%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP270-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:33:16 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 50
% Syntax : Number of formulae : 339 ( 10 unt; 21 def)
% Number of atoms : 1372 ( 363 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1990 ( 957 ~;1012 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 85 ( 85 !; 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_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X3,X4,X1,X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f60,f63]) ).
fof(f67,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f60,f67]) ).
fof(f71,definition,
( sQ3_spl
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f60,f71]) ).
fof(f75,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f60,f75]) ).
fof(f79,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( sQ5_spl
| multiply(sk_c4,sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f60,f79]) ).
fof(f83,definition,
( sQ6_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f83,f63]) ).
fof(f87,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f83,f67]) ).
fof(f88,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f40,f83,f71]) ).
fof(f89,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f41,f83,f75]) ).
fof(f90,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f42,f83,f79]) ).
fof(f91,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f93,plain,
( sQ7_spl
| multiply(sk_c7,sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f91,f63]) ).
fof(f95,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f91,f67]) ).
fof(f96,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f91,f71]) ).
fof(f97,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f91,f75]) ).
fof(f98,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f91,f79]) ).
fof(f99,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f101,plain,
( sQ8_spl
| multiply(sk_c2,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f99,f63]) ).
fof(f103,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f99,f67]) ).
fof(f104,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f99,f71]) ).
fof(f105,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f99,f75]) ).
fof(f106,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f99,f79]) ).
fof(f107,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f107,f63]) ).
fof(f111,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f107,f67]) ).
fof(f112,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f107,f71]) ).
fof(f113,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f107,f75]) ).
fof(f114,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f107,f79]) ).
fof(f115,definition,
! [X0] :
( sQ10_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
! [X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f125,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ13_spl
| sQ12_spl
| ~ sQ1_spl
| sQ11_spl
| ~ sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f115,f91,f118,f63,f121,f124]) ).
fof(f132,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f80,f32]) ).
fof(f134,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f84,f31]) ).
fof(f135,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f68,f31]) ).
fof(f136,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f76,f31]) ).
fof(f137,plain,
( ~ sQ9_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f138,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f139,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f138]) ).
fof(f140,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f72,f32]) ).
fof(f141,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f61,f32]) ).
fof(f142,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f125,f80]) ).
fof(f144,plain,
( ~ sQ13_spl
| sk_c5 != sk_c6
| inverse(identity) != sk_c6 ),
inference(paramodulation,[status(thm)],[f30,f125]) ).
fof(f147,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f76,f142]) ).
fof(f148,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f147]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f151,plain,
! [X0] :
( ~ sQ6_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f134,f32]) ).
fof(f152,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f151]) ).
fof(f153,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f135,f32]) ).
fof(f154,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f153]) ).
fof(f155,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f122,f72]) ).
fof(f158,plain,
( ~ sQ12_spl
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f30,f122]) ).
fof(f160,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f155]) ).
fof(f161,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f160]) ).
fof(f162,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f119,f100]) ).
fof(f169,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f108,f163]) ).
fof(f170,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f169]) ).
fof(f171,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f172,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f116,f61]) ).
fof(f175,plain,
( ~ sQ10_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f30,f116]) ).
fof(f177,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f84,f172]) ).
fof(f178,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f177]) ).
fof(f179,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f180,definition,
( sQ14_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( sQ14_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f191,definition,
( sQ17_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ17_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,definition,
( sQ18_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ18_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ10_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f175,f191,f194,f115]) ).
fof(f198,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f182]) ).
fof(f199,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f202,plain,
! [X0] :
( ~ sQ9_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f137,f32]) ).
fof(f203,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f202]) ).
fof(f204,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| inverse(sk_c6) != sk_c7
| sk_c5 != sk_c6 ),
inference(paramodulation,[status(thm)],[f64,f116]) ).
fof(f205,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f64,f32]) ).
fof(f206,definition,
( sQ19_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ19_spl
| sk_c5 = sk_c6 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( sQ19_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,definition,
( sQ20_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ20_spl
| inverse(sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f204,f206,f209,f115,f63]) ).
fof(f216,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f140]) ).
fof(f223,plain,
! [X0] :
( ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f136,f32]) ).
fof(f224,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f223]) ).
fof(f225,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c3) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f135,f205]) ).
fof(f226,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c2) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f137,f205]) ).
fof(f231,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f140,f154]) ).
fof(f232,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f154]) ).
fof(f233,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,multiply(sk_c3,X0)) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f154,f205]) ).
fof(f242,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c5,multiply(sk_c2,X0)) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f203,f205]) ).
fof(f245,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f132,f224]) ).
fof(f246,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f80,f224]) ).
fof(f247,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c7,multiply(sk_c4,X0)) = multiply(sk_c3,X0) ),
inference(paramodulation,[status(thm)],[f224,f140]) ).
fof(f259,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c3) = multiply(sk_c4,multiply(sk_c6,identity)) ),
inference(paramodulation,[status(thm)],[f225,f132]) ).
fof(f263,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c2) = multiply(sk_c4,multiply(sk_c6,identity)) ),
inference(paramodulation,[status(thm)],[f226,f132]) ).
fof(f265,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c2) = multiply(sk_c6,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f259,f263]) ).
fof(f273,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(multiply(sk_c6,sk_c3),X0) = multiply(sk_c6,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f265,f32]) ).
fof(f276,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c6,multiply(sk_c3,X0)) = multiply(sk_c6,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f32,f273]) ).
fof(f277,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c7,sk_c6) ),
inference(paramodulation,[status(thm)],[f232,f231]) ).
fof(f279,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,multiply(sk_c2,X0)) = multiply(sk_c7,X0) ),
inference(paramodulation,[status(thm)],[f203,f231]) ).
fof(f280,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,multiply(sk_c3,X0)) = multiply(sk_c7,X0) ),
inference(paramodulation,[status(thm)],[f154,f231]) ).
fof(f286,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f64,f277]) ).
fof(f290,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c6,multiply(sk_c3,X0)) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f276,f279]) ).
fof(f304,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f72,f233]) ).
fof(f309,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f246,f304]) ).
fof(f320,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c5,multiply(sk_c4,X0)) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f224,f245]) ).
fof(f323,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f245]) ).
fof(f336,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c6) = multiply(sk_c3,sk_c5) ),
inference(paramodulation,[status(thm)],[f80,f247]) ).
fof(f338,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,multiply(sk_c4,X0)) = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f247,f205]) ).
fof(f343,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f320,f338]) ).
fof(f348,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c4,X0)) ),
inference(backward_demodulation,[status(thm)],[f366,f224]) ).
fof(f349,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ2_spl
| multiply(sk_c5,X0) = multiply(sk_c7,multiply(sk_c7,X0)) ),
inference(backward_demodulation,[status(thm)],[f366,f205]) ).
fof(f352,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c5,multiply(sk_c2,X0)) = multiply(sk_c7,X0) ),
inference(backward_demodulation,[status(thm)],[f366,f242]) ).
fof(f366,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f290,f343]) ).
fof(f372,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f377,f72]) ).
fof(f377,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ2_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f247,f348]) ).
fof(f378,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ2_spl
| multiply(sk_c5,X0) = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f231,f349]) ).
fof(f379,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f381,f309]) ).
fof(f381,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ2_spl
| multiply(sk_c5,X0) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f366,f378]) ).
fof(f385,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c7,multiply(sk_c2,X0)) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f381,f352]) ).
fof(f387,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f395,f203]) ).
fof(f388,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f395,f135]) ).
fof(f390,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f395,f137]) ).
fof(f395,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f203,f385]) ).
fof(f427,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f232,f379]) ).
fof(f428,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f429,f101]) ).
fof(f429,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f372,f427]) ).
fof(f438,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f440,f108]) ).
fof(f440,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f388,f390]) ).
fof(f448,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f387,f428]) ).
fof(f449,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f448]) ).
fof(f450,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f454,definition,
( sQ22_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ22_spl
| identity = sk_c7 ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f456,plain,
( sQ22_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f458,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f158,f194,f191,f121]) ).
fof(f469,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f139]) ).
fof(f470,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f61,f139]) ).
fof(f471,plain,
( ~ sQ7_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f92,f139]) ).
fof(f472,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f100,f139]) ).
fof(f478,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f84,f470]) ).
fof(f479,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f108,f472]) ).
fof(f480,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f92,f479]) ).
fof(f481,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f193]) ).
fof(f482,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f486,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c4,sk_c5) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f480,f81]) ).
fof(f491,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c7) ),
inference(backward_demodulation,[status(thm)],[f480,f471]) ).
fof(f492,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f480,f478]) ).
fof(f502,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f480,f136]) ).
fof(f504,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c7,X0)) ),
inference(backward_demodulation,[status(thm)],[f480,f141]) ).
fof(f511,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f519,f456]) ).
fof(f513,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f519,f30]) ).
fof(f518,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c5) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f519,f196]) ).
fof(f519,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f491]) ).
fof(f566,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f519,f502]) ).
fof(f567,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f480,f65]) ).
fof(f568,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f492,f567]) ).
fof(f571,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f100,f139]) ).
fof(f573,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f108,f571]) ).
fof(f591,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c7,multiply(sk_c2,X0)) = multiply(sk_c1,X0) ),
inference(paramodulation,[status(thm)],[f203,f504]) ).
fof(f597,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| X0 = multiply(sk_c7,X0) ),
inference(backward_demodulation,[status(thm)],[f598,f152]) ).
fof(f598,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f203,f591]) ).
fof(f601,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f597,f203]) ).
fof(f602,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c4 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f597,f566]) ).
fof(f604,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f597,f573]) ).
fof(f608,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f601,f100]) ).
fof(f611,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c5) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f602,f486]) ).
fof(f612,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f511]) ).
fof(f613,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f612]) ).
fof(f615,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f608,f518]) ).
fof(f620,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f513,f611]) ).
fof(f621,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f608,f620]) ).
fof(f622,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f621]) ).
fof(f623,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f622]) ).
fof(f624,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c2) = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f608,f226]) ).
fof(f625,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f597,f624]) ).
fof(f626,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f480,f625]) ).
fof(f627,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f597,f626]) ).
fof(f628,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f630,f108]) ).
fof(f630,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f455,f627]) ).
fof(f648,definition,
( sQ24_spl
<=> inverse(identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( sQ24_spl
| inverse(identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f651,plain,
( ~ sQ13_spl
| ~ sQ19_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f144,f648,f206,f124]) ).
fof(f657,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f615]) ).
fof(f658,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( sQ24_spl
| ~ sQ22_spl
| inverse(sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f455,f650]) ).
fof(f661,plain,
( sQ24_spl
| ~ sQ22_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f480,f660]) ).
fof(f664,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f608,f208]) ).
fof(f665,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f480,f664]) ).
fof(f666,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f665]) ).
fof(f667,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f666]) ).
fof(f668,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f661]) ).
fof(f669,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f668]) ).
fof(f672,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f608,f568]) ).
fof(f673,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f672]) ).
fof(f674,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f673]) ).
fof(f677,plain,
( ~ sQ19_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f480,f207]) ).
fof(f685,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ19_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f677,f518]) ).
fof(f687,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ19_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f677,f519]) ).
fof(f712,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f687,f388]) ).
fof(f713,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ19_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f712,f438]) ).
fof(f714,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f713,f685]) ).
fof(f715,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f723,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c5) = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f323,f304]) ).
fof(f724,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f726,f323]) ).
fof(f726,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f246,f723]) ).
fof(f739,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f336,f216]) ).
fof(f740,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f286,f739]) ).
fof(f741,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f469]) ).
fof(f750,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,multiply(sk_c4,X0)) = multiply(sk_c6,X0) ),
inference(backward_demodulation,[status(thm)],[f755,f320]) ).
fof(f755,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f740,f741]) ).
fof(f768,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f343,f280]) ).
fof(f775,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(forward_demodulation,[status(thm)],[f768,f136]) ).
fof(f776,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| X0 = multiply(sk_c7,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f768,f224]) ).
fof(f779,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c7,multiply(sk_c4,X0)) = X0 ),
inference(backward_demodulation,[status(thm)],[f781,f247]) ).
fof(f781,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f247,f776]) ).
fof(f801,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f755,f93]) ).
fof(f802,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f286,f801]) ).
fof(f803,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f755,f802]) ).
fof(f804,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f803]) ).
fof(f805,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f804]) ).
fof(f816,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f755,f724]) ).
fof(f817,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f768,f816]) ).
fof(f818,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f755,f817]) ).
fof(f842,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c7,multiply(sk_c4,X0)) = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f768,f750]) ).
fof(f843,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c7,multiply(sk_c4,X0)) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f768,f842]) ).
fof(f860,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f865,f818]) ).
fof(f861,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f865,f775]) ).
fof(f862,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f865,f135]) ).
fof(f865,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f843,f779]) ).
fof(f867,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c6) ),
inference(forward_demodulation,[status(thm)],[f755,f471]) ).
fof(f873,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f755,f208]) ).
fof(f874,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f873]) ).
fof(f875,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f874]) ).
fof(f878,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(backward_demodulation,[status(thm)],[f860,f867]) ).
fof(f885,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f861,f862]) ).
fof(f888,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f755,f119]) ).
fof(f889,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f860,f888]) ).
fof(f900,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(forward_demodulation,[status(thm)],[f860,f878]) ).
fof(f901,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f900]) ).
fof(f902,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f861,f901]) ).
fof(f905,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f906,f68]) ).
fof(f906,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f885,f902]) ).
fof(f924,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl
| inverse(sk_c7) != sk_c7 ),
inference(resolution,[status(thm)],[f889,f865]) ).
fof(f927,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f905,f924]) ).
fof(f928,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f927]) ).
fof(f929,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f928]) ).
fof(f930,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f860,f211]) ).
fof(f931,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f905,f930]) ).
fof(f932,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f931]) ).
fof(f933,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f932]) ).
fof(f934,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f78,f82,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f102,f103,f104,f105,f106,f110,f111,f112,f113,f114,f127,f149,f162,f171,f179,f197,f199,f212,f450,f458,f482,f613,f623,f651,f658,f667,f669,f674,f715,f805,f875,f929,f933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP270-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:13:12 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.059199 seconds
% 0.13/0.42 % CPU time: 0.192630 seconds
% 0.13/0.42 % Total memory used: 104.015 MB
% 0.13/0.42 % Net memory used: 103.716 MB
%------------------------------------------------------------------------------