%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:09 PM UTC 2026
% Result : Unsatisfiable 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 46
% Syntax : Number of formulae : 182 ( 11 unt; 22 def)
% Number of atoms : 519 ( 215 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 618 ( 281 ~; 315 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 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,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| inverse(X5) != sk_c7
| multiply(X5,sk_c7) != X4
| multiply(sk_c7,X4) != 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,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f35,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f48,plain,
! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| ! [X5] :
( inverse(X5) != sk_c7
| ! [X4] :
( multiply(X5,sk_c7) != X4
| multiply(sk_c7,X4) != 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] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X1
| multiply(sk_c7,X1) != 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
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c7 ),
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
<=> multiply(sk_c4,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c6) = 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
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c6) = 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
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c6 ),
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(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_c7,sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ6_spl
| multiply(sk_c7,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(f81,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f76,f61]) ).
fof(f82,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f76,f65]) ).
fof(f83,definition,
( sQ7_spl
<=> multiply(sk_c2,sk_c7) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c7) = 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(f88,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f83,f61]) ).
fof(f89,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f83,f65]) ).
fof(f90,definition,
( sQ8_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ8_spl
| inverse(sk_c2) = sk_c7 ),
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(f95,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f90,f61]) ).
fof(f96,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f90,f65]) ).
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
<=> ( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X1
| multiply(sk_c7,X1) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0,X1] :
( ~ sQ10_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
! [X4] :
( sQ11_spl
<=> ( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f104,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
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(f109,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| inverse(sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f104,f62]) ).
fof(f110,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f70,f104]) ).
fof(f111,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f58,f104]) ).
fof(f115,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f66,f109]) ).
fof(f116,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f115]) ).
fof(f117,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f101]) ).
fof(f119,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f98,f70]) ).
fof(f120,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f98,f58]) ).
fof(f125,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f51,f119]) ).
fof(f126,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f125]) ).
fof(f127,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f130,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f77,f27]) ).
fof(f133,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f62,f27]) ).
fof(f147,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f130,f118]) ).
fof(f149,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c7
| multiply(sk_c7,sk_c3) != sk_c6 ),
inference(paramodulation,[status(thm)],[f84,f118]) ).
fof(f150,definition,
( sQ12_spl
<=> multiply(sk_c6,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ12_spl
| multiply(sk_c6,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ13_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f147,f150,f153,f100,f76]) ).
fof(f157,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f149,f76,f90,f100,f83]) ).
fof(f158,definition,
( sQ14_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ14_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,definition,
( sQ15_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( sQ15_spl
| inverse(sk_c1) != sk_c6 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f110,f158,f161,f103,f69]) ).
fof(f165,definition,
( sQ16_spl
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f158,f165,f103,f57]) ).
fof(f170,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f160]) ).
fof(f171,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( sQ15_spl
| ~ sQ0_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f51,f163]) ).
fof(f177,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f54,f26]) ).
fof(f178,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f179,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f25,f178]) ).
fof(f196,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f25,f179]) ).
fof(f200,plain,
( ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f58,f179]) ).
fof(f201,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f62,f179]) ).
fof(f203,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f54,f200]) ).
fof(f204,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f66,f201]) ).
fof(f205,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f152]) ).
fof(f206,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f216,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ10_spl
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f203,f118]) ).
fof(f217,plain,
( ~ sQ10_spl
| inverse(inverse(identity)) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f196,f118]) ).
fof(f219,plain,
( ~ sQ10_spl
| inverse(identity) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f25,f118]) ).
fof(f221,definition,
( sQ17_spl
<=> multiply(sk_c7,sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( sQ17_spl
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ18_spl
<=> inverse(sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ18_spl
| inverse(sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f216,f221,f224,f100,f53,f57]) ).
fof(f228,definition,
( sQ19_spl
<=> multiply(sk_c7,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ19_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,definition,
( sQ20_spl
<=> inverse(inverse(identity)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f217,f228,f231,f100]) ).
fof(f242,definition,
( sQ23_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ10_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f219,f228,f242,f100]) ).
fof(f246,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f203,f230]) ).
fof(f247,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f246]) ).
fof(f248,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f261,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c5,sk_c6) ),
inference(paramodulation,[status(thm)],[f204,f133]) ).
fof(f264,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f204,f179]) ).
fof(f266,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f203,f261]) ).
fof(f267,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f62,f266]) ).
fof(f274,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f26,f264]) ).
fof(f282,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f267,f177]) ).
fof(f288,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f267,f54]) ).
fof(f295,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f296,f25]) ).
fof(f296,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f267,f274]) ).
fof(f305,plain,
( sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f267,f223]) ).
fof(f306,plain,
( sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f295,f305]) ).
fof(f307,plain,
( sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f306]) ).
fof(f308,plain,
( sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f312,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f288,f120]) ).
fof(f313,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f267,f312]) ).
fof(f314,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f313]) ).
fof(f315,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f316,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f267,f226]) ).
fof(f317,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f267,f316]) ).
fof(f349,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f295,f282]) ).
fof(f351,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f352,f288]) ).
fof(f352,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f296,f349]) ).
fof(f353,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f317]) ).
fof(f354,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f373,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f84,f179]) ).
fof(f375,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f91,f373]) ).
fof(f410,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f77,f375]) ).
fof(f411,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sQ15_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f173]) ).
fof(f412,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sQ15_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f411]) ).
fof(f413,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f60,f64,f68,f72,f73,f74,f75,f79,f80,f81,f82,f86,f87,f88,f89,f93,f94,f95,f96,f106,f117,f127,f156,f157,f164,f168,f171,f206,f227,f234,f245,f248,f308,f315,f354,f412]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.37 % Computer : n019.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Sun Sep 20 20:07:15 UTC 2026
% 0.11/10.37 % CPUTime :
% 0.11/10.38 % Drodi V4.1.1
% 0.14/10.41 % Refutation found
% 0.14/10.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.43 % Elapsed time: 0.047147 seconds
% 0.14/10.43 % CPU time: 0.156759 seconds
% 0.14/10.43 % Total memory used: 77.703 MB
% 0.14/10.43 % Net memory used: 77.544 MB
%------------------------------------------------------------------------------