%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP277-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:33:17 PM UTC 2026
% Result : Unsatisfiable 0.01s 0.40s
% Output : CNFRefutation 0.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 34
% Syntax : Number of formulae : 195 ( 16 unt; 18 def)
% Number of atoms : 591 ( 218 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 749 ( 353 ~; 378 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
! [X2,X1,X3,X4] :
( multiply(X4,sk_c7) != sk_c6
| inverse(X3) != X4
| multiply(X3,X4) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/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_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f41,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f50,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f56,plain,
! [X4] :
( multiply(X4,sk_c7) != sk_c6
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != sk_c6
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c7) != sk_c6
| inverse(X2) != X3
| multiply(X2,X3) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f63,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
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_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ2_spl
| inverse(sk_c2) = sk_c7 ),
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_c2,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ3_spl
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f58,f69]) ).
fof(f73,definition,
( sQ4_spl
<=> multiply(sk_c3,sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ4_spl
| multiply(sk_c3,sk_c4) = sk_c6 ),
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
<=> inverse(sk_c3) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ5_spl
| inverse(sk_c3) = sk_c4 ),
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
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ6_spl
| multiply(sk_c4,sk_c7) = sk_c6 ),
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
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
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(f94,definition,
( sQ8_spl
<=> multiply(sk_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( sQ8_spl
| multiply(sk_c7,sk_c5) != sk_c6 ),
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(f103,definition,
( sQ9_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ9_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f105,plain,
( sQ9_spl
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f103,f61]) ).
fof(f112,definition,
! [X0] :
( sQ10_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f113,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
! [X1] :
( sQ11_spl
<=> ( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X2,X3] :
( sQ12_spl
<=> ( multiply(X3,sk_c7) != sk_c6
| inverse(X2) != X3
| multiply(X2,X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sQ12_spl
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != X1
| multiply(X0,X1) != sk_c6 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ12_spl
| sQ11_spl
| ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f57,f112,f94,f103,f61,f115,f118]) ).
fof(f122,plain,
! [X0] :
( ~ sQ12_spl
| multiply(inverse(X0),sk_c7) != sk_c6
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f119]) ).
fof(f124,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f59,f31]) ).
fof(f129,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f66,f30]) ).
fof(f131,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f86,f30]) ).
fof(f132,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f133,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f29,f132]) ).
fof(f135,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f70,f31]) ).
fof(f139,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| multiply(inverse(sk_c3),sk_c7) != sk_c6
| multiply(sk_c3,sk_c4) != sk_c6 ),
inference(paramodulation,[status(thm)],[f78,f122]) ).
fof(f140,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c6
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f86,f122]) ).
fof(f155,definition,
( sQ17_spl
<=> multiply(inverse(sk_c3),sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ17_spl
| multiply(inverse(sk_c3),sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f139,f73,f155,f118,f77]) ).
fof(f159,definition,
( sQ18_spl
<=> multiply(inverse(sk_c1),sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ18_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f140,f58,f159,f118,f85]) ).
fof(f163,plain,
( sQ18_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f86,f161]) ).
fof(f164,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f104,f31]) ).
fof(f165,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f95,f31]) ).
fof(f166,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f131,f31]) ).
fof(f167,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f29,f166]) ).
fof(f170,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| sk_c7 != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f104,f116]) ).
fof(f171,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sk_c7 != sk_c7
| inverse(sk_c2) != sk_c7 ),
inference(paramodulation,[status(thm)],[f70,f116]) ).
fof(f175,definition,
( sQ19_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( sQ19_spl
| inverse(sk_c5) != sk_c7 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ20_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ20_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f170,f175,f178,f115,f103]) ).
fof(f182,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f171,f65,f178,f115,f69]) ).
fof(f197,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f180]) ).
fof(f198,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f208,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(paramodulation,[status(thm)],[f59,f167]) ).
fof(f212,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7) ),
inference(paramodulation,[status(thm)],[f208,f124]) ).
fof(f214,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f59,f212]) ).
fof(f216,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f214,f31]) ).
fof(f227,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c6,multiply(sk_c6,X0)) = multiply(sk_c7,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f164,f165]) ).
fof(f228,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c7,sk_c7) ),
inference(paramodulation,[status(thm)],[f104,f165]) ).
fof(f231,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f216,f227]) ).
fof(f232,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f214,f228]) ).
fof(f247,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c7,sk_c6) ),
inference(paramodulation,[status(thm)],[f232,f231]) ).
fof(f257,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f258,f63]) ).
fof(f258,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f208,f247]) ).
fof(f304,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f232,f133]) ).
fof(f305,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f208,f133]) ).
fof(f306,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f131,f133]) ).
fof(f307,plain,
( ~ sQ8_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f95,f133]) ).
fof(f308,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f133,f133]) ).
fof(f309,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f30,f133]) ).
fof(f316,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f320,f131]) ).
fof(f318,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f320,f29]) ).
fof(f320,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f30,f305]) ).
fof(f321,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = multiply(inverse(sk_c7),sk_c6) ),
inference(forward_demodulation,[status(thm)],[f320,f306]) ).
fof(f325,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f304,f307]) ).
fof(f326,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f257]) ).
fof(f327,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f308,f309]) ).
fof(f330,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 = multiply(sk_c1,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f331,f307]) ).
fof(f331,plain,
( ~ sQ7_spl
| sk_c1 = inverse(sk_c7) ),
inference(forward_demodulation,[status(thm)],[f328,f306]) ).
fof(f332,plain,
( sQ17_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f78,f157]) ).
fof(f333,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f82,f332]) ).
fof(f334,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f333]) ).
fof(f335,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f163]) ).
fof(f338,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f343,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| X0 = multiply(X0,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f344,f328]) ).
fof(f344,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| identity = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f131,f316]) ).
fof(f346,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f318,f62]) ).
fof(f350,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f318,f135]) ).
fof(f352,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c1,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f331,f321]) ).
fof(f357,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f330,f352]) ).
fof(f369,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f344,f129]) ).
fof(f374,plain,
( sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f343,f105]) ).
fof(f379,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ1_spl
| sk_c1 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f346,f357]) ).
fof(f391,plain,
( sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f346,f374]) ).
fof(f392,plain,
( sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f391]) ).
fof(f393,plain,
( sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f397,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f346,f96]) ).
fof(f416,plain,
( ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c3),sk_c6) ),
inference(paramodulation,[status(thm)],[f74,f133]) ).
fof(f420,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f369,f133]) ).
fof(f422,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = inverse(sk_c7) ),
inference(forward_demodulation,[status(thm)],[f343,f420]) ).
fof(f425,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(sk_c1,X0) ),
inference(backward_demodulation,[status(thm)],[f426,f350]) ).
fof(f426,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f331,f422]) ).
fof(f430,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f425,f59]) ).
fof(f432,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sQ8_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f397]) ).
fof(f433,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sQ8_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f434,plain,
( sQ19_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f346,f177]) ).
fof(f435,plain,
( sQ19_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c1 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f331,f434]) ).
fof(f439,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ1_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f435]) ).
fof(f440,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ1_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f480,definition,
( sQ26_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ26_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f490,plain,
( sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f482]) ).
fof(f491,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c4 = multiply(sk_c4,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f78,f416]) ).
fof(f497,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramodulation,[status(thm)],[f59,f113]) ).
fof(f498,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f59,f133]) ).
fof(f500,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f497,f480,f85,f112,f58]) ).
fof(f504,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f70,f133]) ).
fof(f506,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f66,f504]) ).
fof(f527,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f30,f133]) ).
fof(f534,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f328,f527]) ).
fof(f554,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c4) ),
inference(paramodulation,[status(thm)],[f493,f133]) ).
fof(f557,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f30,f554]) ).
fof(f561,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| X0 = multiply(X0,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f557,f328]) ).
fof(f562,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f557,f29]) ).
fof(f569,plain,
( sQ9_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f561,f105]) ).
fof(f574,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 = inverse(sk_c1) ),
inference(backward_demodulation,[status(thm)],[f561,f498]) ).
fof(f576,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f562,f62]) ).
fof(f594,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f574,f85,f77,f73,f58]) ).
fof(f595,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f569]) ).
fof(f596,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f595]) ).
fof(f624,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(X0),X0) ),
inference(paramodulation,[status(thm)],[f561,f133]) ).
fof(f654,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ10_spl
| inverse(inverse(sk_c7)) != sk_c7 ),
inference(resolution,[status(thm)],[f113,f624]) ).
fof(f660,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f534,f654]) ).
fof(f661,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f660]) ).
fof(f662,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f663,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f576,f96]) ).
fof(f664,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f506,f663]) ).
fof(f665,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f664]) ).
fof(f666,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f665]) ).
fof(f667,plain,
$false,
inference(sat_refutation,[status(thm)],[f64,f68,f72,f76,f80,f84,f91,f92,f97,f98,f99,f106,f121,f158,f162,f181,f182,f198,f327,f335,f338,f393,f433,f440,f491,f500,f594,f596,f662,f666]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP277-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:09:02 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.37 % Drodi V4.1.1
% 0.01/0.40 % Refutation found
% 0.01/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.01/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.01/0.43 % Elapsed time: 0.059556 seconds
% 0.01/0.43 % CPU time: 0.207158 seconds
% 0.01/0.43 % Total memory used: 104.627 MB
% 0.01/0.43 % Net memory used: 104.327 MB
%------------------------------------------------------------------------------