]) ).
fof(f114,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f109,f81]) ).
fof(f115,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f109,f85]) ).
fof(f116,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f109,f89]) ).
fof(f117,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f117,f73]) ).
fof(f121,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f122,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f123,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f124,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f125,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f125,f73]) ).
fof(f129,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f125,f77]) ).
fof(f130,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f125,f81]) ).
fof(f131,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f125,f85]) ).
fof(f132,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f125,f89]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
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_c6 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3] :
( sQ14_spl
<=> ( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| ~ sQ8_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f109,f136,f73,f139,f142]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f148,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f86,f146]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f148]) ).
fof(f150,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f160,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f161,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| sk_c7 != sk_c6
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f140]) ).
fof(f164,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f160]) ).
fof(f165,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f164]) ).
fof(f166,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f169,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f126,f36]) ).
fof(f171,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f172,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f171]) ).
fof(f185,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f172]) ).
fof(f191,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f94,f172]) ).
fof(f192,plain,
( ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f118,f172]) ).
fof(f195,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f102,f191]) ).
fof(f196,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f71,f195]) ).
fof(f197,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c7,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f126,f192]) ).
fof(f198,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f110,f197]) ).
fof(f200,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f196,f169]) ).
fof(f203,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f196,f110]) ).
fof(f205,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f196,f94]) ).
fof(f208,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f196,f126]) ).
fof(f213,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f196,f198]) ).
fof(f218,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f137]) ).
fof(f219,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f218]) ).
fof(f221,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(inverse(sk_c5)) != sk_c5
| identity != sk_c5 ),
inference(paramodulation,[status(thm)],[f36,f219]) ).
fof(f222,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(identity) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramodulation,[status(thm)],[f35,f219]) ).
fof(f224,definition,
( sQ15_spl
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ15_spl
| identity != sk_c5 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,definition,
( sQ16_spl
<=> inverse(inverse(sk_c5)) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f221,f224,f227,f70,f101,f93,f136]) ).
fof(f231,definition,
( sQ17_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ17_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,definition,
( sQ18_spl
<=> inverse(identity) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( sQ18_spl
| inverse(identity) != sk_c5 ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f222,f231,f234,f70,f101,f93,f136]) ).
fof(f238,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f233]) ).
fof(f239,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f196,f134]) ).
fof(f241,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f213,f240]) ).
fof(f242,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f241]) ).
fof(f245,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(identity) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramodulation,[status(thm)],[f35,f242]) ).
fof(f248,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f245,f231,f234,f109,f125,f117,f70,f101,f93,f133]) ).
fof(f254,definition,
( sQ19_spl
<=> multiply(sk_c1,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( sQ19_spl
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ20_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ20_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f161,f254,f257,f139,f101]) ).
fof(f271,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f196,f259]) ).
fof(f272,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f213,f271]) ).
fof(f273,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f272]) ).
fof(f274,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f277,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f213,f256]) ).
fof(f278,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f277]) ).
fof(f284,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c5,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f213,f203]) ).
fof(f285,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f284,f172]) ).
fof(f287,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f285]) ).
fof(f288,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f226]) ).
fof(f289,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f291,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f287,f35]) ).
fof(f294,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f287,f236]) ).
fof(f304,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f291,f200]) ).
fof(f306,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f315,f291]) ).
fof(f307,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c5) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f315,f294]) ).
fof(f311,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f315,f208]) ).
fof(f313,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f315,f213]) ).
fof(f314,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f315,f196]) ).
fof(f315,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f287,f304]) ).
fof(f316,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f315,f307]) ).
fof(f317,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f315,f205]) ).
fof(f318,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f313,f317]) ).
fof(f330,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f316]) ).
fof(f331,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f330]) ).
fof(f332,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f313,f75]) ).
fof(f333,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f306,f332]) ).
fof(f334,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f314,f333]) ).
fof(f335,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f315,f334]) ).
fof(f336,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f335]) ).
fof(f337,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f340,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c2) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f278]) ).
fof(f341,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f318,f340]) ).
fof(f342,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f315,f341]) ).
fof(f343,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f342]) ).
fof(f344,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f348,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f313,f143]) ).
fof(f349,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(X0,sk_c2) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f315,f348]) ).
fof(f350,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f313,f349]) ).
fof(f377,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ14_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f350,f311]) ).
fof(f379,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ14_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f306,f377]) ).
fof(f380,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f379]) ).
fof(f381,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f390,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f172,f185]) ).
fof(f398,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f78]) ).
fof(f399,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c5) ),
inference(paramodulation,[status(thm)],[f398,f172]) ).
fof(f401,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f82,f399]) ).
fof(f402,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f74]) ).
fof(f405,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f172]) ).
fof(f407,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f405]) ).
fof(f409,plain,
( ~ sQ3_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f82,f36]) ).
fof(f429,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f431,f82]) ).
fof(f431,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f402,f401]) ).
fof(f436,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f431,f407]) ).
fof(f437,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f431,f436]) ).
fof(f438,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f437,f172]) ).
fof(f440,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f438]) ).
fof(f442,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f440,f390]) ).
fof(f445,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f440,f236]) ).
fof(f471,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f431,f409]) ).
fof(f472,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f442,f471]) ).
fof(f474,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c5) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f483,f445]) ).
fof(f478,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f483,f429]) ).
fof(f483,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f440,f472]) ).
fof(f484,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f483,f474]) ).
fof(f495,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f484]) ).
fof(f496,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f556,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f172]) ).
fof(f558,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f556]) ).
fof(f572,plain,
( ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f172]) ).
fof(f574,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f82,f572]) ).
fof(f575,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f74,f574]) ).
fof(f576,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f575,f78]) ).
fof(f579,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f575,f111]) ).
fof(f581,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f575,f409]) ).
fof(f582,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f575,f90]) ).
fof(f584,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f575,f86]) ).
fof(f585,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f575,f82]) ).
fof(f602,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f575,f558]) ).
fof(f603,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f575,f602]) ).
fof(f604,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f603,f172]) ).
fof(f606,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f604]) ).
fof(f607,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f606,f36]) ).
fof(f609,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f606,f390]) ).
fof(f618,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f576,f172]) ).
fof(f620,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f585,f618]) ).
fof(f621,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f609,f620]) ).
fof(f629,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f621,f579]) ).
fof(f630,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f609,f629]) ).
fof(f631,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f630]) ).
fof(f632,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f641,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f621,f134]) ).
fof(f642,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f575,f641]) ).
fof(f643,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f621,f642]) ).
fof(f645,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f582,f37]) ).
fof(f647,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| X0 = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f609,f645]) ).
fof(f648,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f609,f647]) ).
fof(f653,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f609,f581]) ).
fof(f655,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f662,f621]) ).
fof(f657,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f662,f609]) ).
fof(f660,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f662,f584]) ).
fof(f661,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f662,f575]) ).
fof(f662,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f606,f653]) ).
fof(f663,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f662,f607]) ).
fof(f672,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c4) = sk_c3 ),
inference(paramodulation,[status(thm)],[f660,f663]) ).
fof(f674,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f657,f672]) ).
fof(f676,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f674,f660]) ).
fof(f680,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f674,f661]) ).
fof(f682,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f674,f655]) ).
fof(f684,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f674,f662]) ).
fof(f703,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f684,f643]) ).
fof(f704,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f684,f703]) ).
fof(f705,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f684,f704]) ).
fof(f706,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f705,f676]) ).
fof(f708,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f648,f706]) ).
fof(f709,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f708]) ).
fof(f710,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f711,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f682,f137]) ).
fof(f712,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f684,f711]) ).
fof(f713,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f682,f712]) ).
fof(f731,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ12_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f713,f676]) ).
fof(f733,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ12_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f648,f731]) ).
fof(f734,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f733]) ).
fof(f735,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f734]) ).
fof(f736,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c6) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f682,f72]) ).
fof(f737,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f648,f736]) ).
fof(f738,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f680,f737]) ).
fof(f739,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f684,f738]) ).
fof(f740,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f739]) ).
fof(f741,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f742,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f128,f129,f130,f131,f132,f145,f150,f166,f230,f237,f239,f248,f260,f274,f289,f331,f337,f344,f381,f496,f632,f710,f735,f741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP294-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n016.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 20 20:13:08 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.059844 seconds
% 0.14/0.42 % CPU time: 0.197005 seconds
% 0.14/0.42 % Total memory used: 104.472 MB
% 0.14/0.42 % Net memory used: 104.230 MB
%------------------------------------------------------------------------------