%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP285-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:33:18 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 45
% Syntax : Number of formulae : 166 ( 10 unt; 15 def)
% Number of atoms : 469 ( 220 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 544 ( 241 ~; 288 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 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_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
! [X3,X4,X1,X2,X5,X6] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(X4,sk_c9) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f35,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f47,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f60,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f61,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f64,plain,
! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c7
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X4] : multiply(X4,sk_c9) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,definition,
( sQ0_spl
<=> multiply(sk_c9,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ0_spl
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f68,plain,
( sQ0_spl
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f66,f69]) ).
fof(f73,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f66,f73]) ).
fof(f77,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f81,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f85,definition,
( sQ5_spl
<=> multiply(sk_c9,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ5_spl
| multiply(sk_c9,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f66,f85]) ).
fof(f89,definition,
( sQ6_spl
<=> multiply(sk_c5,sk_c9) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c9) = sk_c6 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f66,f89]) ).
fof(f93,definition,
( sQ7_spl
<=> inverse(sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| inverse(sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f66,f93]) ).
fof(f97,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f43,f97,f69]) ).
fof(f101,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f102,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f103,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f104,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f105,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f106,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f107,definition,
( sQ9_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f107,f69]) ).
fof(f111,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f107,f73]) ).
fof(f112,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f107,f77]) ).
fof(f113,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f107,f81]) ).
fof(f114,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f107,f85]) ).
fof(f115,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f107,f89]) ).
fof(f116,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f107,f93]) ).
fof(f117,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f57,f117,f69]) ).
fof(f121,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f58,f117,f73]) ).
fof(f122,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f123,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f124,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f125,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f126,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f117,f93]) ).
fof(f127,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f128,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
! [X1] :
( sQ12_spl
<=> multiply(X1,sk_c9) != sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f131,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
! [X3] :
( sQ13_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X4,X5] :
( sQ14_spl
<=> ( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f66,f127,f130,f133,f136]) ).
fof(f140,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f158,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c9
| multiply(sk_c9,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f140]) ).
fof(f159,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f98,f140]) ).
fof(f162,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f158,f85,f93,f136,f89]) ).
fof(f163,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f159,f66,f107,f136,f97]) ).
fof(f176,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f34,f35]) ).
fof(f177,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f176]) ).
fof(f196,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f33,f177]) ).
fof(f205,plain,
( ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f177]) ).
fof(f206,plain,
( ~ sQ8_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f98,f177]) ).
fof(f212,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f94,f205]) ).
fof(f213,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f212]) ).
fof(f214,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f108,f206]) ).
fof(f219,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f213,f68]) ).
fof(f221,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f213,f70]) ).
fof(f226,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f213,f74]) ).
fof(f241,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f221,f177]) ).
fof(f243,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f226,f241]) ).
fof(f244,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f219]) ).
fof(f245,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f82]) ).
fof(f248,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f246]) ).
fof(f249,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f248]) ).
fof(f250,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f253,plain,
( ~ sQ12_spl
| sk_c9 != sk_c7 ),
inference(paramodulation,[status(thm)],[f196,f131]) ).
fof(f259,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f67,f214]) ).
fof(f260,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f253]) ).
fof(f261,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f259,f108]) ).
fof(f268,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f259,f98]) ).
fof(f308,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f259,f128]) ).
fof(f309,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f259,f308]) ).
fof(f310,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f309,f263]) ).
fof(f312,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f268,f310]) ).
fof(f313,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f312]) ).
fof(f314,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| multiply(sk_c1,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f263]) ).
fof(f317,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f268,f315]) ).
fof(f318,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f317]) ).
fof(f319,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f324,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f213,f128]) ).
fof(f325,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f213,f324]) ).
fof(f383,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f78,f325]) ).
fof(f387,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f383,f81,f77,f85,f93,f89,f127]) ).
fof(f395,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f213,f253]) ).
fof(f396,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f395]) ).
fof(f397,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f396]) ).
fof(f398,plain,
$false,
inference(sat_refutation,[status(thm)],[f72,f76,f88,f92,f96,f100,f101,f102,f103,f104,f105,f106,f110,f111,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f125,f126,f139,f162,f163,f245,f250,f261,f314,f319,f387,f397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP285-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.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 20:08:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.051644 seconds
% 0.13/0.41 % CPU time: 0.135740 seconds
% 0.13/0.41 % Total memory used: 64.505 MB
% 0.13/0.41 % Net memory used: 64.403 MB
%------------------------------------------------------------------------------