%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP266-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:33:15 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 69
% Syntax : Number of formulae : 259 ( 10 unt; 22 def)
% Number of atoms : 763 ( 342 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 890 ( 386 ~; 482 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
! [X5,X6,X7,X8,X1,X2,X3,X4] :
( inverse(X4) != sk_c9
| multiply(X4,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c10
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| inverse(X6) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f55,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f56,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f58,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f59,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f60,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f61,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f62,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f63,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f64,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f65,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f66,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f67,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f68,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f69,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f70,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f71,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f72,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f73,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f74,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f78,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f79,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f80,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f81,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f85,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f86,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f87,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f88,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f89,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f90,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f91,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f94,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f95,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f96,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f97,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f98,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f99,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f100,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f101,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f102,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f103,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f104,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f106,plain,
! [X4] :
( inverse(X4) != sk_c9
| ! [X3] :
( multiply(X4,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c10
| ! [X2] :
( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X8] :
( inverse(X8) != sk_c10
| ! [X7] :
( multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| ! [X6] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| ! [X5] :
( inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10 ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c10
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ1_spl
<=> multiply(sk_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ1_spl
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f108,f111]) ).
fof(f115,definition,
( sQ2_spl
<=> inverse(sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ2_spl
| inverse(sk_c5) = sk_c11 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f108,f115]) ).
fof(f119,definition,
( sQ3_spl
<=> multiply(sk_c6,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ3_spl
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f108,f119]) ).
fof(f123,definition,
( sQ4_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ4_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f108,f123]) ).
fof(f127,definition,
( sQ5_spl
<=> multiply(sk_c9,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ5_spl
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f108,f127]) ).
fof(f131,definition,
( sQ6_spl
<=> multiply(sk_c7,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f108,f131]) ).
fof(f135,definition,
( sQ7_spl
<=> inverse(sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ7_spl
| inverse(sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f108,f135]) ).
fof(f139,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f64,f139,f111]) ).
fof(f143,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f65,f139,f115]) ).
fof(f144,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f66,f139,f119]) ).
fof(f145,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f67,f139,f123]) ).
fof(f146,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f68,f139,f127]) ).
fof(f147,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f69,f139,f131]) ).
fof(f148,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f70,f139,f135]) ).
fof(f149,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f71,f149,f111]) ).
fof(f153,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f72,f149,f115]) ).
fof(f154,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f73,f149,f119]) ).
fof(f155,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f74,f149,f123]) ).
fof(f159,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f78,f159,f111]) ).
fof(f163,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f79,f159,f115]) ).
fof(f164,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f80,f159,f119]) ).
fof(f165,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f81,f159,f123]) ).
fof(f169,definition,
( sQ11_spl
<=> multiply(sk_c10,sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f169,f111]) ).
fof(f173,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f86,f169,f115]) ).
fof(f174,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f87,f169,f119]) ).
fof(f175,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f88,f169,f123]) ).
fof(f176,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f89,f169,f127]) ).
fof(f177,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f90,f169,f131]) ).
fof(f178,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f91,f169,f135]) ).
fof(f179,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c10) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f179,f111]) ).
fof(f183,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f179,f115]) ).
fof(f184,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f179,f119]) ).
fof(f185,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f95,f179,f123]) ).
fof(f186,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f179,f127]) ).
fof(f187,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f97,f179,f131]) ).
fof(f188,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f98,f179,f135]) ).
fof(f189,definition,
( sQ13_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ13_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f189,f111]) ).
fof(f193,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f189,f115]) ).
fof(f194,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f189,f119]) ).
fof(f195,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f189,f123]) ).
fof(f196,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f189,f127]) ).
fof(f197,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f104,f189,f131]) ).
fof(f198,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f189,f135]) ).
fof(f199,definition,
! [X0] :
( sQ14_spl
<=> ( inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
! [X1] :
( sQ15_spl
<=> ( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f203,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
! [X2,X3] :
( sQ16_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ16_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X6,X7] :
( sQ17_spl
<=> ( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0,X1] :
( ~ sQ17_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f199,f202,f205,f208]) ).
fof(f212,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f209]) ).
fof(f228,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f120,f212]) ).
fof(f229,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c7) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10 ),
inference(paramodulation,[status(thm)],[f132,f212]) ).
fof(f230,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| inverse(sk_c2) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f150,f212]) ).
fof(f231,definition,
( sQ18_spl
<=> multiply(sk_c9,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ18_spl
| multiply(sk_c9,sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f228,f231,f123,f208,f119]) ).
fof(f235,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f229,f127,f135,f208,f131]) ).
fof(f236,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f230,f231,f159,f208,f149]) ).
fof(f237,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f206]) ).
fof(f239,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c10
| multiply(sk_c10,sk_c4) != sk_c9 ),
inference(paramodulation,[status(thm)],[f180,f237]) ).
fof(f240,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f239,f169,f189,f205,f179]) ).
fof(f242,plain,
( ~ sQ4_spl
| multiply(sk_c9,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f124,f55]) ).
fof(f247,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f55,f56]) ).
fof(f248,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f54,f247]) ).
fof(f251,plain,
! [X0] :
( ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f242,f56]) ).
fof(f252,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f54,f251]) ).
fof(f281,plain,
( ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c7),sk_c8) ),
inference(paramodulation,[status(thm)],[f132,f248]) ).
fof(f282,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f109,f248]) ).
fof(f283,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c3),sk_c4) ),
inference(paramodulation,[status(thm)],[f180,f248]) ).
fof(f288,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f136,f281]) ).
fof(f289,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f128,f288]) ).
fof(f290,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f140,f282]) ).
fof(f291,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c10,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f190,f283]) ).
fof(f306,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f289,f203]) ).
fof(f319,definition,
( sQ21_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ21_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f361,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f321]) ).
fof(f362,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f441,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f289,f120]) ).
fof(f519,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c6) != sk_c9 ),
inference(resolution,[status(thm)],[f306,f441]) ).
fof(f534,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f124,f519]) ).
fof(f535,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(X0) != sk_c10
| multiply(sk_c9,multiply(X0,sk_c10)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f289,f237]) ).
fof(f538,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(X0) != sk_c10
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f289,f537]) ).
fof(f539,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f289,f538]) ).
fof(f543,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(sk_c6) != sk_c9 ),
inference(resolution,[status(thm)],[f539,f252]) ).
fof(f555,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f124,f543]) ).
fof(f556,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f555]) ).
fof(f557,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f579,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c11 ),
inference(resolution,[status(thm)],[f200,f112]) ).
fof(f580,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f200,f109]) ).
fof(f585,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f116,f579]) ).
fof(f586,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f585]) ).
fof(f587,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f588,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ8_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f140,f580]) ).
fof(f589,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f588]) ).
fof(f590,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f607,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f290,f248]) ).
fof(f609,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f55,f607]) ).
fof(f611,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f609,f55]) ).
fof(f612,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f609,f54]) ).
fof(f616,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f612,f291]) ).
fof(f619,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f616,f612]) ).
fof(f626,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f616,f190]) ).
fof(f633,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c4,sk_c4) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f616,f170]) ).
fof(f634,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f619,f633]) ).
fof(f639,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f616,f203]) ).
fof(f640,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c9
| sk_c9 != sk_c4 ),
inference(paramodulation,[status(thm)],[f619,f639]) ).
fof(f642,definition,
( sQ28_spl
<=> sk_c9 = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ28_spl
| sk_c9 != sk_c4 ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f645,definition,
( sQ29_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f647,plain,
( sQ29_spl
| inverse(sk_c4) != sk_c9 ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f640,f642,f645,f202,f189,f179,f139,f108]) ).
fof(f659,plain,
( sQ28_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f634,f644]) ).
fof(f660,plain,
( sQ28_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f659]) ).
fof(f661,plain,
( sQ28_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f672,plain,
( sQ18_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c4,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f634,f233]) ).
fof(f673,plain,
( sQ18_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f619,f672]) ).
fof(f674,plain,
( sQ18_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c4 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f616,f673]) ).
fof(f675,plain,
( sQ18_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f616,f674]) ).
fof(f676,plain,
( sQ18_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f675]) ).
fof(f677,plain,
( sQ18_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f676]) ).
fof(f681,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f616,f611]) ).
fof(f682,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c4,sk_c3) = sk_c4 ),
inference(paramodulation,[status(thm)],[f626,f681]) ).
fof(f686,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f619,f682]) ).
fof(f691,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f686,f634]) ).
fof(f692,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f686,f626]) ).
fof(f711,plain,
( sQ29_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c3) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f686,f647]) ).
fof(f712,plain,
( sQ29_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f691,f711]) ).
fof(f721,plain,
( sQ29_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f692,f712]) ).
fof(f722,plain,
( sQ29_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f721]) ).
fof(f723,plain,
( sQ29_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f724,plain,
$false,
inference(sat_refutation,[status(thm)],[f114,f118,f122,f126,f130,f134,f138,f142,f143,f144,f145,f146,f147,f148,f152,f153,f154,f155,f162,f163,f164,f165,f172,f173,f174,f175,f176,f177,f178,f182,f183,f184,f185,f186,f187,f188,f192,f193,f194,f195,f196,f197,f198,f211,f234,f235,f236,f240,f362,f536,f557,f587,f590,f648,f661,f677,f723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP266-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:10:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.057434 seconds
% 0.09/0.44 % CPU time: 0.192260 seconds
% 0.09/0.44 % Total memory used: 105.163 MB
% 0.09/0.44 % Net memory used: 105.057 MB
%------------------------------------------------------------------------------