%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP356-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:33:30 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 51
% Syntax : Number of formulae : 276 ( 10 unt; 17 def)
% Number of atoms : 1131 ( 342 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1653 ( 798 ~; 838 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c8
| 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,X1,X2,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c8
| 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,
! [X5] :
( inverse(X5) != sk_c8
| ! [X2] :
( multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c8,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
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c8) = 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
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c8,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f70,f89]) ).
fof(f93,definition,
( sQ6_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f70,f93]) ).
fof(f97,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
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_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = 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_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
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_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] :
( sQ12_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3,X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f142]) ).
fof(f146,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f164,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f146]) ).
fof(f165,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f146]) ).
fof(f167,definition,
( sQ15_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f164,f167,f81,f142,f77]) ).
fof(f171,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f165,f85,f93,f142,f89]) ).
fof(f176,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f125]) ).
fof(f179,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f116,f176]) ).
fof(f190,definition,
( sQ20_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ20_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f194,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f192]) ).
fof(f195,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f200,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f201,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f200]) ).
fof(f216,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f98,f201]) ).
fof(f219,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f107,f216]) ).
fof(f228,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f219,f201]) ).
fof(f230,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f228]) ).
fof(f231,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c8) != sk_c6 ),
inference(resolution,[status(thm)],[f137,f125]) ).
fof(f234,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f116,f231]) ).
fof(f235,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f234]) ).
fof(f236,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f237,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f107]) ).
fof(f239,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f237]) ).
fof(f240,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f239]) ).
fof(f241,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f247,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f82,f36]) ).
fof(f253,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f94,f36]) ).
fof(f254,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f201]) ).
fof(f256,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f82,f254]) ).
fof(f257,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f74,f256]) ).
fof(f258,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f257,f74]) ).
fof(f266,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f90,f201]) ).
fof(f268,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f94,f266]) ).
fof(f269,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f268]) ).
fof(f275,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f269,f86]) ).
fof(f287,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f269,f258]) ).
fof(f288,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f287,f201]) ).
fof(f290,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f288]) ).
fof(f294,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f290,f35]) ).
fof(f298,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f294,f247]) ).
fof(f299,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f308,f294]) ).
fof(f300,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f308,f290]) ).
fof(f303,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f308,f269]) ).
fof(f305,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f308,f257]) ).
fof(f306,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f308,f94]) ).
fof(f307,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f308,f82]) ).
fof(f308,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f290,f298]) ).
fof(f313,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c3,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f306,f201]) ).
fof(f314,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f299,f313]) ).
fof(f328,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c3) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f303,f134]) ).
fof(f329,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f308,f328]) ).
fof(f330,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f303,f329]) ).
fof(f331,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c3 ),
inference(resolution,[status(thm)],[f330,f299]) ).
fof(f334,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f307,f331]) ).
fof(f335,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f334]) ).
fof(f336,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f337,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c3) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f308,f140]) ).
fof(f338,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f303,f337]) ).
fof(f339,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f308,f338]) ).
fof(f340,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c5) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f308,f275]) ).
fof(f341,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f299,f340]) ).
fof(f343,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f350,f306]) ).
fof(f345,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f350,f299]) ).
fof(f346,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f350,f305]) ).
fof(f347,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f350,f303]) ).
fof(f348,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f350,f300]) ).
fof(f349,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c5 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f350,f308]) ).
fof(f350,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f308,f341]) ).
fof(f367,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c4) = identity ),
inference(forward_demodulation,[status(thm)],[f349,f253]) ).
fof(f368,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f345,f367]) ).
fof(f371,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f379,f343]) ).
fof(f375,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f379,f348]) ).
fof(f376,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f379,f347]) ).
fof(f377,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f379,f346]) ).
fof(f378,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f379,f350]) ).
fof(f379,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f348,f368]) ).
fof(f399,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c4) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f378,f339]) ).
fof(f400,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f378,f399]) ).
fof(f401,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f378,f400]) ).
fof(f402,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f401,f371]) ).
fof(f404,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f314,f402]) ).
fof(f405,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f404]) ).
fof(f406,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f464,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f230,f35]) ).
fof(f473,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f230,f36]) ).
fof(f474,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c2) = sk_c8 ),
inference(paramodulation,[status(thm)],[f125,f473]) ).
fof(f478,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f464,f474]) ).
fof(f483,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f116,f201]) ).
fof(f485,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f125,f483]) ).
fof(f486,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f464,f485]) ).
fof(f489,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c6) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f478,f71]) ).
fof(f490,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f478,f473]) ).
fof(f495,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f478,f464]) ).
fof(f496,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f478,f125]) ).
fof(f498,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f478,f486]) ).
fof(f499,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f478,f75]) ).
fof(f500,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f498,f499]) ).
fof(f501,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f495,f500]) ).
fof(f519,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f478,f98]) ).
fof(f530,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f498,f489]) ).
fof(f532,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,X0) = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f530,f37]) ).
fof(f533,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f495,f532]) ).
fof(f534,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f495,f533]) ).
fof(f539,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c1) = sk_c2 ),
inference(paramodulation,[status(thm)],[f107,f490]) ).
fof(f542,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f534,f539]) ).
fof(f545,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f542,f519]) ).
fof(f546,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f542,f107]) ).
fof(f548,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f495,f545]) ).
fof(f549,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f501]) ).
fof(f550,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f496,f546]) ).
fof(f554,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f498,f179]) ).
fof(f575,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f551,f554]) ).
fof(f576,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f575]) ).
fof(f577,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f578,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(sk_c2,multiply(X0,sk_c8)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f478,f146]) ).
fof(f579,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f495,f578]) ).
fof(f580,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f478,f579]) ).
fof(f581,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f551,f580]) ).
fof(f582,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f478,f581]) ).
fof(f606,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f582,f496]) ).
fof(f608,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f495,f606]) ).
fof(f609,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f608]) ).
fof(f610,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f613,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f614,f257]) ).
fof(f614,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f257,f377]) ).
fof(f616,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f378,f82]) ).
fof(f617,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f614,f616]) ).
fof(f631,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f375,f35]) ).
fof(f666,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c4) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f614,f137]) ).
fof(f667,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f613,f666]) ).
fof(f668,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f614,f667]) ).
fof(f669,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f668,f617]) ).
fof(f671,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f631,f669]) ).
fof(f672,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f671]) ).
fof(f673,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f672]) ).
fof(f675,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f376,f72]) ).
fof(f676,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f631,f675]) ).
fof(f677,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f613,f676]) ).
fof(f678,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f614,f677]) ).
fof(f679,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f678]) ).
fof(f680,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f681,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,f170,f171,f195,f236,f241,f336,f406,f550,f577,f610,f673,f680]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP356-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n014.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:10:20 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.052005 seconds
% 0.13/0.42 % CPU time: 0.096969 seconds
% 0.13/0.42 % Total memory used: 20.157 MB
% 0.13/0.42 % Net memory used: 20.107 MB
%------------------------------------------------------------------------------