%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP387-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:35 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 53
% Syntax : Number of formulae : 290 ( 11 unt; 21 def)
% Number of atoms : 1105 ( 331 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1555 ( 740 ~; 794 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 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_c2,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X2,X1,X3,X4] :
( multiply(X4,sk_c7) != sk_c5
| inverse(X4) != sk_c5
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c2) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f52,plain,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c2) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X4] :
( multiply(X4,sk_c7) != sk_c5
| inverse(X4) != sk_c5
| ! [X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| ! [X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c7) != sk_c5
| inverse(X3) != sk_c5
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c2,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c2) = 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_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c6) = sk_c5 ),
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_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c5 ),
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_c4,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c4,sk_c7) = sk_c5 ),
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_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ7_spl
| multiply(sk_c6,sk_c5) != 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
<=> multiply(sk_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f108,plain,
( sQ8_spl
| multiply(sk_c7,sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f106]) ).
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_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| inverse(sk_c1) = 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_c1,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| multiply(sk_c1,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_c6) != sk_c7
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3] :
( sQ14_spl
<=> ( multiply(X3,sk_c7) != sk_c5
| inverse(X3) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c7) != sk_c5
| inverse(X0) != sk_c5 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f97,f106,f133,f136,f139,f142]) ).
fof(f146,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c5 ),
inference(resolution,[status(thm)],[f143,f94]) ).
fof(f149,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f90,f146]) ).
fof(f150,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f149]) ).
fof(f151,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f155,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f86,f152]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f155]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f74]) ).
fof(f161,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f158]) ).
fof(f162,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f161]) ).
fof(f163,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f173,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f125]) ).
fof(f175,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sk_c5 != sk_c7
| inverse(sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f134]) ).
fof(f177,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f116,f173]) ).
fof(f178,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f177]) ).
fof(f179,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f90,f36]) ).
fof(f183,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f184,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f185,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f184]) ).
fof(f204,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f74,f185]) ).
fof(f205,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c5) ),
inference(paramodulation,[status(thm)],[f82,f185]) ).
fof(f206,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f94,f185]) ).
fof(f209,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f78,f204]) ).
fof(f210,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f86,f205]) ).
fof(f211,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f98,f210]) ).
fof(f212,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f90,f206]) ).
fof(f214,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f211,f183]) ).
fof(f215,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f211,f78]) ).
fof(f216,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f211,f72]) ).
fof(f218,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f211,f98]) ).
fof(f225,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f218,f185]) ).
fof(f227,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f225]) ).
fof(f232,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f227,f181]) ).
fof(f234,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f227,f35]) ).
fof(f241,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c6 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f211,f212]) ).
fof(f246,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c6) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f251,f216]) ).
fof(f247,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f251,f215]) ).
fof(f251,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f234,f241]) ).
fof(f256,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f251,f246]) ).
fof(f282,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f251,f214]) ).
fof(f283,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f234,f282]) ).
fof(f285,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f286,f247]) ).
fof(f286,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f227,f283]) ).
fof(f287,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f256]) ).
fof(f288,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f315,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f71,f36]) ).
fof(f325,plain,
( ~ sQ8_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f107,f185]) ).
fof(f327,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f71,f325]) ).
fof(f336,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f210,f185]) ).
fof(f338,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f336]) ).
fof(f339,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f210,f99]) ).
fof(f360,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f338,f36]) ).
fof(f364,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f338,f35]) ).
fof(f365,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f364,f212]) ).
fof(f370,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c6 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f365,f339]) ).
fof(f374,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f365,f107]) ).
fof(f375,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f365,f209]) ).
fof(f377,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f365,f78]) ).
fof(f380,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f364,f374]) ).
fof(f381,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f365,f375]) ).
fof(f382,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f364,f381]) ).
fof(f383,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f380,f370]) ).
fof(f384,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f390,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f364,f232]) ).
fof(f392,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f365,f108]) ).
fof(f393,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f364,f392]) ).
fof(f395,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(paramodulation,[status(thm)],[f90,f360]) ).
fof(f398,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f364,f395]) ).
fof(f402,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f382,f86]) ).
fof(f410,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c6 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f390,f251]) ).
fof(f412,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c2 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f390,f286]) ).
fof(f413,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f390,f393]) ).
fof(f414,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f410,f413]) ).
fof(f415,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f414]) ).
fof(f416,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f417,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f398,f393]) ).
fof(f418,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f398,f382]) ).
fof(f419,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f417]) ).
fof(f420,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f442,definition,
( sQ15_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ15_spl
| inverse(sk_c3) != sk_c7 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
( sQ16_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ16_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f175,f442,f445,f133,f81]) ).
fof(f453,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f398,f365]) ).
fof(f464,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f412,f377]) ).
fof(f465,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f398,f464]) ).
fof(f469,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c3) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f398,f402]) ).
fof(f472,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f398,f364]) ).
fof(f488,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f398,f360]) ).
fof(f489,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c3) = sk_c4 ),
inference(paramodulation,[status(thm)],[f469,f488]) ).
fof(f493,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f472,f489]) ).
fof(f505,plain,
( sQ15_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f493,f444]) ).
fof(f506,plain,
( sQ15_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c4 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f465,f505]) ).
fof(f507,plain,
( sQ15_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f453,f506]) ).
fof(f508,plain,
( sQ15_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f507]) ).
fof(f509,plain,
( sQ15_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f398,f447]) ).
fof(f511,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f453,f510]) ).
fof(f512,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f511]) ).
fof(f513,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f514,definition,
( sQ18_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ18_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f518,plain,
( sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f516]) ).
fof(f519,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f531,plain,
( ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f125,f185]) ).
fof(f533,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f116,f531]) ).
fof(f555,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f533,f185]) ).
fof(f557,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f71,f555]) ).
fof(f558,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f327,f557]) ).
fof(f561,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f558,f98]) ).
fof(f562,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f558,f107]) ).
fof(f563,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f558,f315]) ).
fof(f567,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f558,f71]) ).
fof(f568,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f558,f116]) ).
fof(f574,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c6
| sk_c6 != sk_c5 ),
inference(paramodulation,[status(thm)],[f35,f140]) ).
fof(f578,definition,
( sQ20_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ20_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f585,definition,
( sQ22_spl
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f587,plain,
( sQ22_spl
| sk_c6 != sk_c5 ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f588,definition,
( sQ23_spl
<=> inverse(identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ23_spl
| inverse(identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( ~ sQ13_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f574,f585,f588,f139]) ).
fof(f603,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f580]) ).
fof(f604,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f605,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f558,f137]) ).
fof(f606,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f558,f605]) ).
fof(f623,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f561,f563]) ).
fof(f627,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c5) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f623,f590]) ).
fof(f628,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f623,f36]) ).
fof(f629,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f623,f35]) ).
fof(f631,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f567,f627]) ).
fof(f632,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f631]) ).
fof(f633,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f632]) ).
fof(f636,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c5 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f629,f562]) ).
fof(f660,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f558,f143]) ).
fof(f669,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f636,f587]) ).
fof(f670,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f669]) ).
fof(f671,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f670]) ).
fof(f674,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c5,sk_c1) = sk_c5 ),
inference(paramodulation,[status(thm)],[f568,f628]) ).
fof(f677,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f629,f674]) ).
fof(f681,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f677,f628]) ).
fof(f682,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c1 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f677,f636]) ).
fof(f683,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f677,f629]) ).
fof(f685,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f677,f568]) ).
fof(f711,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c1) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f677,f606]) ).
fof(f712,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f682,f711]) ).
fof(f713,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f677,f712]) ).
fof(f714,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c1 ),
inference(resolution,[status(thm)],[f713,f683]) ).
fof(f717,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f685,f714]) ).
fof(f718,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f717]) ).
fof(f719,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f718]) ).
fof(f720,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f677,f660]) ).
fof(f721,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(X0,sk_c1) != sk_c5
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f677,f720]) ).
fof(f722,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(X0,sk_c1) != sk_c1
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f677,f721]) ).
fof(f737,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ14_spl
| inverse(inverse(sk_c1)) != sk_c1 ),
inference(resolution,[status(thm)],[f722,f681]) ).
fof(f742,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f685,f737]) ).
fof(f743,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ14_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f685,f742]) ).
fof(f744,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f743]) ).
fof(f745,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f746,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f100,f101,f102,f103,f104,f105,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f145,f151,f157,f163,f179,f288,f384,f416,f420,f448,f509,f513,f519,f591,f604,f633,f671,f719,f745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP387-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:15:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.054762 seconds
% 0.11/0.44 % CPU time: 0.220423 seconds
% 0.11/0.44 % Total memory used: 99.540 MB
% 0.11/0.44 % Net memory used: 99.280 MB
%------------------------------------------------------------------------------