%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP265-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:15 PM UTC 2026
% Result : Unsatisfiable 0.05s 0.33s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 50
% Syntax : Number of formulae : 206 ( 12 unt; 22 def)
% Number of atoms : 572 ( 247 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 660 ( 294 ~; 344 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 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_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
! [X3,X4,X1,X2,X5,X6] :
( inverse(X6) != sk_c7
| multiply(X6,sk_c7) != X5
| multiply(sk_c7,X5) != sk_c8
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8 ),
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_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f38,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f40,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f47,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f60,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f61,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f64,plain,
! [X6] :
( inverse(X6) != sk_c7
| ! [X5] :
( multiply(X6,sk_c7) != X5
| multiply(sk_c7,X5) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c7
| multiply(X5,sk_c7) != X4
| multiply(sk_c7,X4) != sk_c8
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c9) = sk_c8 ),
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(f80,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f66,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(f84,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f66,f81]) ).
fof(f85,definition,
( sQ5_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ5_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
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_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c7) = 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_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| inverse(sk_c5) = sk_c7 ),
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
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c9 ),
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
<=> multiply(sk_c2,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f107]) ).
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
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
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
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f131,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != 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_c7
| multiply(X5,sk_c7) != X4
| multiply(sk_c7,X4) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f65,f127,f130,f133,f136]) ).
fof(f140,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f147,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f108,f35]) ).
fof(f155,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(paramodulation,[status(thm)],[f90,f140]) ).
fof(f160,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f155,f85,f93,f136,f89]) ).
fof(f170,plain,
( ~ sQ8_spl
| multiply(sk_c9,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f98,f34]) ).
fof(f171,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f118,f34]) ).
fof(f172,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f34,f35]) ).
fof(f173,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f172]) ).
fof(f182,plain,
! [X0] :
( ~ sQ8_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f170,f35]) ).
fof(f183,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c9,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f33,f182]) ).
fof(f186,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(resolution,[status(thm)],[f131,f118]) ).
fof(f187,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| sk_c7 != sk_c8
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f131]) ).
fof(f191,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f108,f186]) ).
fof(f192,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f191]) ).
fof(f193,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c9) != sk_c8 ),
inference(resolution,[status(thm)],[f128,f74]) ).
fof(f195,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(resolution,[status(thm)],[f128,f98]) ).
fof(f200,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f70,f194]) ).
fof(f201,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f200]) ).
fof(f202,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f201]) ).
fof(f203,definition,
( sQ17_spl
<=> multiply(sk_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ17_spl
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ18_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ18_spl
| sk_c7 = sk_c8 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( sQ18_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f187,f203,f206,f130,f81]) ).
fof(f217,definition,
( sQ21_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( sQ21_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f242,plain,
( ~ sQ10_spl
| sk_c2 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f171,f173]) ).
fof(f250,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f33,f173]) ).
fof(f254,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f173]) ).
fof(f259,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f94,f254]) ).
fof(f260,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f86,f259]) ).
fof(f261,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f208]) ).
fof(f262,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f266,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f260,f78]) ).
fof(f274,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f260,f134]) ).
fof(f284,definition,
( sQ26_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ26_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f295,plain,
( sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f286]) ).
fof(f296,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f340,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f266,f274]) ).
fof(f344,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f340]) ).
fof(f345,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f344]) ).
fof(f346,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f350,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f260,f205]) ).
fof(f351,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f266,f350]) ).
fof(f352,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f351]) ).
fof(f353,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f379,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f108,f173]) ).
fof(f381,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f118,f379]) ).
fof(f382,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f381,f173]) ).
fof(f384,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f34,f382]) ).
fof(f394,definition,
( sQ33_spl
<=> multiply(sk_c7,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( ~ sQ33_spl
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f396,plain,
( sQ33_spl
| multiply(sk_c7,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f417,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f384,f171]) ).
fof(f418,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f384,f34]) ).
fof(f419,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(inverse(sk_c7),X0) ),
inference(backward_demodulation,[status(thm)],[f384,f250]) ).
fof(f421,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f384,f33]) ).
fof(f424,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f421,f140]) ).
fof(f429,plain,
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f424,f133,f117,f107,f136]) ).
fof(f437,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f421,f396]) ).
fof(f465,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f219]) ).
fof(f466,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f467,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(sk_c2,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f421,f147]) ).
fof(f468,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c2 = multiply(sk_c2,sk_c7) ),
inference(paramodulation,[status(thm)],[f417,f467]) ).
fof(f473,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c7
| sk_c2 != sk_c8 ),
inference(paramodulation,[status(thm)],[f468,f134]) ).
fof(f476,definition,
( sQ36_spl
<=> sk_c2 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ36_spl
| sk_c2 != sk_c8 ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,definition,
( sQ37_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( sQ37_spl
| inverse(sk_c2) != sk_c7 ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f473,f476,f479,f133,f107,f117]) ).
fof(f483,plain,
( sQ37_spl
| ~ sQ10_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f118,f481]) ).
fof(f491,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c2 = multiply(inverse(sk_c8),sk_c7) ),
inference(forward_demodulation,[status(thm)],[f384,f242]) ).
fof(f510,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(paramodulation,[status(thm)],[f67,f183]) ).
fof(f518,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f510,f173]) ).
fof(f522,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f418,f518]) ).
fof(f523,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f437]) ).
fof(f524,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f522,f206,f117,f107,f97,f66]) ).
fof(f526,plain,
( ~ sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f421,f395]) ).
fof(f531,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f67,f195]) ).
fof(f532,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f531]) ).
fof(f533,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f546,plain,
( ~ sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f483]) ).
fof(f547,plain,
( ~ sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f555,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ18_spl
| sk_c2 = multiply(inverse(sk_c7),sk_c7) ),
inference(backward_demodulation,[status(thm)],[f207,f491]) ).
fof(f557,plain,
( sQ36_spl
| ~ sQ18_spl
| sk_c2 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f207,f478]) ).
fof(f571,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ18_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f419,f555]) ).
fof(f603,plain,
( sQ36_spl
| ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f571,f557]) ).
fof(f604,plain,
( sQ36_spl
| ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f603]) ).
fof(f605,plain,
( sQ36_spl
| ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f606,plain,
$false,
inference(sat_refutation,[status(thm)],[f72,f76,f80,f84,f88,f92,f96,f100,f101,f102,f103,f104,f105,f106,f112,f113,f114,f115,f116,f122,f123,f124,f125,f126,f139,f160,f193,f202,f209,f262,f296,f346,f353,f429,f466,f482,f524,f525,f533,f547,f605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP265-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Sun Sep 20 20:07:36 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 % Drodi V4.1.1
% 0.05/0.33 % Refutation found
% 0.05/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.05/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.34 % Elapsed time: 0.042439 seconds
% 0.08/0.34 % CPU time: 0.104290 seconds
% 0.08/0.34 % Total memory used: 103.734 MB
% 0.08/0.34 % Net memory used: 103.511 MB
%------------------------------------------------------------------------------