%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP236-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:33:10 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 62
% Syntax : Number of formulae : 261 ( 15 unt; 35 def)
% Number of atoms : 810 ( 312 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1046 ( 497 ~; 514 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 36 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 67 ( 67 !; 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_c8) = sk_c7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,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
| multiply(X6,sk_c8) != sk_c7
| inverse(X5) != X6
| multiply(X5,X6) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/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,
inverse(sk_c8) = sk_c7,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f35,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f37,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f39,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f40,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f54,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f56,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f57,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f58,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f60,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] :
( multiply(X6,sk_c8) != sk_c7
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c7
| ! [X4] :
( multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| inverse(sk_c8) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f61,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
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| inverse(sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c8 ),
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
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c7) = 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_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c6) = 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_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
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_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ5_spl
| inverse(sk_c5) = 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_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ6_spl
| multiply(sk_c1,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(f93,definition,
( sQ7_spl
<=> multiply(sk_c2,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c3) = 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
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ8_spl
| inverse(sk_c2) = sk_c3 ),
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
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ9_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
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
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ10_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
! [X0] :
( sQ11_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f121,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
! [X1,X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0,X1] :
( ~ sQ12_spl
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != X1
| multiply(X0,X1) != sk_c7 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,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(f127,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)],[f126]) ).
fof(f129,plain,
( sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f61,f117,f120,f123,f126]) ).
fof(f130,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f127]) ).
fof(f136,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f94,f33]) ).
fof(f137,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f110,f33]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(multiply(X0,X1)) != sk_c8
| multiply(sk_c8,multiply(X0,multiply(X1,sk_c8))) != sk_c7 ),
inference(paramodulation,[status(thm)],[f33,f130]) ).
fof(f144,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f130]) ).
fof(f145,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f110,f130]) ).
fof(f146,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f144,f73,f81,f126,f77]) ).
fof(f147,definition,
( sQ14_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ14_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ15_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f145,f147,f150,f126,f109]) ).
fof(f154,plain,
! [X0] :
( ~ sQ12_spl
| multiply(inverse(X0),sk_c8) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f155,plain,
( sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f34,f119]) ).
fof(f156,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f155]) ).
fof(f157,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f66,f154]) ).
fof(f159,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c5,inverse(sk_c5)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f154]) ).
fof(f161,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| multiply(sk_c3,sk_c8) != sk_c7
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f154]) ).
fof(f162,plain,
( ~ sQ12_spl
| multiply(sk_c7,sk_c8) != sk_c7
| multiply(sk_c8,inverse(sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f34,f154]) ).
fof(f163,definition,
( sQ16_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f166,definition,
( sQ17_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ17_spl
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ17_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f158,f163,f166,f123,f65]) ).
fof(f170,definition,
( sQ18_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ18_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c7 ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f159,f170,f166,f123,f81]) ).
fof(f178,definition,
( sQ20_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ20_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f161,f178,f109,f123,f101]) ).
fof(f182,definition,
( sQ21_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ21_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c7 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ22_spl
<=> multiply(sk_c7,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f162,f182,f185,f123]) ).
fof(f189,plain,
( sQ21_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f34,f184]) ).
fof(f190,plain,
( sQ20_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c3) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f180]) ).
fof(f191,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f94,f190]) ).
fof(f192,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f191]) ).
fof(f193,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f82,f32]) ).
fof(f197,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f63,f32]) ).
fof(f198,plain,
multiply(sk_c7,sk_c8) = identity,
inference(paramodulation,[status(thm)],[f34,f32]) ).
fof(f199,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f32,f33]) ).
fof(f200,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f31,f199]) ).
fof(f216,plain,
( ~ sQ0_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f197,f200]) ).
fof(f218,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f195,f200]) ).
fof(f219,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f200]) ).
fof(f222,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f31,f200]) ).
fof(f225,plain,
( ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f70,f200]) ).
fof(f226,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f78,f200]) ).
fof(f227,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f86,f200]) ).
fof(f230,plain,
( ~ sQ0_spl
| sk_c1 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f34,f216]) ).
fof(f232,plain,
( ~ sQ5_spl
| sk_c5 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f34,f218]) ).
fof(f233,plain,
( ~ sQ3_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f34,f219]) ).
fof(f235,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f66,f225]) ).
fof(f236,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f168]) ).
fof(f237,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f82,f226]) ).
fof(f239,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f238]) ).
fof(f240,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f63,f227]) ).
fof(f243,plain,
( sQ18_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f172]) ).
fof(f244,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f243]) ).
fof(f246,plain,
( ~ sQ12_spl
| identity != sk_c7
| multiply(sk_c8,inverse(sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f32,f154]) ).
fof(f251,definition,
( sQ23_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f246,f182,f251,f123]) ).
fof(f281,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f239,f74]) ).
fof(f285,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f239,f70]) ).
fof(f288,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f239,f66]) ).
fof(f342,definition,
( sQ27_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ27_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f347,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f281,f200]) ).
fof(f349,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f32,f347]) ).
fof(f350,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f285,f200]) ).
fof(f352,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f288,f350]) ).
fof(f353,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f233,f352]) ).
fof(f354,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f244]) ).
fof(f355,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f356,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f121]) ).
fof(f357,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(X0,sk_c7) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f356]) ).
fof(f360,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c7,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f349,f232]) ).
fof(f362,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f349,f31]) ).
fof(f363,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f281,f360]) ).
fof(f368,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f353,f288]) ).
fof(f376,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f378,f353]) ).
fof(f378,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f353,f363]) ).
fof(f380,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f378,f362]) ).
fof(f387,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f378,f368]) ).
fof(f388,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f387,f200]) ).
fof(f389,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f380,f388]) ).
fof(f400,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(X0,sk_c7) != sk_c7
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f376,f357]) ).
fof(f401,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(X0,sk_c5) != sk_c7
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f376,f400]) ).
fof(f402,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f376,f401]) ).
fof(f403,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c5) != sk_c5 ),
inference(resolution,[status(thm)],[f402,f387]) ).
fof(f407,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f389,f403]) ).
fof(f408,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f407]) ).
fof(f409,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f410,plain,
( sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f344]) ).
fof(f411,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f456,plain,
( ~ sQ13_spl
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f198,f130]) ).
fof(f457,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f31,f130]) ).
fof(f458,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f167,f130]) ).
fof(f459,plain,
( ~ sQ13_spl
| inverse(inverse(identity)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f222,f130]) ).
fof(f460,plain,
( ~ sQ13_spl
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f32,f130]) ).
fof(f463,definition,
( sQ28_spl
<=> multiply(sk_c8,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f466,definition,
( sQ29_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( ~ sQ13_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f456,f463,f466,f126]) ).
fof(f470,definition,
( sQ30_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( sQ30_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( ~ sQ13_spl
| ~ sQ30_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f457,f166,f470,f126]) ).
fof(f474,definition,
( sQ31_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ31_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f458,f147,f474,f126,f166]) ).
fof(f478,definition,
( sQ32_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ13_spl
| ~ sQ32_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f459,f166,f478,f126]) ).
fof(f482,definition,
( sQ33_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( ~ sQ13_spl
| ~ sQ33_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f460,f463,f482,f126]) ).
fof(f488,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f240,f166,f62,f85]) ).
fof(f490,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c2,sk_c7) ),
inference(paramodulation,[status(thm)],[f110,f136]) ).
fof(f493,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| identity = multiply(sk_c2,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f198,f490]) ).
fof(f514,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(multiply(sk_c3,sk_c8)) != sk_c8
| multiply(sk_c8,multiply(sk_c7,sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f137,f143]) ).
fof(f517,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| inverse(multiply(sk_c2,sk_c3)) != sk_c8
| multiply(sk_c8,multiply(sk_c7,sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f136,f143]) ).
fof(f519,plain,
! [X0] :
( ~ sQ13_spl
| inverse(multiply(inverse(X0),X0)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f200,f143]) ).
fof(f520,plain,
! [X0] :
( ~ sQ13_spl
| inverse(multiply(inverse(multiply(X0,sk_c8)),X0)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f32,f143]) ).
fof(f528,definition,
( sQ34_spl
<=> multiply(sk_c8,multiply(sk_c7,sk_c8)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f531,definition,
( sQ35_spl
<=> inverse(multiply(sk_c3,sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f514,f528,f531,f126,f109]) ).
fof(f543,definition,
( sQ38_spl
<=> inverse(multiply(sk_c2,sk_c3)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ38_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f517,f528,f543,f126,f93]) ).
fof(f548,definition,
! [X0] :
( sQ39_spl
<=> inverse(multiply(inverse(X0),X0)) != sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( ~ sQ13_spl
| sQ39_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f519,f166,f548,f126]) ).
fof(f552,definition,
! [X0] :
( sQ40_spl
<=> inverse(multiply(inverse(multiply(X0,sk_c8)),X0)) != sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f555,plain,
( ~ sQ13_spl
| sQ40_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f520,f463,f552,f126]) ).
fof(f576,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c2),identity) ),
inference(paramodulation,[status(thm)],[f493,f200]) ).
fof(f578,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c3,identity) ),
inference(forward_demodulation,[status(thm)],[f102,f576]) ).
fof(f585,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,identity) = multiply(sk_c2,sk_c7) ),
inference(paramodulation,[status(thm)],[f578,f136]) ).
fof(f588,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c2,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f230,f585]) ).
fof(f589,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f493,f588]) ).
fof(f597,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c1) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f589,f472]) ).
fof(f602,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c1),X0) ),
inference(backward_demodulation,[status(thm)],[f589,f222]) ).
fof(f603,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f589,f31]) ).
fof(f608,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f63,f597]) ).
fof(f609,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f608]) ).
fof(f610,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f611,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f63,f602]) ).
fof(f615,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f611,f167]) ).
fof(f616,plain,
( sQ14_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f611,f149]) ).
fof(f623,plain,
( sQ14_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f616,f342,f62,f101,f93,f109,f147]) ).
fof(f626,plain,
( sQ21_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f189,f147,f182]) ).
fof(f636,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f615,f63]) ).
fof(f649,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f615,f121]) ).
fof(f650,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,sk_c7) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f615,f649]) ).
fof(f686,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c7) != sk_c7 ),
inference(resolution,[status(thm)],[f636,f650]) ).
fof(f690,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f603,f686]) ).
fof(f691,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f690]) ).
fof(f692,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f691]) ).
fof(f693,plain,
$false,
inference(sat_refutation,[status(thm)],[f68,f72,f76,f80,f84,f88,f89,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f112,f113,f114,f115,f116,f129,f146,f153,f157,f169,f173,f181,f188,f193,f237,f254,f355,f409,f411,f469,f473,f477,f481,f485,f488,f534,f546,f551,f555,f610,f623,f626,f692]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP236-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:08:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.43 % Refutation found
% 0.10/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.072767 seconds
% 0.10/0.45 % CPU time: 0.215386 seconds
% 0.10/0.45 % Total memory used: 104.873 MB
% 0.10/0.45 % Net memory used: 104.564 MB
%------------------------------------------------------------------------------