%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP230-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:33:09 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 61
% Syntax : Number of formulae : 300 ( 13 unt; 34 def)
% Number of atoms : 1099 ( 337 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1536 ( 737 ~; 765 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 35 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 71 !; 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_c3,sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
! [X3,X4,X2,X1,X5,X6] :
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X2) != X1
| multiply(X2,X1) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f30,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f56,plain,
! [X6] :
( inverse(X6) != sk_c8
| ! [X5] :
( multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| ! [X2] :
( inverse(X2) != X1
| multiply(X2,X1) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| ! [X3] :
( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f57,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(X2) != X3
| multiply(X2,X3) != sk_c8
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f58,f61]) ).
fof(f65,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c4 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f58,f65]) ).
fof(f69,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f58,f69]) ).
fof(f73,definition,
( sQ4_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f58,f73]) ).
fof(f77,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f58,f77]) ).
fof(f81,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f58,f81]) ).
fof(f85,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ7_spl
| multiply(sk_c1,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f38,f85,f61]) ).
fof(f89,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f39,f85,f65]) ).
fof(f91,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f85,f73]) ).
fof(f92,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f85,f77]) ).
fof(f93,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f85,f81]) ).
fof(f94,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( sQ8_spl
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f94,f61]) ).
fof(f98,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f94,f65]) ).
fof(f99,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f94,f69]) ).
fof(f100,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f94,f73]) ).
fof(f101,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f94,f77]) ).
fof(f102,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f94,f81]) ).
fof(f103,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f103,f61]) ).
fof(f107,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f103,f65]) ).
fof(f108,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f103,f69]) ).
fof(f109,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f103,f73]) ).
fof(f110,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f103,f77]) ).
fof(f111,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f103,f81]) ).
fof(f112,definition,
! [X0] :
( sQ10_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f113,plain,
! [X0] :
( ~ sQ10_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
! [X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X2,X3] :
( sQ12_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X2) != X3
| multiply(X2,X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sQ12_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X4,X5] :
( sQ13_spl
<=> ( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f122,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)],[f121]) ).
fof(f124,plain,
( sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f57,f112,f115,f118,f121]) ).
fof(f125,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f122]) ).
fof(f156,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f125]) ).
fof(f164,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f156,f73,f81,f121,f77]) ).
fof(f165,plain,
! [X0] :
( ~ sQ12_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f119]) ).
fof(f166,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| multiply(sk_c4,sk_c7) != sk_c8
| multiply(sk_c3,inverse(sk_c3)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f66,f165]) ).
fof(f168,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c7) != sk_c8
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f59,f165]) ).
fof(f169,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(sk_c2,inverse(sk_c2)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f104,f165]) ).
fof(f170,definition,
( sQ16_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ16_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c8 ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f166,f170,f69,f118,f65]) ).
fof(f177,definition,
( sQ18_spl
<=> multiply(sk_c8,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ18_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f181,definition,
( sQ19_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f168,f181,f177,f118,f58]) ).
fof(f185,definition,
( sQ20_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ20_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c8 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
( sQ21_spl
<=> multiply(sk_c7,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f169,f185,f188,f118,f103]) ).
fof(f193,plain,
( sQ20_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f104,f187]) ).
fof(f194,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f95,f193]) ).
fof(f195,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f194]) ).
fof(f196,plain,
( sQ20_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f199,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f82,f30]) ).
fof(f201,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f202,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f29,f201]) ).
fof(f223,plain,
( ~ sQ1_spl
| sk_c4 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f62,f202]) ).
fof(f231,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f78,f202]) ).
fof(f234,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c4,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f66,f223]) ).
fof(f236,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f82,f231]) ).
fof(f237,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f236]) ).
fof(f239,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f237,f199]) ).
fof(f241,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c2,sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f237,f96]) ).
fof(f249,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f237,f82]) ).
fof(f259,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c4,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f237,f234]) ).
fof(f260,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c4) ),
inference(paramodulation,[status(thm)],[f259,f202]) ).
fof(f262,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f30,f260]) ).
fof(f267,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f262,f29]) ).
fof(f270,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f267,f239]) ).
fof(f271,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f277,f267]) ).
fof(f272,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f277,f262]) ).
fof(f274,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f277,f249]) ).
fof(f275,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f277,f237]) ).
fof(f276,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f277,f104]) ).
fof(f277,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f262,f270]) ).
fof(f284,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c2,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f277,f241]) ).
fof(f285,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c2,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f277,f284]) ).
fof(f298,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f276,f202]) ).
fof(f299,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f271,f298]) ).
fof(f300,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| sk_c5 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f299,f285]) ).
fof(f303,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f300]) ).
fof(f304,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f303]) ).
fof(f305,plain,
( sQ16_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c4) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f66,f172]) ).
fof(f308,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f86,f202]) ).
fof(f310,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f59,f308]) ).
fof(f312,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramodulation,[status(thm)],[f86,f116]) ).
fof(f315,definition,
( sQ22_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ22_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,definition,
( sQ23_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ23_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f320,plain,
( sQ23_spl
| inverse(sk_c1) != sk_c7 ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f312,f315,f318,f115,f85]) ).
fof(f322,plain,
( sQ23_spl
| ~ sQ0_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f59,f320]) ).
fof(f323,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f317]) ).
fof(f324,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f325,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f95,f202]) ).
fof(f327,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f104,f325]) ).
fof(f328,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f29,f202]) ).
fof(f368,plain,
( ~ sQ1_spl
| sQ16_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f305]) ).
fof(f369,plain,
( ~ sQ1_spl
| sQ16_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f388,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f202,f328]) ).
fof(f393,definition,
( sQ25_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f396,definition,
( sQ26_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( sQ26_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f416,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f388,f125]) ).
fof(f417,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f327,f125]) ).
fof(f418,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f310,f125]) ).
fof(f420,plain,
( ~ sQ13_spl
| inverse(inverse(identity)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f328,f125]) ).
fof(f422,definition,
( sQ27_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ27_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,definition,
( sQ28_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( ~ sQ13_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f416,f422,f425,f121]) ).
fof(f429,definition,
( sQ29_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ29_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,definition,
( sQ30_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ30_spl
| inverse(sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f417,f429,f432,f121,f103,f94]) ).
fof(f436,definition,
( sQ31_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ31_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f418,f429,f436,f121,f58,f85]) ).
fof(f441,plain,
( ~ sQ13_spl
| ~ sQ25_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f420,f422,f393,f121]) ).
fof(f442,plain,
( sQ27_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f310,f424]) ).
fof(f443,plain,
( sQ27_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f442]) ).
fof(f444,plain,
( sQ27_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f453,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c1) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f275,f59]) ).
fof(f458,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f272,f29]) ).
fof(f466,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f272,f30]) ).
fof(f472,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f275,f113]) ).
fof(f473,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,sk_c5) != sk_c8
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f277,f472]) ).
fof(f474,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f275,f473]) ).
fof(f475,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ10_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(resolution,[status(thm)],[f474,f466]) ).
fof(f480,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ10_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f274,f475]) ).
fof(f481,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f274,f480]) ).
fof(f482,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f481]) ).
fof(f483,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f484,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f277,f116]) ).
fof(f485,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f275,f484]) ).
fof(f486,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f277,f485]) ).
fof(f490,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c1,sk_c5) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f277,f87]) ).
fof(f491,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c1,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f275,f490]) ).
fof(f494,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c1) = sk_c5 ),
inference(paramodulation,[status(thm)],[f453,f466]) ).
fof(f496,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f458,f494]) ).
fof(f499,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f496,f491]) ).
fof(f500,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f458,f499]) ).
fof(f501,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f500]) ).
fof(f502,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f503,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f275,f322]) ).
fof(f504,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f277,f503]) ).
fof(f505,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f504]) ).
fof(f506,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f512,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f113,f86]) ).
fof(f516,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f59,f512]) ).
fof(f517,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f516]) ).
fof(f518,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f527,plain,
( ~ sQ9_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f104,f30]) ).
fof(f542,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f327,f202]) ).
fof(f544,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f30,f542]) ).
fof(f547,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f544,f30]) ).
fof(f550,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f544,f388]) ).
fof(f561,plain,
( sQ29_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f550,f431]) ).
fof(f562,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f550,f310]) ).
fof(f565,plain,
( sQ29_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f561]) ).
fof(f566,plain,
( sQ29_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f567,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f562,f322]) ).
fof(f568,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f569,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f550,f179]) ).
fof(f571,plain,
( ~ sQ23_spl
| ~ sQ0_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f59,f319]) ).
fof(f572,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f562,f569]) ).
fof(f573,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f572]) ).
fof(f575,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f571,f550]) ).
fof(f576,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f571,f544]) ).
fof(f579,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f571,f59]) ).
fof(f581,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f571,f547]) ).
fof(f586,plain,
( sQ26_spl
| ~ sQ23_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f571,f398]) ).
fof(f587,plain,
( sQ26_spl
| ~ sQ23_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f586]) ).
fof(f588,plain,
( sQ26_spl
| ~ sQ23_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f594,plain,
( sQ30_spl
| ~ sQ23_spl
| ~ sQ0_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f571,f434]) ).
fof(f597,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f571,f165]) ).
fof(f598,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c7) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f571,f597]) ).
fof(f601,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f104,f598]) ).
fof(f605,definition,
( sQ33_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( sQ33_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f605]) ).
fof(f609,definition,
( sQ34_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f612,definition,
( sQ35_spl
<=> multiply(sk_c7,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f601,f609,f612,f58,f318,f118,f103]) ).
fof(f617,plain,
( sQ33_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f607]) ).
fof(f618,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f624,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ12_spl
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c1,inverse(sk_c1)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f579,f598]) ).
fof(f625,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c1) = sk_c7 ),
inference(paramodulation,[status(thm)],[f579,f581]) ).
fof(f627,definition,
( sQ36_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ12_spl
| ~ sQ35_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f624,f627,f612,f118,f318,f58]) ).
fof(f631,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f575,f625]) ).
fof(f634,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f631,f579]) ).
fof(f645,plain,
( sQ30_spl
| ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f634,f594]) ).
fof(f646,plain,
( sQ30_spl
| ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f645]) ).
fof(f647,plain,
( sQ30_spl
| ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f657,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ23_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f575,f527]) ).
fof(f658,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f670,f634]) ).
fof(f660,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f670,f575]) ).
fof(f662,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(inverse(X0),sk_c7) != sk_c2
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f670,f598]) ).
fof(f670,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ23_spl
| ~ sQ0_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f576,f657]) ).
fof(f671,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f670,f658]) ).
fof(f673,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(inverse(X0),sk_c7) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f670,f662]) ).
fof(f674,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f670,f673]) ).
fof(f685,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c2) != sk_c2
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(paramodulation,[status(thm)],[f671,f674]) ).
fof(f686,definition,
( sQ37_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( sQ37_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(component_clause,[status(thm)],[f686]) ).
fof(f689,definition,
( sQ38_spl
<=> multiply(sk_c2,sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( sQ38_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f685,f686,f689,f118,f103,f94,f318,f58]) ).
fof(f693,plain,
( sQ37_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f660,f688]) ).
fof(f694,plain,
( sQ37_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f671,f693]) ).
fof(f695,plain,
( sQ37_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f694]) ).
fof(f696,plain,
( sQ37_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f695]) ).
fof(f697,plain,
( sQ38_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f660,f691]) ).
fof(f698,plain,
( sQ38_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f697]) ).
fof(f699,plain,
( sQ38_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ23_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f698]) ).
fof(f718,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f272,f30]) ).
fof(f747,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(resolution,[status(thm)],[f486,f718]) ).
fof(f753,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f274,f747]) ).
fof(f754,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f274,f753]) ).
fof(f755,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f754]) ).
fof(f756,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f755]) ).
fof(f757,plain,
$false,
inference(sat_refutation,[status(thm)],[f64,f68,f72,f76,f80,f84,f88,f89,f91,f92,f93,f97,f98,f99,f100,f101,f102,f106,f107,f108,f109,f110,f111,f124,f164,f173,f184,f191,f196,f304,f321,f324,f369,f428,f435,f439,f441,f444,f483,f502,f506,f518,f566,f568,f573,f588,f615,f618,f630,f647,f692,f696,f699,f756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP230-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:07:18 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % 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
% 0.13/0.40 % Elapsed time: 0.047742 seconds
% 0.13/0.40 % CPU time: 0.146303 seconds
% 0.13/0.40 % Total memory used: 27.548 MB
% 0.13/0.40 % Net memory used: 27.480 MB
%------------------------------------------------------------------------------