%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP286-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:33:19 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 62
% Syntax : Number of formulae : 285 ( 13 unt; 31 def)
% Number of atoms : 943 ( 324 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1237 ( 579 ~; 627 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 32 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 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_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/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_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f44,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
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_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ) ) ) ) ),
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_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c7,sk_c8) != 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_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c7 ),
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(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(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(f97,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| inverse(sk_c1) = 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
<=> multiply(sk_c2,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c6 ),
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
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f124,f73]) ).
fof(f128,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f124,f77]) ).
fof(f129,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f124,f81]) ).
fof(f130,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f124,f85]) ).
fof(f131,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f124,f89]) ).
fof(f132,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f124,f93]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ) ),
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_c6 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3,X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f142]) ).
fof(f146,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f149,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c8,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f71,f37]) ).
fof(f162,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c7) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f149,f146]) ).
fof(f164,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f146]) ).
fof(f165,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f98,f146]) ).
fof(f166,definition,
( sQ15_spl
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ15_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,definition,
( sQ16_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f162,f166,f169,f142,f70]) ).
fof(f173,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f164,f85,f93,f142,f89]) ).
fof(f174,definition,
( sQ17_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ17_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f165,f174,f106,f142,f97]) ).
fof(f178,plain,
( sQ17_spl
| ~ sQ0_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f71,f176]) ).
fof(f179,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f180,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f125]) ).
fof(f184,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f179]) ).
fof(f185,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f184]) ).
fof(f186,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f191,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f192,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f191]) ).
fof(f213,plain,
( ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f98,f192]) ).
fof(f216,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f107,f213]) ).
fof(f217,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f216]) ).
fof(f228,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f230,plain,
( ~ sQ12_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f35,f137]) ).
fof(f233,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f125,f228]) ).
fof(f234,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f233]) ).
fof(f235,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f236,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sk_c7 != sk_c8
| multiply(sk_c3,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f134]) ).
fof(f238,definition,
( sQ18_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f241,definition,
( sQ19_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ19_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f236,f238,f241,f133,f81]) ).
fof(f287,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f216,f192]) ).
fof(f289,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f287]) ).
fof(f295,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f289,f35]) ).
fof(f302,plain,
( ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f78,f192]) ).
fof(f304,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f82,f302]) ).
fof(f305,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f295,f304]) ).
fof(f306,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f243]) ).
fof(f307,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f312,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f125,f36]) ).
fof(f316,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f192]) ).
fof(f321,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c8) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f332,f168]) ).
fof(f322,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f332,f74]) ).
fof(f328,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f332,f86]) ).
fof(f330,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f332,f82]) ).
fof(f332,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f74,f304]) ).
fof(f354,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f332,f134]) ).
fof(f357,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| sk_c6 != sk_c8
| multiply(sk_c3,sk_c8) != sk_c6 ),
inference(paramodulation,[status(thm)],[f330,f354]) ).
fof(f358,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c8 != sk_c8
| multiply(sk_c4,sk_c8) != sk_c6 ),
inference(paramodulation,[status(thm)],[f94,f354]) ).
fof(f363,definition,
( sQ22_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( sQ22_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f367,definition,
( sQ23_spl
<=> multiply(sk_c3,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ22_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f357,f367,f363,f133,f73,f77,f81]) ).
fof(f371,definition,
( sQ24_spl
<=> multiply(sk_c4,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( sQ24_spl
| multiply(sk_c4,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,definition,
( sQ25_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ25_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f358,f371,f374,f73,f81,f77,f133,f93]) ).
fof(f378,plain,
( sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f376]) ).
fof(f379,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( sQ24_spl
| ~ sQ5_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f90,f373]) ).
fof(f381,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f332,f72]) ).
fof(f382,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f322,f192]) ).
fof(f384,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f382]) ).
fof(f389,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f384,f35]) ).
fof(f408,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f322,f321]) ).
fof(f409,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f408]) ).
fof(f410,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f419,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f389,f328]) ).
fof(f420,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ24_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f380]) ).
fof(f421,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ24_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f389,f381]) ).
fof(f424,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f423]) ).
fof(f425,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f433,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f332,f137]) ).
fof(f434,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f332,f433]) ).
fof(f442,definition,
( sQ28_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ28_spl
| sk_c7 = sk_c6 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f444,plain,
( sQ28_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
( sQ29_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ12_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f230,f442,f445,f136]) ).
fof(f452,plain,
( sQ28_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f332,f444]) ).
fof(f453,plain,
( sQ28_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f452]) ).
fof(f454,plain,
( sQ28_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f453]) ).
fof(f456,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f217,f134]) ).
fof(f457,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f217,f456]) ).
fof(f468,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(inverse(sk_c7),X0) ),
inference(forward_demodulation,[status(thm)],[f289,f316]) ).
fof(f471,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(inverse(sk_c7)) != sk_c6
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f468,f457]) ).
fof(f474,definition,
( sQ31_spl
<=> inverse(inverse(sk_c7)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( sQ31_spl
| inverse(inverse(sk_c7)) != sk_c6 ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ31_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f471,f442,f474,f70,f133,f106,f97]) ).
fof(f478,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f295,f312]) ).
fof(f480,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f486,f444]) ).
fof(f484,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f486,f125]) ).
fof(f485,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f486,f289]) ).
fof(f486,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f289,f478]) ).
fof(f496,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f485,f35]) ).
fof(f525,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f496,f116]) ).
fof(f526,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f486,f525]) ).
fof(f527,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f480]) ).
fof(f528,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f217,f365]) ).
fof(f530,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f529]) ).
fof(f531,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f537,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(inverse(sk_c2)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f486,f476]) ).
fof(f538,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f484,f537]) ).
fof(f539,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f484,f538]) ).
fof(f580,plain,
( ~ sQ28_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f486,f443]) ).
fof(f585,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f178,f442,f70,f174]) ).
fof(f601,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f539]) ).
fof(f602,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f609,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f496,f180]) ).
fof(f610,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f486,f609]) ).
fof(f611,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f217,f610]) ).
fof(f619,definition,
( sQ34_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( sQ34_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f619]) ).
fof(f637,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ28_spl
| ~ sQ10_spl
| sk_c8 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f580,f217]) ).
fof(f640,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ28_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f580,f611]) ).
fof(f641,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f640]) ).
fof(f642,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f641]) ).
fof(f643,plain,
( sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f621]) ).
fof(f644,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f662,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f384,f35]) ).
fof(f667,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f384,f36]) ).
fof(f679,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c4) = sk_c8 ),
inference(paramodulation,[status(thm)],[f94,f667]) ).
fof(f680,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f94,f192]) ).
fof(f681,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f662,f679]) ).
fof(f682,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f662,f680]) ).
fof(f683,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f681,f94]) ).
fof(f742,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f419,f434]) ).
fof(f743,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f419,f742]) ).
fof(f744,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f419,f743]) ).
fof(f746,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sk_c4 != sk_c5
| multiply(sk_c4,sk_c5) != sk_c5 ),
inference(paramodulation,[status(thm)],[f683,f744]) ).
fof(f749,definition,
( sQ35_spl
<=> multiply(sk_c4,sk_c5) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f751,plain,
( sQ35_spl
| multiply(sk_c4,sk_c5) != sk_c5 ),
inference(component_clause,[status(thm)],[f749]) ).
fof(f752,definition,
( sQ36_spl
<=> sk_c4 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( sQ36_spl
| sk_c4 != sk_c5 ),
inference(component_clause,[status(thm)],[f752]) ).
fof(f755,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f746,f749,f752,f85,f136,f81,f77,f73,f93]) ).
fof(f759,definition,
( sQ38_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( sQ38_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f763,plain,
( sQ35_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f682,f751]) ).
fof(f764,plain,
( sQ35_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f763]) ).
fof(f765,plain,
( sQ35_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f764]) ).
fof(f767,plain,
( sQ38_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f761]) ).
fof(f768,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f769,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f682,f90]) ).
fof(f770,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f681,f769]) ).
fof(f806,plain,
( sQ36_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f770,f754]) ).
fof(f807,plain,
( sQ36_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f806]) ).
fof(f808,plain,
( sQ36_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f807]) ).
fof(f810,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ28_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f443,f486]) ).
fof(f816,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f485,f289]) ).
fof(f819,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f816,f75]) ).
fof(f820,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ28_spl
| multiply(sk_c2,sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f637,f819]) ).
fof(f821,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ28_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f810,f820]) ).
fof(f822,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ28_spl
| sk_c2 != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f496,f821]) ).
fof(f825,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f822]) ).
fof(f826,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f825]) ).
fof(f827,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f100,f101,f102,f103,f104,f105,f109,f110,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f145,f172,f173,f177,f186,f235,f244,f307,f370,f377,f379,f410,f421,f425,f448,f454,f477,f528,f531,f585,f602,f642,f644,f755,f765,f768,f808,f826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP286-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:08:33 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.052256 seconds
% 0.12/0.40 % CPU time: 0.143358 seconds
% 0.12/0.40 % Total memory used: 34.464 MB
% 0.12/0.40 % Net memory used: 34.354 MB
%------------------------------------------------------------------------------