%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP346-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.09s 0.62s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 65
% Syntax : Number of formulae : 305 ( 14 unt; 26 def)
% Number of atoms : 983 ( 350 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1252 ( 574 ~; 652 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
! [X3,X4,X1,X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c5
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f50,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f51,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
( inverse(sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f53,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f59,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f60,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f61,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f64,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f65,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f66,plain,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f67,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f68,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f70,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f71,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f72,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f73,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f74,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f75,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f76,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f77,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f78,plain,
! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c5
| ! [X1] :
( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| ! [X4] :
( multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| ! [X3] :
( multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c5
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f82,plain,
( sQ0_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ1_spl
| multiply(sk_c6,sk_c5) != sk_c7 ),
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
<=> multiply(sk_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f89,plain,
( sQ2_spl
| multiply(sk_c7,sk_c5) != sk_c6 ),
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
<=> inverse(sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ3_spl
| inverse(sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f93,plain,
( sQ3_spl
| inverse(sk_c7) != sk_c5 ),
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
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ4_spl
| multiply(sk_c3,sk_c6) = 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
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ5_spl
| inverse(sk_c3) = sk_c6 ),
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_c4,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ6_spl
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f80,f103]) ).
fof(f107,definition,
( sQ7_spl
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ7_spl
| inverse(sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f80,f107]) ).
fof(f111,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f111,f83]) ).
fof(f115,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f111,f87]) ).
fof(f116,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f111,f91]) ).
fof(f117,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f111,f95]) ).
fof(f118,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f111,f99]) ).
fof(f119,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f111,f103]) ).
fof(f120,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f111,f107]) ).
fof(f121,definition,
( sQ9_spl
<=> multiply(sk_c1,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f121,f83]) ).
fof(f125,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f121,f87]) ).
fof(f126,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f121,f91]) ).
fof(f127,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f121,f95]) ).
fof(f128,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f121,f99]) ).
fof(f129,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f121,f103]) ).
fof(f130,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f121,f107]) ).
fof(f131,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f131,f83]) ).
fof(f135,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f131,f87]) ).
fof(f136,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f131,f91]) ).
fof(f137,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f131,f95]) ).
fof(f138,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f131,f99]) ).
fof(f139,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f131,f103]) ).
fof(f140,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f131,f107]) ).
fof(f141,definition,
( sQ11_spl
<=> multiply(sk_c2,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f141,f83]) ).
fof(f145,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f141,f87]) ).
fof(f146,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f141,f91]) ).
fof(f147,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f141,f95]) ).
fof(f148,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f141,f99]) ).
fof(f149,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f141,f103]) ).
fof(f150,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f141,f107]) ).
fof(f151,definition,
! [X0] :
( sQ12_spl
<=> ( multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
! [X1] :
( sQ13_spl
<=> ( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X2] :
( sQ14_spl
<=> ( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3] :
( sQ15_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f80,f151,f154,f83,f87,f91,f157,f160]) ).
fof(f168,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f122,f42]) ).
fof(f170,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f100,f41]) ).
fof(f171,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f108,f41]) ).
fof(f172,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f112,f41]) ).
fof(f173,plain,
( ~ sQ10_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f132,f41]) ).
fof(f174,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f41,f42]) ).
fof(f175,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f40,f174]) ).
fof(f177,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f96,f42]) ).
fof(f178,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f161,f104]) ).
fof(f183,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f108,f178]) ).
fof(f184,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f183]) ).
fof(f185,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f187,plain,
! [X0] :
( ~ sQ5_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f170,f42]) ).
fof(f188,plain,
! [X0] :
( ~ sQ5_spl
| X0 = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f40,f187]) ).
fof(f191,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f158,f96]) ).
fof(f194,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f41,f158]) ).
fof(f196,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f122,f158]) ).
fof(f198,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f100,f191]) ).
fof(f199,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f198]) ).
fof(f200,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f201,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f155,f142]) ).
fof(f203,plain,
( ~ sQ13_spl
| sk_c5 != sk_c6
| inverse(identity) != sk_c6 ),
inference(paramodulation,[status(thm)],[f40,f155]) ).
fof(f206,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f132,f201]) ).
fof(f207,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f206]) ).
fof(f208,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f152,f122]) ).
fof(f211,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| sk_c7 != sk_c7
| inverse(sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f96,f152]) ).
fof(f212,plain,
( ~ sQ12_spl
| identity != sk_c7
| inverse(inverse(sk_c6)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f41,f152]) ).
fof(f213,plain,
( ~ sQ12_spl
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f40,f152]) ).
fof(f217,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f112,f210]) ).
fof(f218,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f217]) ).
fof(f219,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f220,definition,
( sQ16_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ16_spl
| inverse(sk_c3) != sk_c7 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ17_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ17_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f211,f220,f223,f151,f95]) ).
fof(f227,definition,
( sQ18_spl
<=> inverse(inverse(sk_c6)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( sQ18_spl
| inverse(inverse(sk_c6)) != sk_c7 ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,definition,
( sQ19_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f212,f227,f230,f151]) ).
fof(f234,definition,
( sQ20_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f237,definition,
( sQ21_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ21_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ sQ12_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f213,f234,f237,f151]) ).
fof(f242,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f225]) ).
fof(f243,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f242]) ).
fof(f244,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f92,f41]) ).
fof(f248,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f88,f42]) ).
fof(f276,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c7,identity) ),
inference(paramodulation,[status(thm)],[f244,f248]) ).
fof(f279,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c7,identity) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f276,f82]) ).
fof(f285,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(paramodulation,[status(thm)],[f96,f188]) ).
fof(f286,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,multiply(sk_c3,X0)) = multiply(sk_c3,X0) ),
inference(paramodulation,[status(thm)],[f188,f177]) ).
fof(f288,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f290,f279]) ).
fof(f290,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f276,f285]) ).
fof(f296,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(identity,X0)) ),
inference(paramodulation,[status(thm)],[f290,f42]) ).
fof(f298,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(backward_demodulation,[status(thm)],[f310,f188]) ).
fof(f300,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f310,f170]) ).
fof(f301,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f310,f84]) ).
fof(f310,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f40,f296]) ).
fof(f315,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f286,f298]) ).
fof(f318,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c7 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f325,f288]) ).
fof(f325,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f88,f301]) ).
fof(f345,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f300,f42]) ).
fof(f348,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f40,f345]) ).
fof(f349,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f356,f300]) ).
fof(f350,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f356,f171]) ).
fof(f356,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f315,f348]) ).
fof(f361,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f364,f108]) ).
fof(f362,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f364,f104]) ).
fof(f364,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f349,f350]) ).
fof(f372,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f362]) ).
fof(f373,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f318]) ).
fof(f374,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f375,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f361,f222]) ).
fof(f376,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f395,definition,
( sQ24_spl
<=> inverse(identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( sQ24_spl
| inverse(identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,definition,
( sQ25_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f400,plain,
( sQ25_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,plain,
( ~ sQ13_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f203,f395,f398,f154]) ).
fof(f413,plain,
( sQ24_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c3) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f349,f397]) ).
fof(f414,plain,
( sQ24_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f361,f413]) ).
fof(f415,plain,
( sQ24_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f325,f414]) ).
fof(f416,plain,
( sQ24_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f415]) ).
fof(f417,plain,
( sQ24_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f418,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f372,f400]) ).
fof(f419,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f325,f418]) ).
fof(f420,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f419]) ).
fof(f421,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f423,definition,
( sQ27_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ27_spl
| inverse(sk_c1) != sk_c6 ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ27_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f196,f223,f423,f157,f121]) ).
fof(f428,definition,
( sQ28_spl
<=> inverse(inverse(sk_c6)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( sQ28_spl
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,plain,
( ~ sQ14_spl
| ~ sQ28_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f194,f230,f428,f157]) ).
fof(f433,plain,
( sQ27_spl
| ~ sQ8_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f112,f425]) ).
fof(f446,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f175,f175]) ).
fof(f448,plain,
( ~ sQ8_spl
| sk_c1 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f172,f175]) ).
fof(f451,plain,
( ~ sQ10_spl
| sk_c2 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f173,f175]) ).
fof(f453,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f81,f175]) ).
fof(f454,plain,
( ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f122,f175]) ).
fof(f458,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f112,f454]) ).
fof(f460,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c2) = multiply(sk_c1,identity) ),
inference(paramodulation,[status(thm)],[f173,f168]) ).
fof(f470,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f40,f175]) ).
fof(f474,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f41,f175]) ).
fof(f476,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c2) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f479,f460]) ).
fof(f477,plain,
( ~ sQ10_spl
| sk_c2 = inverse(sk_c6) ),
inference(backward_demodulation,[status(thm)],[f479,f451]) ).
fof(f478,plain,
( ~ sQ8_spl
| sk_c1 = inverse(sk_c7) ),
inference(backward_demodulation,[status(thm)],[f479,f448]) ).
fof(f479,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f446,f474]) ).
fof(f481,plain,
( sQ18_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f477,f229]) ).
fof(f482,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f477,f453]) ).
fof(f484,plain,
( sQ28_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f477,f430]) ).
fof(f485,plain,
( sQ3_spl
| ~ sQ8_spl
| sk_c1 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f478,f93]) ).
fof(f487,plain,
( sQ18_spl
| ~ sQ10_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f132,f481]) ).
fof(f488,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f142,f482]) ).
fof(f489,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f239]) ).
fof(f490,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f491,plain,
( sQ28_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f484,f131,f428]) ).
fof(f512,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f488,f173]) ).
fof(f521,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f488,f458]) ).
fof(f523,plain,
( sQ18_spl
| ~ sQ10_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f487,f237,f131,f227]) ).
fof(f524,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f433,f237,f111,f423]) ).
fof(f532,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f537,f172]) ).
fof(f535,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| X0 = multiply(X0,sk_c1) ),
inference(backward_demodulation,[status(thm)],[f537,f479]) ).
fof(f536,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| X0 = multiply(inverse(sk_c1),X0) ),
inference(backward_demodulation,[status(thm)],[f537,f470]) ).
fof(f537,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f476,f512]) ).
fof(f545,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f488,f81]) ).
fof(f548,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f521,f545]) ).
fof(f560,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f548,f89]) ).
fof(f561,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f521,f560]) ).
fof(f562,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f488,f561]) ).
fof(f563,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f562]) ).
fof(f564,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f575,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f535,f532]) ).
fof(f579,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f112,f536]) ).
fof(f625,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c1 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f548,f485]) ).
fof(f631,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f575,f112]) ).
fof(f632,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| X0 = multiply(X0,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f575,f535]) ).
fof(f638,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f575,f625]) ).
fof(f639,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f638]) ).
fof(f640,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f639]) ).
fof(f662,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(X0) != sk_c7
| X0 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f632,f161]) ).
fof(f663,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(X0) != sk_c7
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f548,f662]) ).
fof(f664,plain,
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c7) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f663]) ).
fof(f665,plain,
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f664,f631]) ).
fof(f666,plain,
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f488,f85]) ).
fof(f669,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f579,f668]) ).
fof(f670,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f548,f669]) ).
fof(f671,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f670]) ).
fof(f672,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f671]) ).
fof(f673,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f90,f94,f98,f102,f106,f110,f114,f115,f116,f117,f118,f119,f120,f124,f125,f126,f127,f128,f129,f130,f134,f135,f136,f137,f138,f139,f140,f144,f145,f146,f147,f148,f149,f150,f163,f185,f200,f208,f219,f226,f233,f240,f243,f374,f377,f401,f417,f421,f426,f431,f490,f491,f523,f524,f564,f640,f666,f672]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP346-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n006.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Sun Sep 20 20:09:44 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.60 % Drodi V4.1.1
% 0.09/0.62 % Refutation found
% 0.09/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.65 % Elapsed time: 0.057805 seconds
% 0.13/0.65 % CPU time: 0.183175 seconds
% 0.13/0.65 % Total memory used: 103.696 MB
% 0.13/0.65 % Net memory used: 103.526 MB
%------------------------------------------------------------------------------