%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP343-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:33:28 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 73
% Syntax : Number of formulae : 392 ( 19 unt; 36 def)
% Number of atoms : 1469 ( 432 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 2044 ( 967 ~;1041 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 37 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 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_c9) = sk_c7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
! [X3,X4,X1,X2,X5,X6] :
( multiply(X5,sk_c9) != X6
| inverse(X6) != sk_c9
| inverse(X5) != X6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f39,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
multiply(sk_c8,sk_c9) = sk_c7,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f43,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f44,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f47,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f49,plain,
( multiply(sk_c6,sk_c9) = sk_c5
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f53,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f57,plain,
( multiply(sk_c6,sk_c9) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f60,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f62,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f63,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f64,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f65,plain,
( multiply(sk_c6,sk_c9) = sk_c5
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f66,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f67,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f68,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f70,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f71,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f72,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f73,plain,
( multiply(sk_c6,sk_c9) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f74,plain,
! [X5,X6] :
( multiply(X5,sk_c9) != X6
| inverse(X6) != sk_c9
| inverse(X5) != X6
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X4] :
( multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| ! [X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4,X5] :
( multiply(X4,sk_c9) != X5
| inverse(X5) != sk_c9
| inverse(X4) != X5
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f76,f79]) ).
fof(f83,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f76,f83]) ).
fof(f87,definition,
( sQ3_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ3_spl
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f89,plain,
( sQ3_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f76,f87]) ).
fof(f91,definition,
( sQ4_spl
<=> multiply(sk_c4,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ4_spl
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f76,f91]) ).
fof(f95,definition,
( sQ5_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f76,f95]) ).
fof(f99,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f76,f99]) ).
fof(f103,definition,
( sQ7_spl
<=> inverse(sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ7_spl
| inverse(sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f76,f103]) ).
fof(f107,definition,
( sQ8_spl
<=> multiply(sk_c6,sk_c9) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c9) = sk_c5 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f76,f107]) ).
fof(f111,definition,
( sQ9_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f111,f79]) ).
fof(f115,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f111,f83]) ).
fof(f116,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f111,f87]) ).
fof(f117,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f111,f91]) ).
fof(f118,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f111,f95]) ).
fof(f119,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f111,f99]) ).
fof(f120,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f111,f103]) ).
fof(f121,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f111,f107]) ).
fof(f122,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f58,f122,f79]) ).
fof(f126,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f122,f83]) ).
fof(f127,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f60,f122,f87]) ).
fof(f128,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f61,f122,f91]) ).
fof(f129,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f122,f95]) ).
fof(f130,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f122,f99]) ).
fof(f131,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f122,f103]) ).
fof(f132,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f122,f107]) ).
fof(f133,definition,
( sQ11_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f66,f133,f79]) ).
fof(f137,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f67,f133,f83]) ).
fof(f138,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f133,f87]) ).
fof(f139,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f133,f91]) ).
fof(f140,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f133,f95]) ).
fof(f141,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f133,f99]) ).
fof(f142,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f133,f103]) ).
fof(f143,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f133,f107]) ).
fof(f144,definition,
( sQ12_spl
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ12_spl
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
! [X0] :
( sQ13_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f148,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
! [X1] :
( sQ14_spl
<=> ( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f151,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
! [X2] :
( sQ15_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f154,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
! [X3] :
( sQ16_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f157,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
! [X4,X5] :
( sQ17_spl
<=> ( multiply(X4,sk_c9) != X5
| inverse(X5) != sk_c9
| inverse(X4) != X5 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f160,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X0,sk_c9) != X1
| inverse(X1) != sk_c9
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ17_spl
| sQ16_spl
| ~ sQ3_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f75,f144,f147,f150,f153,f87,f156,f159]) ).
fof(f163,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f160]) ).
fof(f169,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f134,f40]) ).
fof(f170,plain,
! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c9,X0)),
inference(paramodulation,[status(thm)],[f41,f40]) ).
fof(f173,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| multiply(sk_c3,sk_c9) != inverse(sk_c3)
| inverse(sk_c9) != sk_c9 ),
inference(paramodulation,[status(thm)],[f84,f163]) ).
fof(f174,plain,
( ~ sQ5_spl
| ~ sQ17_spl
| multiply(sk_c4,sk_c9) != inverse(sk_c4)
| inverse(sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f96,f163]) ).
fof(f175,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| multiply(sk_c6,sk_c9) != inverse(sk_c6)
| inverse(sk_c5) != sk_c9 ),
inference(paramodulation,[status(thm)],[f100,f163]) ).
fof(f178,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| multiply(sk_c2,sk_c9) != inverse(sk_c2)
| inverse(sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f123,f163]) ).
fof(f179,definition,
( sQ18_spl
<=> inverse(sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ18_spl
| inverse(sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ19_spl
<=> multiply(sk_c3,sk_c9) = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ19_spl
| multiply(sk_c3,sk_c9) != inverse(sk_c3) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f173,f179,f182,f159,f83]) ).
fof(f186,definition,
( sQ20_spl
<=> inverse(sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ20_spl
| inverse(sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ21_spl
<=> multiply(sk_c4,sk_c9) = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ21_spl
| multiply(sk_c4,sk_c9) != inverse(sk_c4) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ5_spl
| ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f174,f186,f189,f159,f95]) ).
fof(f193,definition,
( sQ22_spl
<=> multiply(sk_c6,sk_c9) = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ22_spl
| multiply(sk_c6,sk_c9) != inverse(sk_c6) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f175,f103,f193,f159,f99]) ).
fof(f205,definition,
( sQ25_spl
<=> multiply(sk_c2,sk_c9) = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ25_spl
| multiply(sk_c2,sk_c9) != inverse(sk_c2) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f178,f186,f205,f159,f122]) ).
fof(f209,plain,
( sQ25_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f123,f207]) ).
fof(f211,plain,
( sQ22_spl
| ~ sQ8_spl
| sk_c5 != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f108,f195]) ).
fof(f212,plain,
( sQ19_spl
| ~ sQ1_spl
| sk_c8 != inverse(sk_c3) ),
inference(forward_demodulation,[status(thm)],[f80,f184]) ).
fof(f214,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| sk_c9 != sk_c8
| multiply(sk_c1,sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f77,f157]) ).
fof(f216,definition,
( sQ26_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ26_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ26_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f214,f111,f216,f156,f76]) ).
fof(f223,definition,
( sQ28_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ28_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f227,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f225]) ).
fof(f228,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f231,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f123,f39]) ).
fof(f232,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f39,f40]) ).
fof(f233,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f38,f232]) ).
fof(f239,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| sk_c9 != sk_c9
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f77,f154]) ).
fof(f241,definition,
( sQ29_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ29_spl
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
( sQ30_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( sQ30_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f239,f241,f244,f153,f76]) ).
fof(f252,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f246]) ).
fof(f253,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f252]) ).
fof(f254,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c8 ),
inference(resolution,[status(thm)],[f151,f134]) ).
fof(f255,plain,
( ~ sQ14_spl
| identity != sk_c8
| inverse(inverse(sk_c7)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f39,f151]) ).
fof(f259,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f123,f254]) ).
fof(f260,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f259]) ).
fof(f261,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f262,plain,
( ~ sQ6_spl
| sQ22_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f211]) ).
fof(f263,plain,
( ~ sQ6_spl
| sQ22_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f84,f212]) ).
fof(f267,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c8) != sk_c9
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f84,f148]) ).
fof(f269,definition,
( sQ32_spl
<=> multiply(sk_c3,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ32_spl
| multiply(sk_c3,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ32_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f267,f244,f269,f147,f83]) ).
fof(f273,plain,
( sQ12_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f41,f146]) ).
fof(f274,plain,
( sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f273]) ).
fof(f275,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f284,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f148,f112]) ).
fof(f291,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f77,f284]) ).
fof(f292,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f291]) ).
fof(f293,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f301,plain,
( sQ21_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f96,f191]) ).
fof(f307,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f112,f233]) ).
fof(f313,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f38,f233]) ).
fof(f315,plain,
( ~ sQ1_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f80,f233]) ).
fof(f316,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f92,f233]) ).
fof(f323,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f84,f315]) ).
fof(f324,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f96,f316]) ).
fof(f325,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f41,f324]) ).
fof(f328,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c9) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f325,f301]) ).
fof(f331,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c7) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f325,f271]) ).
fof(f334,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c9,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f325,f88]) ).
fof(f335,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f325,f96]) ).
fof(f339,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c9 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f325,f218]) ).
fof(f340,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f325,f80]) ).
fof(f341,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f325,f92]) ).
fof(f343,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f325,f41]) ).
fof(f345,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f335,f39]) ).
fof(f349,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f325,f157]) ).
fof(f350,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f325,f349]) ).
fof(f352,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c9 ),
inference(paramodulation,[status(thm)],[f38,f350]) ).
fof(f354,definition,
( sQ33_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ33_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f361,definition,
( sQ35_spl
<=> sk_c7 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ35_spl
| sk_c7 != sk_c9 ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,definition,
( sQ36_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( sQ36_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f367,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f352,f361,f364,f95,f91,f156]) ).
fof(f368,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f325,f154]) ).
fof(f373,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f325,f323]) ).
fof(f374,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f334,f373]) ).
fof(f375,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f339]) ).
fof(f376,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f265,f216,f83,f79,f182]) ).
fof(f380,plain,
( sQ33_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| identity != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f374,f356]) ).
fof(f389,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f374,f104]) ).
fof(f390,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f374,f84]) ).
fof(f395,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f340]) ).
fof(f398,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f363]) ).
fof(f399,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f398]) ).
fof(f400,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f405,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f341]) ).
fof(f415,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f313,f233]) ).
fof(f421,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f328]) ).
fof(f422,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f405,f421]) ).
fof(f423,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f422]) ).
fof(f424,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f430,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f395,f331]) ).
fof(f431,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f430]) ).
fof(f432,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f431]) ).
fof(f433,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f436,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f343]) ).
fof(f437,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f436,f233]) ).
fof(f439,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f39,f437]) ).
fof(f443,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f439,f39]) ).
fof(f444,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f439,f38]) ).
fof(f448,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f444,f345]) ).
fof(f449,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f462,f444]) ).
fof(f450,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f462,f439]) ).
fof(f454,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c3) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f462,f390]) ).
fof(f455,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f462,f389]) ).
fof(f458,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f462,f374]) ).
fof(f460,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f462,f335]) ).
fof(f461,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f462,f325]) ).
fof(f462,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f439,f448]) ).
fof(f466,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f458,f368]) ).
fof(f467,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f462,f466]) ).
fof(f468,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f458,f467]) ).
fof(f490,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ15_spl
| sk_c4 != sk_c4
| multiply(sk_c3,sk_c4) != sk_c4 ),
inference(paramodulation,[status(thm)],[f454,f468]) ).
fof(f491,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c4,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f454,f233]) ).
fof(f492,definition,
( sQ39_spl
<=> multiply(sk_c3,sk_c4) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ39_spl
| multiply(sk_c3,sk_c4) != sk_c4 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,definition,
( sQ40_spl
<=> sk_c4 = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ40_spl
| sk_c4 != sk_c4 ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f490,f492,f495,f153,f87,f95,f91,f79,f83]) ).
fof(f499,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f449,f491]) ).
fof(f508,plain,
( sQ40_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f497]) ).
fof(f509,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f450,f366]) ).
fof(f511,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f462,f510]) ).
fof(f512,plain,
( sQ33_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c4 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f450,f380]) ).
fof(f513,plain,
( sQ33_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f462,f512]) ).
fof(f514,plain,
( sQ33_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f513]) ).
fof(f515,plain,
( sQ33_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f527,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f462,f443]) ).
fof(f528,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(paramodulation,[status(thm)],[f455,f527]) ).
fof(f529,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c3) = sk_c4 ),
inference(paramodulation,[status(thm)],[f454,f527]) ).
fof(f533,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f449,f528]) ).
fof(f534,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f449,f529]) ).
fof(f542,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c8 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f533,f461]) ).
fof(f545,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f533,f462]) ).
fof(f546,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f533,f534]) ).
fof(f547,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(sk_c5) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f533,f460]) ).
fof(f548,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f533,f547]) ).
fof(f550,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f546,f499]) ).
fof(f561,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(sk_c5) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f533,f511]) ).
fof(f562,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c5 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f548,f561]) ).
fof(f563,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f533,f562]) ).
fof(f564,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f563]) ).
fof(f565,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f566,plain,
( sQ39_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c5,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f546,f494]) ).
fof(f567,plain,
( sQ39_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f550,f566]) ).
fof(f568,plain,
( sQ39_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c5 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f533,f567]) ).
fof(f569,plain,
( sQ39_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f533,f568]) ).
fof(f570,plain,
( sQ39_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f569]) ).
fof(f571,plain,
( sQ39_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f578,definition,
( sQ42_spl
<=> inverse(inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ42_spl
| inverse(inverse(sk_c7)) != sk_c8 ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f581,definition,
( sQ43_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( sQ43_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f584,plain,
( ~ sQ14_spl
| ~ sQ43_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f255,f578,f581,f150]) ).
fof(f597,plain,
( sQ42_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(inverse(sk_c5)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f545,f580]) ).
fof(f598,plain,
( sQ42_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(sk_c5) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f548,f597]) ).
fof(f599,plain,
( sQ42_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c5 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f548,f598]) ).
fof(f600,plain,
( sQ42_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f542,f599]) ).
fof(f601,plain,
( sQ42_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f600]) ).
fof(f602,plain,
( sQ42_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f629,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f323,f233]) ).
fof(f631,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f39,f629]) ).
fof(f632,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f631,f583]) ).
fof(f633,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f632]) ).
fof(f636,plain,
( ~ sQ11_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f134,f233]) ).
fof(f638,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f123,f636]) ).
fof(f680,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f39,f415]) ).
fof(f695,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f77,f307]) ).
fof(f696,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c9) = multiply(sk_c8,sk_c8) ),
inference(paramodulation,[status(thm)],[f695,f170]) ).
fof(f701,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f638,f696]) ).
fof(f703,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c8,sk_c9) = multiply(sk_c2,sk_c7) ),
inference(paramodulation,[status(thm)],[f701,f169]) ).
fof(f704,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f701,f233]) ).
fof(f706,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c2,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f41,f703]) ).
fof(f707,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f134,f706]) ).
fof(f710,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f39,f704]) ).
fof(f722,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(identity) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f710,f680]) ).
fof(f724,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c8,sk_c2) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f710,f231]) ).
fof(f726,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f710,f39]) ).
fof(f727,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f710,f38]) ).
fof(f728,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f710,f722]) ).
fof(f729,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f728,f181]) ).
fof(f730,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f732,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c9,sk_c9) ),
inference(backward_demodulation,[status(thm)],[f707,f695]) ).
fof(f738,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c9,sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f707,f89]) ).
fof(f742,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c9) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f707,f243]) ).
fof(f745,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c9) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f707,f209]) ).
fof(f749,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c7) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f707,f188]) ).
fof(f767,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c9,sk_c1) = sk_c9 ),
inference(paramodulation,[status(thm)],[f77,f726]) ).
fof(f770,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c1 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f727,f767]) ).
fof(f772,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f727,f738]) ).
fof(f773,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f772]) ).
fof(f774,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f773]) ).
fof(f784,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c9 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f707,f218]) ).
fof(f787,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c7) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f770,f749]) ).
fof(f788,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c9) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f770,f728]) ).
fof(f789,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f770,f727]) ).
fof(f797,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f770,f788]) ).
fof(f807,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c2) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f707,f724]) ).
fof(f808,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c2) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f770,f807]) ).
fof(f814,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c1,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f770,f732]) ).
fof(f815,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f789,f814]) ).
fof(f816,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f770,f815]) ).
fof(f819,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c1 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f770,f784]) ).
fof(f823,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c2) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f816,f808]) ).
fof(f825,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f816,f787]) ).
fof(f831,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f789,f823]) ).
fof(f833,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f797,f825]) ).
fof(f834,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f833]) ).
fof(f835,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f834]) ).
fof(f854,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f816,f819]) ).
fof(f855,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f854]) ).
fof(f856,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f855]) ).
fof(f862,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f831,f816]) ).
fof(f864,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f831,f789]) ).
fof(f867,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c2 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f831,f770]) ).
fof(f903,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f831,f742]) ).
fof(f904,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c9 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f864,f903]) ).
fof(f905,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f867,f904]) ).
fof(f906,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f862,f905]) ).
fof(f907,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f906]) ).
fof(f908,plain,
( sQ29_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f907]) ).
fof(f912,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f864,f745]) ).
fof(f913,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f867,f912]) ).
fof(f914,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f862,f913]) ).
fof(f915,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f914]) ).
fof(f916,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f915]) ).
fof(f917,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f86,f90,f94,f98,f102,f106,f110,f114,f115,f116,f117,f118,f119,f120,f121,f125,f126,f127,f128,f129,f130,f131,f132,f136,f137,f138,f139,f140,f141,f142,f143,f162,f185,f192,f196,f208,f219,f228,f247,f253,f261,f263,f272,f275,f293,f367,f376,f377,f400,f424,f433,f498,f509,f515,f565,f571,f584,f602,f633,f730,f774,f835,f856,f908,f916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP343-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:07:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.061378 seconds
% 0.14/0.43 % CPU time: 0.190978 seconds
% 0.14/0.43 % Total memory used: 103.995 MB
% 0.14/0.43 % Net memory used: 103.803 MB
%------------------------------------------------------------------------------