%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP222-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:33:08 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 41
% Syntax : Number of formulae : 201 ( 12 unt; 23 def)
% Number of atoms : 600 ( 220 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 759 ( 360 ~; 376 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 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_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X5,sk_c7) != sk_c6
| inverse(X4) != X5
| multiply(X4,X5) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f35,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f48,plain,
! [X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| ! [X5] :
( multiply(X5,sk_c7) != sk_c6
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c6
| ! [X3] :
( multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != X2
| multiply(X1,X2) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f50,f53]) ).
fof(f57,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f50,f57]) ).
fof(f61,definition,
( sQ3_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ3_spl
| inverse(sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f50,f61]) ).
fof(f65,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f50,f65]) ).
fof(f69,definition,
( sQ5_spl
<=> multiply(sk_c1,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ5_spl
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f71,plain,
( sQ5_spl
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f32,f69,f53]) ).
fof(f73,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f33,f69,f57]) ).
fof(f74,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f34,f69,f61]) ).
fof(f75,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f35,f69,f65]) ).
fof(f76,definition,
( sQ6_spl
<=> multiply(sk_c2,sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ6_spl
| multiply(sk_c2,sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f36,f76,f53]) ).
fof(f80,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f37,f76,f57]) ).
fof(f83,definition,
( sQ7_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ7_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f83,f53]) ).
fof(f87,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f83,f57]) ).
fof(f90,definition,
( sQ8_spl
<=> multiply(sk_c3,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ8_spl
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f90,f53]) ).
fof(f94,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f90,f57]) ).
fof(f97,definition,
! [X0] :
( sQ9_spl
<=> ( multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f98,plain,
! [X0] :
( ~ sQ9_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
! [X1,X2] :
( sQ10_spl
<=> ( multiply(X2,sk_c7) != sk_c6
| inverse(X1) != X2
| multiply(X1,X2) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0,X1] :
( ~ sQ10_spl
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != X1
| multiply(X0,X1) != sk_c6 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
! [X3] :
( sQ11_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f104,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f49,f97,f100,f103]) ).
fof(f108,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f104,f54]) ).
fof(f111,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f58,f108]) ).
fof(f112,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f111]) ).
fof(f113,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0] :
( ~ sQ10_spl
| multiply(inverse(X0),sk_c7) != sk_c6
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f101]) ).
fof(f115,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f98,f70]) ).
fof(f116,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f98,f66]) ).
fof(f119,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f51,f115]) ).
fof(f120,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f119]) ).
fof(f121,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f123,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f70,f27]) ).
fof(f124,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f77,f27]) ).
fof(f126,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f54,f27]) ).
fof(f130,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c1,inverse(sk_c1)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f51,f114]) ).
fof(f132,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c5,inverse(sk_c5)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f62,f114]) ).
fof(f133,definition,
( sQ12_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f136,definition,
( sQ13_spl
<=> multiply(sk_c7,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ13_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f130,f133,f136,f100,f50]) ).
fof(f144,definition,
( sQ15_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ15_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c6 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f132,f144,f136,f100,f61]) ).
fof(f148,definition,
( sQ16_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ16_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f156,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f150]) ).
fof(f157,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f167,definition,
( sQ18_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f51,f26]) ).
fof(f175,plain,
( ~ sQ7_spl
| multiply(sk_c3,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f84,f26]) ).
fof(f178,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f179,definition,
( sQ20_spl
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ20_spl
| identity != sk_c6 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f186,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f25,f178]) ).
fof(f187,plain,
( sQ15_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f62,f146]) ).
fof(f191,plain,
( ~ sQ10_spl
| identity != sk_c6
| multiply(sk_c7,inverse(sk_c7)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f26,f114]) ).
fof(f192,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c4,inverse(sk_c4)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f58,f114]) ).
fof(f194,definition,
( sQ22_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ22_spl
| multiply(sk_c7,inverse(sk_c7)) != sk_c6 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f191,f194,f179,f100]) ).
fof(f198,definition,
( sQ23_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ23_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c6 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f192,f198,f136,f100,f57]) ).
fof(f203,plain,
( sQ23_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f58,f200]) ).
fof(f204,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f54,f203]) ).
fof(f205,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f204]) ).
fof(f206,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f62,f116]) ).
fof(f209,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f208]) ).
fof(f210,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f213,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(resolution,[status(thm)],[f104,f51]) ).
fof(f214,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c7 != sk_c7
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f51,f104]) ).
fof(f215,definition,
( sQ24_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f218,definition,
( sQ25_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ25_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f214,f215,f218,f103,f50]) ).
fof(f244,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f70,f186]) ).
fof(f246,plain,
( ~ sQ6_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f77,f186]) ).
fof(f249,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f25,f186]) ).
fof(f254,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f51,f244]) ).
fof(f255,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c3 = multiply(sk_c3,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f84,f246]) ).
fof(f259,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f255,f186]) ).
fof(f261,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f26,f259]) ).
fof(f262,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f181]) ).
fof(f263,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c3,sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f261,f175]) ).
fof(f267,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f261,f25]) ).
fof(f286,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| X0 = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f267,f124]) ).
fof(f287,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c2 = multiply(sk_c2,sk_c6) ),
inference(paramodulation,[status(thm)],[f264,f286]) ).
fof(f289,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(paramodulation,[status(thm)],[f91,f286]) ).
fof(f359,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f361,f213]) ).
fof(f361,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f267,f123]) ).
fof(f365,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f359]) ).
fof(f366,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f365]) ).
fof(f367,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f370,plain,
( sQ13_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f138]) ).
fof(f371,plain,
( sQ13_spl
| ~ sQ5_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f370]) ).
fof(f372,plain,
( sQ13_spl
| ~ sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f371]) ).
fof(f374,plain,
( sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f220]) ).
fof(f375,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f379,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f54,f186]) ).
fof(f381,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f58,f379]) ).
fof(f391,plain,
( ~ sQ10_spl
| sk_c7 != sk_c6
| multiply(identity,inverse(identity)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f249,f114]) ).
fof(f395,definition,
( sQ39_spl
<=> multiply(identity,inverse(identity)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( ~ sQ10_spl
| ~ sQ18_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f391,f395,f167,f100]) ).
fof(f404,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f58,f26]) ).
fof(f405,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f62,f26]) ).
fof(f419,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f381,f186]) ).
fof(f421,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f26,f419]) ).
fof(f424,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f421,f26]) ).
fof(f425,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f421,f174]) ).
fof(f428,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f421,f25]) ).
fof(f434,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| sk_c6 != sk_c6
| multiply(sk_c7,inverse(sk_c7)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f424,f114]) ).
fof(f437,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f434,f194,f148,f100,f57,f53]) ).
fof(f441,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f421,f404]) ).
fof(f445,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f421,f405]) ).
fof(f466,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f428,f126]) ).
fof(f467,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = multiply(sk_c4,sk_c6) ),
inference(paramodulation,[status(thm)],[f425,f466]) ).
fof(f468,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(paramodulation,[status(thm)],[f445,f466]) ).
fof(f469,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c4 = multiply(sk_c4,sk_c6) ),
inference(paramodulation,[status(thm)],[f441,f466]) ).
fof(f480,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f483,f71]) ).
fof(f483,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c5 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f467,f468]) ).
fof(f484,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f66,f480]) ).
fof(f485,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f484]) ).
fof(f486,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f485]) ).
fof(f538,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,inverse(sk_c2)) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f541,f196]) ).
fof(f541,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f287,f289]) ).
fof(f543,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f541,f538]) ).
fof(f544,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c3) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f84,f543]) ).
fof(f545,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f77,f544]) ).
fof(f546,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f545]) ).
fof(f547,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f597,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f600,f468]) ).
fof(f598,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f600,f54]) ).
fof(f600,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f468,f469]) ).
fof(f601,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f66,f597]) ).
fof(f602,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f187]) ).
fof(f603,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f621,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f601,f598]) ).
fof(f647,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f601,f138]) ).
fof(f648,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f601,f647]) ).
fof(f649,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f621,f648]) ).
fof(f650,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f649]) ).
fof(f651,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f652,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f60,f64,f68,f72,f73,f74,f75,f79,f80,f86,f87,f93,f94,f106,f113,f121,f139,f147,f157,f197,f201,f206,f210,f221,f263,f367,f372,f375,f398,f437,f486,f547,f603,f651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP222-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 20:07:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.042638 seconds
% 0.14/0.41 % CPU time: 0.107058 seconds
% 0.14/0.41 % Total memory used: 26.487 MB
% 0.14/0.41 % Net memory used: 26.445 MB
%------------------------------------------------------------------------------