%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP241-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:33:11 PM UTC 2026
% Result : Unsatisfiable 0.13s 10.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 53
% Syntax : Number of formulae : 204 ( 12 unt; 16 def)
% Number of atoms : 569 ( 263 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 636 ( 271 ~; 349 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 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,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/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,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f56,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f60,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f61,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f68,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f70,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f71,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f72,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f73,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f74,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f75,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f76,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f77,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f78,plain,
! [X3] :
( inverse(X3) != sk_c8
| ! [X2] :
( multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| ! [X6] :
( inverse(X6) != sk_c8
| ! [X5] :
( multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f82,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c8 ),
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_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
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
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
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_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
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_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c8 ),
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
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ6_spl
| inverse(sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f108,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f50,f103,f91]) ).
fof(f109,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f51,f103,f95]) ).
fof(f110,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f52,f103,f99]) ).
fof(f111,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f53,f111,f83]) ).
fof(f115,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f111,f87]) ).
fof(f116,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f111,f91]) ).
fof(f117,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f56,f111,f95]) ).
fof(f118,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f57,f111,f99]) ).
fof(f119,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f119,f83]) ).
fof(f123,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f119,f87]) ).
fof(f124,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f119,f91]) ).
fof(f125,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f119,f95]) ).
fof(f126,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f119,f99]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f127,f83]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f127,f87]) ).
fof(f132,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f91]) ).
fof(f133,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f127,f95]) ).
fof(f134,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f127,f99]) ).
fof(f135,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f135,f83]) ).
fof(f139,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f135,f87]) ).
fof(f140,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f135,f91]) ).
fof(f141,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f135,f95]) ).
fof(f142,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f135,f99]) ).
fof(f143,definition,
( sQ11_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f143,f83]) ).
fof(f147,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f143,f87]) ).
fof(f148,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f143,f91]) ).
fof(f149,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f143,f95]) ).
fof(f150,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f143,f99]) ).
fof(f151,definition,
! [X0] :
( sQ12_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
! [X1,X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X3] :
( sQ14_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f80,f103,f151,f154,f157]) ).
fof(f161,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f158,f112]) ).
fof(f162,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f158,f88]) ).
fof(f165,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ8_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f120,f161]) ).
fof(f166,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f84,f162]) ).
fof(f167,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f166]) ).
fof(f168,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f155]) ).
fof(f176,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f96,f42]) ).
fof(f183,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c8
| multiply(sk_c8,sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f136,f169]) ).
fof(f184,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f96,f169]) ).
fof(f185,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f183,f127,f143,f154,f135]) ).
fof(f186,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f184,f91,f99,f154,f95]) ).
fof(f187,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f152,f112]) ).
fof(f188,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f152,f88]) ).
fof(f192,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f120,f187]) ).
fof(f193,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f192]) ).
fof(f194,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f198,definition,
( sQ16_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ16_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f209,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f41,f42]) ).
fof(f210,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f40,f209]) ).
fof(f232,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f40,f210]) ).
fof(f236,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f136,f210]) ).
fof(f241,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f96,f210]) ).
fof(f248,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f144,f236]) ).
fof(f249,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f128,f248]) ).
fof(f250,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f165]) ).
fof(f251,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f100,f241]) ).
fof(f255,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f200]) ).
fof(f256,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f263,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f232,f210]) ).
fof(f265,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f92,f210]) ).
fof(f268,plain,
( ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f88,f210]) ).
fof(f270,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f84,f268]) ).
fof(f274,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f92,f253]) ).
fof(f279,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f274,f105]) ).
fof(f280,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f274,f84]) ).
fof(f283,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f274,f81]) ).
fof(f284,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f274,f96]) ).
fof(f290,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f279]) ).
fof(f291,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f297,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(forward_demodulation,[status(thm)],[f274,f265]) ).
fof(f298,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f297]) ).
fof(f300,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f274,f82]) ).
fof(f302,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f298,f41]) ).
fof(f303,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f298,f40]) ).
fof(f323,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f280,f188]) ).
fof(f324,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f323]) ).
fof(f325,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f339,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f274,f270]) ).
fof(f340,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f274,f339]) ).
fof(f376,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| X0 = multiply(inverse(inverse(sk_c6)),X0) ),
inference(forward_demodulation,[status(thm)],[f298,f263]) ).
fof(f379,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c6) = sk_c6 ),
inference(paramodulation,[status(thm)],[f302,f376]) ).
fof(f393,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| X0 = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f303,f176]) ).
fof(f394,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| X0 = multiply(sk_c5,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f274,f393]) ).
fof(f398,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = multiply(sk_c5,sk_c7) ),
inference(paramodulation,[status(thm)],[f340,f394]) ).
fof(f404,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f284,f398]) ).
fof(f435,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f404,f300]) ).
fof(f452,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f404,f435]) ).
fof(f453,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f379,f452]) ).
fof(f454,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f453]) ).
fof(f455,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f454]) ).
fof(f456,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f90,f94,f98,f102,f108,f109,f110,f114,f115,f116,f117,f118,f122,f123,f124,f125,f126,f130,f131,f132,f133,f134,f138,f139,f140,f141,f142,f146,f147,f148,f149,f150,f160,f168,f185,f186,f194,f251,f256,f291,f325,f455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP241-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n002.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sun Sep 20 20:09:57 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 % Drodi V4.1.1
% 0.13/10.41 % Refutation found
% 0.13/10.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.44 % Elapsed time: 0.057063 seconds
% 0.13/10.44 % CPU time: 0.180148 seconds
% 0.13/10.44 % Total memory used: 103.696 MB
% 0.13/10.44 % Net memory used: 103.530 MB
%------------------------------------------------------------------------------