%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP383-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:35 PM UTC 2026
% Result : Unsatisfiable 0.13s 10.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 60
% Syntax : Number of formulae : 277 ( 13 unt; 22 def)
% Number of atoms : 904 ( 330 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1154 ( 527 ~; 605 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 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_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f41,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f48,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f51,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f53,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f71,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f75,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f76,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f77,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f78,plain,
! [X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| ! [X5] :
( multiply(X5,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| ! [X3] :
( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f82,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ1_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f80,f83]) ).
fof(f87,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f80,f87]) ).
fof(f91,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f80,f91]) ).
fof(f95,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f80,f95]) ).
fof(f99,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f80,f99]) ).
fof(f103,definition,
( sQ6_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f105,plain,
( sQ6_spl
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f48,f103,f83]) ).
fof(f107,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f49,f103,f87]) ).
fof(f108,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f50,f103,f91]) ).
fof(f109,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f51,f103,f95]) ).
fof(f110,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f52,f103,f99]) ).
fof(f111,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f53,f111,f83]) ).
fof(f115,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f111,f87]) ).
fof(f116,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f111,f91]) ).
fof(f117,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f56,f111,f95]) ).
fof(f118,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f57,f111,f99]) ).
fof(f119,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f119,f83]) ).
fof(f123,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f119,f87]) ).
fof(f124,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f119,f91]) ).
fof(f125,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f119,f95]) ).
fof(f126,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f119,f99]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f127,f83]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f127,f87]) ).
fof(f132,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f91]) ).
fof(f133,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f127,f95]) ).
fof(f134,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f127,f99]) ).
fof(f135,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f135,f83]) ).
fof(f139,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f135,f87]) ).
fof(f140,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f135,f91]) ).
fof(f141,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f135,f95]) ).
fof(f142,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f135,f99]) ).
fof(f143,definition,
( sQ11_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f143,f87]) ).
fof(f148,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f143,f91]) ).
fof(f149,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f143,f95]) ).
fof(f150,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f143,f99]) ).
fof(f151,definition,
! [X0] :
( sQ12_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
! [X1,X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != X1
| multiply(X0,X1) != sk_c7 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X4] :
( sQ14_spl
<=> ( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ14_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f80,f103,f151,f154,f83,f157]) ).
fof(f161,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f158,f100]) ).
fof(f163,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f96,f161]) ).
fof(f164,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f163]) ).
fof(f165,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f166,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c8) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f155]) ).
fof(f179,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| multiply(sk_c7,sk_c8) != sk_c7
| multiply(sk_c8,inverse(sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f81,f166]) ).
fof(f180,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,inverse(sk_c1)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f112,f166]) ).
fof(f181,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c8) != sk_c7
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f136,f166]) ).
fof(f182,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f88,f166]) ).
fof(f183,definition,
( sQ15_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ15_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c7 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ16_spl
<=> multiply(sk_c7,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ16_spl
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f188,plain,
( sQ16_spl
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f179,f183,f186,f154,f80]) ).
fof(f190,definition,
( sQ17_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f193,definition,
( sQ18_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ18_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f180,f190,f193,f154,f111]) ).
fof(f197,definition,
( sQ19_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( sQ19_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f181,f197,f143,f154,f135]) ).
fof(f201,definition,
( sQ20_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f182,f201,f193,f154,f87]) ).
fof(f205,plain,
( sQ19_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c3) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f136,f199]) ).
fof(f206,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f128,f205]) ).
fof(f207,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f206]) ).
fof(f208,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( sQ15_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f81,f185]) ).
fof(f212,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f152,f120]) ).
fof(f213,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f152,f92]) ).
fof(f217,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f112,f212]) ).
fof(f218,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f217]) ).
fof(f219,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f81,f41]) ).
fof(f222,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f112,f41]) ).
fof(f224,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f41,f42]) ).
fof(f225,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f40,f224]) ).
fof(f226,plain,
( sQ1_spl
| ~ sQ0_spl
| identity != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f221,f85]) ).
fof(f236,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f222,f225]) ).
fof(f239,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f40,f225]) ).
fof(f245,plain,
( ~ sQ9_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f128,f225]) ).
fof(f250,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f81,f236]) ).
fof(f252,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = multiply(sk_c3,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f136,f245]) ).
fof(f261,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f239,f225]) ).
fof(f266,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f252,f225]) ).
fof(f268,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f266]) ).
fof(f270,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c1 = multiply(sk_c7,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f268,f250]) ).
fof(f273,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f268,f226]) ).
fof(f275,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f268,f41]) ).
fof(f276,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f268,f40]) ).
fof(f278,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f276,f104]) ).
fof(f281,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(paramodulation,[status(thm)],[f81,f275]) ).
fof(f286,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f276,f281]) ).
fof(f289,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f278,f81]) ).
fof(f290,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f278,f120]) ).
fof(f294,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(paramodulation,[status(thm)],[f289,f275]) ).
fof(f295,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f289,f225]) ).
fof(f296,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f276,f294]) ).
fof(f297,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f273]) ).
fof(f298,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f297]) ).
fof(f299,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f276,f295]) ).
fof(f305,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f313,f289]) ).
fof(f313,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f278,f286]) ).
fof(f317,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f313,f290]) ).
fof(f319,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f317,f42]) ).
fof(f321,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f299,f319]) ).
fof(f322,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f299,f321]) ).
fof(f334,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c1 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f313,f270]) ).
fof(f335,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f299,f334]) ).
fof(f337,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| inverse(sk_c6) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f343,f305]) ).
fof(f341,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c1 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f343,f313]) ).
fof(f343,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c1 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f313,f335]) ).
fof(f344,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f343,f337]) ).
fof(f351,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f341,f158]) ).
fof(f352,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(X0,sk_c1) != sk_c7
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f343,f351]) ).
fof(f353,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(X0,sk_c1) != sk_c1
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f341,f352]) ).
fof(f355,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ7_spl
| inverse(sk_c1) != sk_c1 ),
inference(resolution,[status(thm)],[f353,f322]) ).
fof(f362,definition,
( sQ23_spl
<=> sk_c1 = sk_c1 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ23_spl
| sk_c1 != sk_c1 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f370,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f364]) ).
fof(f371,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f380,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ7_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f344,f355]) ).
fof(f381,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f380]) ).
fof(f382,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f387,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f92,f225]) ).
fof(f389,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f88,f387]) ).
fof(f390,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f100,f225]) ).
fof(f392,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f96,f390]) ).
fof(f393,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f84,f225]) ).
fof(f397,plain,
( sQ16_spl
| ~ sQ1_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f84,f188]) ).
fof(f400,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f195]) ).
fof(f401,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f402,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f392,f225]) ).
fof(f442,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f261,f41]) ).
fof(f491,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f500,f389]) ).
fof(f498,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f500,f82]) ).
fof(f499,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f500,f88]) ).
fof(f500,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f393,f402]) ).
fof(f502,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f500,f491]) ).
fof(f503,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f392,f502]) ).
fof(f504,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f397]) ).
fof(f505,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f500,f187]) ).
fof(f508,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f392,f507]) ).
fof(f548,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f508,f500]) ).
fof(f549,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f508,f499]) ).
fof(f553,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f508,f498]) ).
fof(f554,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f508,f553]) ).
fof(f577,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f508,f392]) ).
fof(f578,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f508,f577]) ).
fof(f579,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f578,f225]) ).
fof(f581,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f579]) ).
fof(f584,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| inverse(identity) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f581,f442]) ).
fof(f588,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f581,f584]) ).
fof(f589,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f554]) ).
fof(f590,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f603,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| multiply(sk_c6,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f548,f210]) ).
fof(f604,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f508,f603]) ).
fof(f605,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f578,f604]) ).
fof(f606,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f508,f605]) ).
fof(f607,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f606]) ).
fof(f608,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f609,plain,
( sQ6_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f508,f105]) ).
fof(f610,plain,
( sQ6_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f578,f609]) ).
fof(f611,plain,
( sQ6_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f548,f610]) ).
fof(f612,plain,
( sQ6_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f611]) ).
fof(f613,plain,
( sQ6_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f612]) ).
fof(f634,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f213]) ).
fof(f635,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f548,f634]) ).
fof(f636,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f635]) ).
fof(f637,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f638,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f90,f94,f98,f102,f106,f107,f108,f109,f110,f114,f115,f116,f117,f118,f122,f123,f124,f125,f126,f130,f131,f132,f133,f134,f138,f139,f140,f141,f142,f147,f148,f149,f150,f160,f165,f189,f196,f200,f204,f208,f219,f298,f371,f382,f401,f505,f590,f608,f613,f637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP383-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.38 % Computer : n018.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Sun Sep 20 20:12:53 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.13/10.40 % Drodi V4.1.1
% 0.13/10.43 % Refutation found
% 0.13/10.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/10.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.45 % Elapsed time: 0.053866 seconds
% 0.13/10.45 % CPU time: 0.176927 seconds
% 0.13/10.45 % Total memory used: 78.932 MB
% 0.13/10.45 % Net memory used: 78.781 MB
%------------------------------------------------------------------------------