%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP310-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:33:23 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 44
% Syntax : Number of formulae : 191 ( 13 unt; 14 def)
% Number of atoms : 602 ( 241 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 745 ( 334 ~; 397 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 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_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f32,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f33,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f34,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f37,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f42,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f43,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f53,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f56,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f57,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f60,plain,
! [X5] :
( inverse(X5) != sk_c8
| ! [X2] :
( multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c8
| ! [X3] :
( multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f64,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f62,f65]) ).
fof(f69,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f62,f69]) ).
fof(f73,definition,
( sQ3_spl
<=> multiply(sk_c8,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f62,f73]) ).
fof(f77,definition,
( sQ4_spl
<=> multiply(sk_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ4_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f62,f77]) ).
fof(f81,definition,
( sQ5_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f62,f81]) ).
fof(f85,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ6_spl
| multiply(sk_c6,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f40,f85,f65]) ).
fof(f89,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f41,f85,f69]) ).
fof(f90,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f42,f85,f73]) ).
fof(f91,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f85,f77]) ).
fof(f92,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f85,f81]) ).
fof(f93,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f93,f65]) ).
fof(f97,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f93,f69]) ).
fof(f98,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f93,f73]) ).
fof(f99,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f93,f77]) ).
fof(f100,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f93,f81]) ).
fof(f101,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c8) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f101,f65]) ).
fof(f105,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f101,f69]) ).
fof(f106,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f101,f73]) ).
fof(f107,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f101,f77]) ).
fof(f108,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f101,f81]) ).
fof(f109,definition,
( sQ9_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f109,f65]) ).
fof(f113,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f109,f69]) ).
fof(f114,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f109,f73]) ).
fof(f115,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f109,f77]) ).
fof(f116,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f109,f81]) ).
fof(f117,definition,
( sQ10_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ10_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
! [X0,X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f121,plain,
! [X0,X1] :
( ~ sQ11_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
! [X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ12_spl
| sQ11_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f61,f117,f62,f85,f120,f123]) ).
fof(f127,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f124,f66]) ).
fof(f130,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c8
| sk_c2 != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f124]) ).
fof(f131,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f70,f127]) ).
fof(f132,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f121]) ).
fof(f135,plain,
( sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f34,f119]) ).
fof(f136,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f135]) ).
fof(f137,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f136]) ).
fof(f145,plain,
! [X0] : multiply(sk_c6,X0) = multiply(sk_c8,multiply(sk_c7,X0)),
inference(paramodulation,[status(thm)],[f34,f33]) ).
fof(f150,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f134]) ).
fof(f151,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c2) != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f134]) ).
fof(f156,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f150,f73,f81,f120,f77]) ).
fof(f157,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f151,f93,f109,f120,f101]) ).
fof(f162,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f32,f33]) ).
fof(f163,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f31,f162]) ).
fof(f177,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f66,f163]) ).
fof(f178,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f78,f163]) ).
fof(f179,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f102,f163]) ).
fof(f186,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f70,f177]) ).
fof(f187,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f34,f186]) ).
fof(f188,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f82,f178]) ).
fof(f189,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f188]) ).
fof(f190,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c8,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f110,f179]) ).
fof(f196,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f187,f70]) ).
fof(f197,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f187,f64]) ).
fof(f199,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f187,f74]) ).
fof(f203,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f187,f82]) ).
fof(f205,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f187,f189]) ).
fof(f207,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f196,f32]) ).
fof(f214,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f203,f32]) ).
fof(f230,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f205,f199]) ).
fof(f231,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f230,f163]) ).
fof(f233,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f32,f231]) ).
fof(f234,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f233,f32]) ).
fof(f235,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f233,f31]) ).
fof(f322,definition,
( sQ14_spl
<=> sk_c2 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( sQ14_spl
| sk_c2 != sk_c7 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f130,f322,f109,f123,f101]) ).
fof(f330,plain,
( ~ sQ7_spl
| sk_c2 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f94,f163]) ).
fof(f332,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f63,f330]) ).
fof(f333,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f86,f332]) ).
fof(f334,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f333,f94]) ).
fof(f347,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = multiply(sk_c8,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f333,f190]) ).
fof(f348,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = multiply(sk_c2,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f333,f347]) ).
fof(f372,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f348,f334]) ).
fof(f373,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f324]) ).
fof(f374,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f375,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| identity = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f32,f234]) ).
fof(f382,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f187,f34]) ).
fof(f383,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f205,f382]) ).
fof(f390,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f205,f87]) ).
fof(f391,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f383,f390]) ).
fof(f392,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f187,f391]) ).
fof(f393,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f392]) ).
fof(f394,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f393]) ).
fof(f407,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f205,f199]) ).
fof(f433,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f375,f214]) ).
fof(f443,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c3) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f375,f207]) ).
fof(f460,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f187,f145]) ).
fof(f461,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f205,f460]) ).
fof(f463,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c3) = multiply(sk_c6,sk_c5) ),
inference(paramodulation,[status(thm)],[f443,f461]) ).
fof(f470,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f443,f463]) ).
fof(f471,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f407,f470]) ).
fof(f492,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f471,f433]) ).
fof(f496,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c6) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f471,f197]) ).
fof(f499,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f471,f203]) ).
fof(f511,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f235,f492]) ).
fof(f513,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f471,f496]) ).
fof(f557,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f511,f499]) ).
fof(f566,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f511,f513]) ).
fof(f567,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c4 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f557,f566]) ).
fof(f568,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f511,f567]) ).
fof(f569,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f568]) ).
fof(f570,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f571,plain,
$false,
inference(sat_refutation,[status(thm)],[f68,f72,f76,f80,f84,f88,f89,f90,f91,f92,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f112,f113,f114,f115,f116,f126,f133,f137,f156,f157,f325,f374,f394,f570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP310-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:09:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.041483 seconds
% 0.14/0.42 % CPU time: 0.116078 seconds
% 0.14/0.42 % Total memory used: 23.772 MB
% 0.14/0.42 % Net memory used: 23.708 MB
%------------------------------------------------------------------------------