%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP328-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:33:25 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 47
% Syntax : Number of formulae : 228 ( 9 unt; 13 def)
% Number of atoms : 867 ( 286 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1193 ( 554 ~; 626 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 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_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( inverse(X2) != sk_c8
| ! [X1] :
( multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| ! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> inverse(sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( sQ2_spl
| inverse(sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c8,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c5) = 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_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c8 ),
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_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
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_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c3) = sk_c7 ),
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_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = sk_c3 ),
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_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
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_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1,X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f77]) ).
fof(f140,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f142,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f74,f37]) ).
fof(f169,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c8
| multiply(sk_c8,sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f118,f140]) ).
fof(f170,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f86,f140]) ).
fof(f171,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f169,f109,f125,f136,f117]) ).
fof(f172,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f170,f81,f89,f136,f85]) ).
fof(f173,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f176,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f173]) ).
fof(f177,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f176]) ).
fof(f178,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f181,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f126,f36]) ).
fof(f182,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f90,f36]) ).
fof(f183,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f184,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f183]) ).
fof(f207,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f94,f184]) ).
fof(f209,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f118,f184]) ).
fof(f213,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f86,f184]) ).
fof(f216,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f102,f207]) ).
fof(f217,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f216]) ).
fof(f219,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f126,f209]) ).
fof(f220,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f110,f219]) ).
fof(f221,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f90,f213]) ).
fof(f224,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c6) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f217,f75]) ).
fof(f225,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f217,f71]) ).
fof(f230,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f217,f110]) ).
fof(f233,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f239,f181]) ).
fof(f239,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f217,f220]) ).
fof(f252,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f239,f224]) ).
fof(f253,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f239,f225]) ).
fof(f254,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f252]) ).
fof(f255,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f254]) ).
fof(f267,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f239,f79]) ).
fof(f274,plain,
( ~ sQ2_spl
| multiply(sk_c6,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f282,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f221]) ).
fof(f283,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c6) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f282,f74]) ).
fof(f284,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f283,f184]) ).
fof(f286,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f284]) ).
fof(f288,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f286,f36]) ).
fof(f289,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f286,f35]) ).
fof(f292,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f286,f182]) ).
fof(f293,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c4 = multiply(inverse(sk_c8),sk_c6) ),
inference(paramodulation,[status(thm)],[f292,f184]) ).
fof(f295,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f78,f293]) ).
fof(f296,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f289,f295]) ).
fof(f299,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f296,f289]) ).
fof(f300,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f296,f286]) ).
fof(f302,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(sk_c8) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f296,f78]) ).
fof(f303,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(inverse(sk_c4),X0) ),
inference(paramodulation,[status(thm)],[f299,f184]) ).
fof(f305,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f90,f303]) ).
fof(f308,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f312,f302]) ).
fof(f310,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f312,f282]) ).
fof(f312,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f299,f86]) ).
fof(f317,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f312,f305]) ).
fof(f325,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f310,f72]) ).
fof(f326,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f317,f325]) ).
fof(f327,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f312,f326]) ).
fof(f328,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f296,f327]) ).
fof(f329,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c8) = identity ),
inference(forward_demodulation,[status(thm)],[f296,f274]) ).
fof(f330,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f299,f329]) ).
fof(f331,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f312,f330]) ).
fof(f332,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f300,f331]) ).
fof(f333,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f328]) ).
fof(f334,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f434,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f332,f310]) ).
fof(f439,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f440,f282]) ).
fof(f440,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f282,f434]) ).
fof(f441,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f332,f308]) ).
fof(f472,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f296,f288]) ).
fof(f498,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f439,f134]) ).
fof(f499,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f440,f498]) ).
fof(f500,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f439,f499]) ).
fof(f501,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl
| inverse(inverse(sk_c4)) != sk_c4 ),
inference(resolution,[status(thm)],[f500,f472]) ).
fof(f508,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f441,f501]) ).
fof(f509,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f441,f508]) ).
fof(f510,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f509]) ).
fof(f511,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f519,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c3) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f239,f230]) ).
fof(f522,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f239,f126]) ).
fof(f600,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f239,f142]) ).
fof(f601,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f217,f600]) ).
fof(f606,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(inverse(sk_c6),multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f601,f184]) ).
fof(f610,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f184,f606]) ).
fof(f616,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ1_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f610,f519]) ).
fof(f617,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c6),X0) ),
inference(paramodulation,[status(thm)],[f610,f184]) ).
fof(f698,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f616,f610]) ).
fof(f701,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f616,f267]) ).
fof(f702,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f616,f701]) ).
fof(f703,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f616,f522]) ).
fof(f720,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c3),X0) ),
inference(forward_demodulation,[status(thm)],[f616,f617]) ).
fof(f731,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f616,f233]) ).
fof(f734,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f698,f731]) ).
fof(f753,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f734,f36]) ).
fof(f754,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c3 = sk_c2 ),
inference(paramodulation,[status(thm)],[f720,f753]) ).
fof(f762,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f754,f703]) ).
fof(f763,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f754,f702]) ).
fof(f769,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f754,f763]) ).
fof(f773,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f762,f769]) ).
fof(f774,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f773]) ).
fof(f775,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f774]) ).
fof(f776,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,f139,f171,f172,f178,f255,f334,f511,f775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP328-1 : 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 : n019.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 20:09:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.058695 seconds
% 0.15/0.44 % CPU time: 0.183761 seconds
% 0.15/0.44 % Total memory used: 103.625 MB
% 0.15/0.44 % Net memory used: 103.365 MB
%------------------------------------------------------------------------------