%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP342-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:28 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 62
% Syntax : Number of formulae : 278 ( 15 unt; 28 def)
% Number of atoms : 898 ( 319 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1150 ( 530 ~; 592 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 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_c8,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X2,X1,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X2) != X1
| multiply(X2,X1) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c6
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| ! [X2] :
( inverse(X2) != X1
| multiply(X2,X1) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| ! [X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| ! [X3] :
( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != X3
| multiply(X2,X3) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> multiply(sk_c3,sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> inverse(sk_c3) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c4 ),
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_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f70,f89]) ).
fof(f93,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f70,f93]) ).
fof(f97,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f106,f73]) ).
fof(f110,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f106,f77]) ).
fof(f111,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f106,f81]) ).
fof(f112,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f106,f85]) ).
fof(f113,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f106,f89]) ).
fof(f114,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f106,f93]) ).
fof(f115,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f115,f73]) ).
fof(f119,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f115,f77]) ).
fof(f120,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f115,f81]) ).
fof(f121,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f115,f85]) ).
fof(f122,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f115,f89]) ).
fof(f123,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f115,f93]) ).
fof(f124,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f124,f73]) ).
fof(f128,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f124,f77]) ).
fof(f129,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f124,f81]) ).
fof(f130,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f124,f85]) ).
fof(f131,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f124,f89]) ).
fof(f132,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f124,f93]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2,X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X2) != X3
| multiply(X2,X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
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(f147,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f150,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f94,f147]) ).
fof(f151,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f154,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f125]) ).
fof(f156,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f116,f154]) ).
fof(f157,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f165,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f125,f37]) ).
fof(f169,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c7) != sk_c8
| multiply(sk_c3,inverse(sk_c3)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f82,f153]) ).
fof(f178,definition,
( sQ17_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ17_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c8 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f169,f178,f85,f139,f81]) ).
fof(f186,plain,
( sQ17_spl
| ~ sQ3_spl
| multiply(sk_c3,sk_c4) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f82,f180]) ).
fof(f187,plain,
( sQ17_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f186]) ).
fof(f188,plain,
( sQ17_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f187]) ).
fof(f189,plain,
( sQ17_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f194,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f94,f36]) ).
fof(f196,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f197,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f196]) ).
fof(f206,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f197]) ).
fof(f209,plain,
( ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f197]) ).
fof(f210,plain,
( ~ sQ2_spl
| sk_c4 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f78,f197]) ).
fof(f213,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f197]) ).
fof(f217,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = multiply(sk_c4,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f82,f210]) ).
fof(f218,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f94,f213]) ).
fof(f219,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f218]) ).
fof(f222,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c6) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f219,f74]) ).
fof(f231,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f206,f197]) ).
fof(f233,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c4) ),
inference(paramodulation,[status(thm)],[f217,f197]) ).
fof(f235,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f233]) ).
fof(f238,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f235,f194]) ).
fof(f240,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f235,f35]) ).
fof(f247,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(X0,sk_c8) != sk_c8
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f219,f134]) ).
fof(f252,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c6 != sk_c8
| inverse(sk_c5) != sk_c8 ),
inference(paramodulation,[status(thm)],[f90,f247]) ).
fof(f253,definition,
( sQ19_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ19_spl
| inverse(sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
( sQ20_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ20_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f267,definition,
( sQ23_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ23_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ23_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f252,f93,f267,f73,f133,f89]) ).
fof(f271,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f219,f72]) ).
fof(f272,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f240,f271]) ).
fof(f273,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f281,f240]) ).
fof(f277,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f281,f219]) ).
fof(f278,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f281,f94]) ).
fof(f281,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f240,f222]) ).
fof(f286,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f281,f272]) ).
fof(f287,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f286]) ).
fof(f288,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f289,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f281,f269]) ).
fof(f290,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f289]) ).
fof(f291,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f304,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c6,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f278,f197]) ).
fof(f305,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f304]) ).
fof(f322,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c5) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f281,f238]) ).
fof(f323,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f273,f322]) ).
fof(f326,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f333,f278]) ).
fof(f329,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f333,f277]) ).
fof(f333,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f281,f323]) ).
fof(f384,definition,
( sQ26_spl
<=> sk_c2 = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ26_spl
| sk_c2 != sk_c2 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f392,plain,
( sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f386]) ).
fof(f393,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f422,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f329,f137]) ).
fof(f423,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(X0,sk_c5) != sk_c7
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f333,f422]) ).
fof(f424,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f329,f423]) ).
fof(f425,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c5 ),
inference(resolution,[status(thm)],[f424,f305]) ).
fof(f428,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f326,f425]) ).
fof(f429,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f428]) ).
fof(f430,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f431,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f258]) ).
fof(f432,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f440,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f71,f37]) ).
fof(f447,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f107,f197]) ).
fof(f449,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f98,f447]) ).
fof(f450,plain,
( ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f125,f197]) ).
fof(f452,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f116,f450]) ).
fof(f453,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f107]) ).
fof(f459,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f453]) ).
fof(f460,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f459]) ).
fof(f461,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f467,plain,
( ~ sQ13_spl
| identity != sk_c8
| multiply(sk_c7,inverse(sk_c7)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f36,f153]) ).
fof(f470,definition,
( sQ28_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f473,definition,
( sQ29_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( sQ29_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,plain,
( ~ sQ13_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f467,f470,f473,f139]) ).
fof(f502,plain,
( ~ sQ13_spl
| sk_c7 != sk_c8
| multiply(identity,inverse(identity)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f206,f153]) ).
fof(f507,definition,
( sQ32_spl
<=> multiply(identity,inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ32_spl
| multiply(identity,inverse(identity)) != sk_c8 ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,definition,
( sQ33_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( ~ sQ13_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f502,f507,f510,f139]) ).
fof(f514,plain,
( sQ32_spl
| inverse(identity) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f35,f509]) ).
fof(f521,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| sk_c6 != sk_c8
| multiply(sk_c8,inverse(sk_c8)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f209,f153]) ).
fof(f524,definition,
( sQ34_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( sQ34_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ23_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f521,f524,f267,f139,f73]) ).
fof(f530,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f36,f231]) ).
fof(f537,definition,
( sQ35_spl
<=> multiply(inverse(identity),inverse(inverse(identity))) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ35_spl
| multiply(inverse(identity),inverse(inverse(identity))) != sk_c8 ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f541,plain,
( sQ35_spl
| inverse(inverse(identity)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f206,f539]) ).
fof(f543,plain,
( sQ32_spl
| identity != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f530,f514]) ).
fof(f546,plain,
( ~ sQ13_spl
| multiply(identity,sk_c7) != sk_c8
| multiply(identity,inverse(identity)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f530,f153]) ).
fof(f550,definition,
( sQ36_spl
<=> multiply(identity,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( ~ sQ13_spl
| ~ sQ36_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f546,f507,f550,f139]) ).
fof(f569,plain,
( sQ35_spl
| inverse(identity) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f530,f541]) ).
fof(f570,plain,
( sQ35_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f530,f569]) ).
fof(f604,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c8) = multiply(sk_c7,sk_c7) ),
inference(paramodulation,[status(thm)],[f449,f440]) ).
fof(f609,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f452,f604]) ).
fof(f613,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c2,sk_c6) ),
inference(paramodulation,[status(thm)],[f609,f165]) ).
fof(f615,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f609,f197]) ).
fof(f617,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c2,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f71,f613]) ).
fof(f618,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f125,f617]) ).
fof(f621,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f615]) ).
fof(f622,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f475]) ).
fof(f623,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f622]) ).
fof(f624,definition,
( sQ37_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( sQ37_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f631,plain,
( sQ37_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f626]) ).
fof(f632,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f646,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c6) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f618,f107]) ).
fof(f652,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(identity) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f621,f530]) ).
fof(f656,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f621,f35]) ).
fof(f657,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f621,f652]) ).
fof(f679,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramodulation,[status(thm)],[f656,f143]) ).
fof(f682,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f679,f267,f253,f142,f115,f124,f70,f97,f106]) ).
fof(f687,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f646,f197]) ).
fof(f689,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f98,f687]) ).
fof(f690,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f656,f689]) ).
fof(f691,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f690,f269]) ).
fof(f692,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f691]) ).
fof(f694,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f657,f255]) ).
fof(f695,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f694]) ).
fof(f696,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f695]) ).
fof(f697,plain,
( sQ32_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f543,f473,f507]) ).
fof(f701,plain,
( sQ34_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f656,f526]) ).
fof(f702,plain,
( sQ34_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f657,f701]) ).
fof(f703,plain,
( sQ34_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f702]) ).
fof(f704,plain,
( sQ34_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f703]) ).
fof(f708,plain,
( sQ35_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f570,f473,f537]) ).
fof(f712,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f656,f75]) ).
fof(f713,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f618,f712]) ).
fof(f714,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f713]) ).
fof(f715,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f716,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f100,f101,f102,f103,f104,f105,f109,f110,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f145,f152,f158,f181,f189,f270,f288,f291,f393,f430,f432,f461,f476,f513,f527,f553,f623,f632,f682,f692,f696,f697,f704,f708,f715]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP342-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:10:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.072184 seconds
% 0.14/0.44 % CPU time: 0.185233 seconds
% 0.14/0.44 % Total memory used: 49.199 MB
% 0.14/0.44 % Net memory used: 49.129 MB
%------------------------------------------------------------------------------