%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:33:13 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 38
% Syntax : Number of formulae : 174 ( 12 unt; 16 def)
% Number of atoms : 511 ( 204 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 624 ( 287 ~; 321 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 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
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [X2,X3,X4,X1] :
( inverse(sk_c5) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f35,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f37,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f42,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f44,plain,
( inverse(sk_c5) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| ! [X4] :
( multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( inverse(sk_c5) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f26,f46,f49]) ).
fof(f53,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f27,f46,f53]) ).
fof(f57,definition,
( sQ3_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ3_spl
| inverse(sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f59,plain,
( sQ3_spl
| inverse(sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f46,f57]) ).
fof(f61,definition,
( sQ4_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ4_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f29,f61,f49]) ).
fof(f65,plain,
( sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f30,f61,f53]) ).
fof(f66,plain,
( sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f31,f61,f57]) ).
fof(f67,definition,
( sQ5_spl
<=> multiply(sk_c2,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ5_spl
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f32,f67,f49]) ).
fof(f71,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f33,f67,f53]) ).
fof(f72,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f34,f67,f57]) ).
fof(f73,definition,
( sQ6_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ6_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f35,f73,f49]) ).
fof(f77,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f36,f73,f53]) ).
fof(f78,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f37,f73,f57]) ).
fof(f79,definition,
( sQ7_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ7_spl
| inverse(sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f38,f79,f49]) ).
fof(f83,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f39,f79,f53]) ).
fof(f84,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f79,f57]) ).
fof(f85,definition,
( sQ8_spl
<=> multiply(sk_c3,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ8_spl
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f41,f85,f49]) ).
fof(f89,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f42,f85,f53]) ).
fof(f90,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f43,f85,f57]) ).
fof(f91,definition,
! [X0] :
( sQ9_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f92,plain,
! [X0] :
( ~ sQ9_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,definition,
! [X1] :
( sQ10_spl
<=> ( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f95,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
! [X2] :
( sQ11_spl
<=> ( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f98,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( ~ sQ3_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f45,f91,f94,f97,f57]) ).
fof(f101,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f98,f86]) ).
fof(f103,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f80,f101]) ).
fof(f104,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f103]) ).
fof(f105,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f95,f68]) ).
fof(f108,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f74,f106]) ).
fof(f109,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f108]) ).
fof(f110,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f111,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f92,f47]) ).
fof(f112,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f92,f50]) ).
fof(f115,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f62,f111]) ).
fof(f116,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f115]) ).
fof(f117,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f118,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f54,f112]) ).
fof(f119,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f118]) ).
fof(f120,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f121,definition,
( sQ12_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ12_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f125,plain,
( sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f123]) ).
fof(f126,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f125]) ).
fof(f129,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f50,f25]) ).
fof(f137,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f24,f25]) ).
fof(f138,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f23,f137]) ).
fof(f157,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f23,f138]) ).
fof(f159,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f47,f138]) ).
fof(f160,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f50,f138]) ).
fof(f162,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f62,f159]) ).
fof(f163,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f54,f160]) ).
fof(f171,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f162,f138]) ).
fof(f173,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f24,f171]) ).
fof(f212,definition,
( sQ13_spl
<=> inverse(inverse(sk_c5)) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ13_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f220,plain,
( sQ13_spl
| ~ sQ3_spl
| inverse(sk_c6) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f58,f214]) ).
fof(f234,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f138,f157]) ).
fof(f236,plain,
( ~ sQ10_spl
| inverse(inverse(identity)) != sk_c6
| sk_c6 != sk_c5 ),
inference(paramodulation,[status(thm)],[f157,f95]) ).
fof(f239,definition,
( sQ16_spl
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ16_spl
| sk_c6 != sk_c5 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ17_spl
<=> inverse(inverse(identity)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( sQ17_spl
| inverse(inverse(identity)) != sk_c6 ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f236,f239,f242,f94]) ).
fof(f260,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c7) ),
inference(paramodulation,[status(thm)],[f163,f129]) ).
fof(f263,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f50,f260]) ).
fof(f287,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f263,f138]) ).
fof(f293,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f24,f287]) ).
fof(f294,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f293,f244]) ).
fof(f296,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f293,f24]) ).
fof(f301,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f293,f234]) ).
fof(f309,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(paramodulation,[status(thm)],[f58,f296]) ).
fof(f315,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f301,f309]) ).
fof(f316,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f241]) ).
fof(f317,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f319,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f315,f296]) ).
fof(f324,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f315,f58]) ).
fof(f326,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f98]) ).
fof(f327,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f326]) ).
fof(f331,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sk_c5 != sk_c5
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(paramodulation,[status(thm)],[f319,f327]) ).
fof(f334,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f331,f212,f121,f97,f57,f53,f49]) ).
fof(f336,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f220]) ).
fof(f351,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f324,f336]) ).
fof(f352,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f351]) ).
fof(f353,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(inverse(sk_c5)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f315,f294]) ).
fof(f355,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f324,f354]) ).
fof(f356,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f324,f355]) ).
fof(f357,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f356]) ).
fof(f358,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f362,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f173,f234]) ).
fof(f365,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f80,f138]) ).
fof(f366,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f362,f365]) ).
fof(f380,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f386,f59]) ).
fof(f382,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f386,f80]) ).
fof(f383,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f386,f362]) ).
fof(f384,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f386,f173]) ).
fof(f386,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f366,f86]) ).
fof(f393,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f384,f24]) ).
fof(f394,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c3) = sk_c5 ),
inference(paramodulation,[status(thm)],[f382,f393]) ).
fof(f399,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f383,f394]) ).
fof(f404,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f399,f382]) ).
fof(f406,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f399,f380]) ).
fof(f409,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f399,f406]) ).
fof(f415,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f404,f409]) ).
fof(f416,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f415]) ).
fof(f417,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f418,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f56,f60,f64,f65,f66,f70,f71,f72,f76,f77,f78,f82,f83,f84,f88,f89,f90,f100,f105,f110,f117,f120,f126,f245,f317,f334,f353,f359,f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP253-1 : 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 : n011.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 20:07:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.065263 seconds
% 0.14/0.44 % CPU time: 0.223691 seconds
% 0.14/0.44 % Total memory used: 80.885 MB
% 0.14/0.44 % Net memory used: 80.679 MB
%------------------------------------------------------------------------------