%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP316-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:33:23 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 55
% Syntax : Number of formulae : 279 ( 13 unt; 21 def)
% Number of atoms : 1058 ( 331 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1480 ( 701 ~; 758 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| 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_c6,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X5] :
( inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c8
| ! [X1] :
( multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| 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_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c6,sk_c8) != 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_c8,sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c3,sk_c8) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c8) = 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
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c6) = 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
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c6 ),
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
<=> 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,X3] :
( sQ13_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c8 ),
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,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f148,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f94,f146]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f148]) ).
fof(f150,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f152,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f154,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f125,f152]) ).
fof(f155,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f167,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c4) != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f151]) ).
fof(f168,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f98,f151]) ).
fof(f169,definition,
( sQ15_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ15_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
( sQ16_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ16_spl
| inverse(sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f176,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f167,f77,f85,f139,f81]) ).
fof(f177,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f168,f169,f106,f139,f97]) ).
fof(f181,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f125,f36]) ).
fof(f182,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f183,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f182]) ).
fof(f202,plain,
( ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c4) ),
inference(paramodulation,[status(thm)],[f82,f183]) ).
fof(f203,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c8) ),
inference(paramodulation,[status(thm)],[f90,f183]) ).
fof(f205,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f86,f202]) ).
fof(f206,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f205]) ).
fof(f207,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f94,f203]) ).
fof(f208,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f207]) ).
fof(f212,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f206,f74]) ).
fof(f214,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c4) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f206,f78]) ).
fof(f217,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f223,f206]) ).
fof(f222,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f223,f86]) ).
fof(f223,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f206,f208]) ).
fof(f244,definition,
( sQ17_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( sQ17_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f262,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f246]) ).
fof(f263,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f217,f72]) ).
fof(f265,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f223,f264]) ).
fof(f266,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f223,f212]) ).
fof(f267,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f223,f266]) ).
fof(f268,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f267,f183]) ).
fof(f270,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f268]) ).
fof(f275,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f270,f35]) ).
fof(f366,plain,
( ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f116,f183]) ).
fof(f368,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f125,f366]) ).
fof(f369,plain,
( ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f98,f183]) ).
fof(f371,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f107,f369]) ).
fof(f380,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f98]) ).
fof(f381,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c6) != sk_c8
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f74,f134]) ).
fof(f386,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f107,f380]) ).
fof(f387,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f386]) ).
fof(f388,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f389,definition,
( sQ22_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( sQ22_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f381,f389,f172,f133,f73]) ).
fof(f393,definition,
( sQ23_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ23_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f401,definition,
( sQ25_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( sQ25_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f408,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f74,f212]) ).
fof(f416,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f408,f208]) ).
fof(f417,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f270,f35]) ).
fof(f421,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c4) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f416,f214]) ).
fof(f422,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f416,f421]) ).
fof(f427,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c4 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f275,f422]) ).
fof(f431,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f427,f94]) ).
fof(f433,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f427,f270]) ).
fof(f434,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f427,f217]) ).
fof(f435,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c4 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f427,f416]) ).
fof(f436,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f427,f222]) ).
fof(f442,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f427,f417]) ).
fof(f455,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f433,f36]) ).
fof(f457,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(paramodulation,[status(thm)],[f431,f455]) ).
fof(f459,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c3) = sk_c4 ),
inference(paramodulation,[status(thm)],[f436,f455]) ).
fof(f463,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f442,f457]) ).
fof(f465,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f442,f459]) ).
fof(f476,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f463,f455]) ).
fof(f483,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c5 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f463,f435]) ).
fof(f484,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f463,f434]) ).
fof(f485,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f463,f433]) ).
fof(f486,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f463,f427]) ).
fof(f547,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f391]) ).
fof(f548,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f554,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f555,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f183,f554]) ).
fof(f564,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f371,f183]) ).
fof(f566,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f564]) ).
fof(f567,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f566,f555]) ).
fof(f569,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f566,f36]) ).
fof(f573,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f371,f171]) ).
fof(f591,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f592,f403]) ).
fof(f592,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f567,f71]) ).
fof(f601,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f567,f181]) ).
fof(f605,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f610,f567]) ).
fof(f607,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f610,f125]) ).
fof(f609,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f610,f395]) ).
fof(f610,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f566,f601]) ).
fof(f616,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f610,f368]) ).
fof(f617,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = multiply(sk_c2,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f610,f616]) ).
fof(f618,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f605,f617]) ).
fof(f619,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f618,f609]) ).
fof(f620,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f621,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f591,f393,f106,f97,f70,f401]) ).
fof(f623,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f573,f401,f106,f97,f169]) ).
fof(f629,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f592,f143]) ).
fof(f632,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f618,f592]) ).
fof(f633,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f610,f569]) ).
fof(f676,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f618,f629]) ).
fof(f677,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f618,f676]) ).
fof(f678,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f618,f677]) ).
fof(f679,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f678,f633]) ).
fof(f686,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f607,f679]) ).
fof(f687,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f607,f686]) ).
fof(f688,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f687]) ).
fof(f689,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f698,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f465,f463]) ).
fof(f701,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f698,f86]) ).
fof(f702,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f483,f701]) ).
fof(f705,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f485,f35]) ).
fof(f720,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f486,f265]) ).
fof(f721,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f705,f720]) ).
fof(f722,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f486,f721]) ).
fof(f723,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f486,f722]) ).
fof(f724,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f723]) ).
fof(f725,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f724]) ).
fof(f747,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f484,f137]) ).
fof(f748,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f486,f747]) ).
fof(f749,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f484,f748]) ).
fof(f821,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(resolution,[status(thm)],[f749,f476]) ).
fof(f826,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f702,f821]) ).
fof(f827,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f702,f826]) ).
fof(f828,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f827]) ).
fof(f829,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f828]) ).
fof(f830,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(sk_c5) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f486,f174]) ).
fof(f831,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f702,f830]) ).
fof(f832,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f483,f831]) ).
fof(f833,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f832]) ).
fof(f834,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f833]) ).
fof(f838,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f610,f71]) ).
fof(f839,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f632,f838]) ).
fof(f840,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f618,f839]) ).
fof(f843,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f618,f75]) ).
fof(f844,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f632,f843]) ).
fof(f845,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f840,f844]) ).
fof(f846,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f610,f845]) ).
fof(f847,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f846]) ).
fof(f848,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f847]) ).
fof(f849,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,f150,f156,f176,f177,f263,f388,f392,f548,f620,f621,f623,f689,f725,f829,f834,f848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP316-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:09:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.050865 seconds
% 0.14/0.43 % CPU time: 0.197385 seconds
% 0.14/0.43 % Total memory used: 48.075 MB
% 0.14/0.43 % Net memory used: 47.903 MB
%------------------------------------------------------------------------------