%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP223-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:33:08 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 53
% Syntax : Number of formulae : 209 ( 11 unt; 19 def)
% Number of atoms : 635 ( 267 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 763 ( 337 ~; 407 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 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_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X4,X5,X6,X2,X1,X3,X7] :
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X2) != X1
| multiply(X2,X1) != sk_c9
| inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X7] :
( inverse(X7) != sk_c9
| ! [X3] :
( multiply(X7,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| ! [X1] :
( multiply(X1,sk_c8) != sk_c9
| ! [X2] :
( inverse(X2) != X1
| multiply(X2,X1) != sk_c9
| ! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| ! [X4] :
( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f70,f89]) ).
fof(f93,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f70,f93]) ).
fof(f97,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> multiply(sk_c9,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f106,f73]) ).
fof(f110,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f106,f77]) ).
fof(f111,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f106,f81]) ).
fof(f112,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f106,f85]) ).
fof(f113,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f106,f89]) ).
fof(f114,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f106,f93]) ).
fof(f115,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c9) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f115,f73]) ).
fof(f119,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f115,f77]) ).
fof(f120,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f115,f81]) ).
fof(f121,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f115,f85]) ).
fof(f122,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f115,f89]) ).
fof(f123,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f115,f93]) ).
fof(f124,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f124,f73]) ).
fof(f128,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f124,f77]) ).
fof(f129,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f124,f81]) ).
fof(f130,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f124,f85]) ).
fof(f131,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f124,f89]) ).
fof(f132,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f124,f93]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1,X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3,X4] :
( sQ13_spl
<=> ( multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c8) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ13_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f133,f136,f139]) ).
fof(f143,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c8) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f170,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| multiply(sk_c5,sk_c8) != sk_c9
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f78,f143]) ).
fof(f172,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f71,f143]) ).
fof(f174,definition,
( sQ14_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ14_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f170,f174,f81,f139,f77]) ).
fof(f181,definition,
( sQ16_spl
<=> multiply(sk_c9,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ16_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f185,definition,
( sQ17_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ17_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f172,f185,f181,f139,f70]) ).
fof(f196,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f198,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f90,f196]) ).
fof(f199,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c9
| multiply(sk_c9,sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f116,f196]) ).
fof(f200,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f198,f85,f93,f136,f89]) ).
fof(f201,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f199,f106,f124,f136,f115]) ).
fof(f206,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f207,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f206]) ).
fof(f219,plain,
( sQ14_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f78,f176]) ).
fof(f220,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f74,f219]) ).
fof(f221,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f220]) ).
fof(f222,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f228,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f134,f98]) ).
fof(f235,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f71,f228]) ).
fof(f236,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f235]) ).
fof(f237,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f241,definition,
( sQ20_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ20_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f281,plain,
( ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f74,f207]) ).
fof(f283,plain,
( ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f207]) ).
fof(f290,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c5,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f78,f281]) ).
fof(f293,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f283]) ).
fof(f294,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f86,f293]) ).
fof(f303,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(X0,sk_c8) != sk_c8
| inverse(X0) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f294,f134]) ).
fof(f313,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(X0,sk_c8) != sk_c8
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f294,f303]) ).
fof(f324,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c5,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f294,f290]) ).
fof(f325,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f324,f207]) ).
fof(f327,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f325]) ).
fof(f332,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f327,f35]) ).
fof(f349,definition,
( sQ28_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( sQ28_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f353,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f351]) ).
fof(f354,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f355,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f243]) ).
fof(f356,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f361,plain,
( ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f98,f207]) ).
fof(f363,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f71,f361]) ).
fof(f367,plain,
( ~ sQ9_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f116,f207]) ).
fof(f369,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f125,f367]) ).
fof(f370,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f107,f369]) ).
fof(f375,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f370,f98]) ).
fof(f376,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c9,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f370,f183]) ).
fof(f377,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f370,f71]) ).
fof(f383,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f370,f376]) ).
fof(f429,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f370,f363]) ).
fof(f430,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f370,f429]) ).
fof(f456,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f430,f383]) ).
fof(f457,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f456]) ).
fof(f458,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f459,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f377,f187]) ).
fof(f460,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f375,f459]) ).
fof(f461,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f370,f460]) ).
fof(f462,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f461]) ).
fof(f463,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f522,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f294,f82]) ).
fof(f526,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f522,f37]) ).
fof(f528,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f332,f526]) ).
fof(f529,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f332,f528]) ).
fof(f548,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c5) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f294,f74]) ).
fof(f549,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f548,f207]) ).
fof(f550,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f548,f37]) ).
fof(f551,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c5,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f78,f549]) ).
fof(f552,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f529,f551]) ).
fof(f555,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f332,f550]) ).
fof(f556,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f529,f555]) ).
fof(f559,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f552,f78]) ).
fof(f561,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f556,f313]) ).
fof(f571,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f559,f561]) ).
fof(f572,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f571]) ).
fof(f573,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f572]) ).
fof(f574,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f100,f101,f102,f103,f104,f105,f109,f110,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f142,f177,f188,f200,f201,f222,f237,f354,f356,f458,f463,f573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP223-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:11:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.054842 seconds
% 0.12/0.42 % CPU time: 0.172349 seconds
% 0.12/0.42 % Total memory used: 103.372 MB
% 0.12/0.42 % Net memory used: 103.197 MB
%------------------------------------------------------------------------------