%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP348-1 : 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 12:33:29 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 35
% Syntax : Number of formulae : 183 ( 12 unt; 11 def)
% Number of atoms : 593 ( 218 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 768 ( 358 ~; 399 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 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_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
! [X2,X3,X1] :
( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c5
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
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_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f48,plain,
! [X1] :
( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| ! [X3] :
( multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c5
| ! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f49,plain,
! [X0,X1,X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(X1,sk_c4) != sk_c5
| inverse(X1) != sk_c5
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,definition,
( sQ0_spl
<=> multiply(sk_c5,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ0_spl
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f52,plain,
( sQ0_spl
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f55,plain,
( sQ1_spl
| inverse(sk_c4) != sk_c5 ),
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_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f59,plain,
( sQ2_spl
| multiply(sk_c4,sk_c5) != sk_c6 ),
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_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c6 ),
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_c3,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ4_spl
| multiply(sk_c3,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
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ5_spl
| inverse(sk_c1) = sk_c6 ),
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_c1,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c5) = 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
<=> inverse(sk_c2) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ7_spl
| inverse(sk_c2) = sk_c5 ),
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
<=> multiply(sk_c2,sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c4) = sk_c5 ),
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_c5) != sk_c6
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f98,plain,
! [X0] :
( ~ sQ9_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
! [X1] :
( sQ10_spl
<=> ( multiply(X1,sk_c4) != sk_c5
| inverse(X1) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0] :
( ~ sQ10_spl
| multiply(X0,sk_c4) != sk_c5
| inverse(X0) != sk_c5 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ10_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f50,f97,f100,f53,f57]) ).
fof(f104,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c5 ),
inference(resolution,[status(thm)],[f101,f91]) ).
fof(f106,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f84,f104]) ).
fof(f107,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c6 ),
inference(resolution,[status(thm)],[f98,f77]) ).
fof(f111,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f98,f66]) ).
fof(f116,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f70,f110]) ).
fof(f117,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f116]) ).
fof(f118,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f62,f111]) ).
fof(f120,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f119]) ).
fof(f121,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f133,plain,
( ~ sQ7_spl
| multiply(sk_c5,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f84,f26]) ).
fof(f134,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f70,f26]) ).
fof(f135,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f136,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f25,f135]) ).
fof(f144,plain,
( ~ sQ5_spl
| sk_c1 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f134,f136]) ).
fof(f147,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f25,f136]) ).
fof(f149,plain,
( ~ sQ7_spl
| sk_c2 = multiply(inverse(sk_c5),identity) ),
inference(paramodulation,[status(thm)],[f133,f136]) ).
fof(f151,plain,
( ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c4) ),
inference(paramodulation,[status(thm)],[f51,f136]) ).
fof(f152,plain,
( ~ sQ6_spl
| sk_c5 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f77,f136]) ).
fof(f153,plain,
( ~ sQ8_spl
| sk_c4 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f91,f136]) ).
fof(f156,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f70,f152]) ).
fof(f157,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c4 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f84,f153]) ).
fof(f163,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f147,f136]) ).
fof(f166,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f156,f136]) ).
fof(f168,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c4) ),
inference(paramodulation,[status(thm)],[f157,f136]) ).
fof(f239,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f26,f163]) ).
fof(f254,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(backward_demodulation,[status(thm)],[f276,f166]) ).
fof(f264,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 = multiply(inverse(sk_c6),identity) ),
inference(backward_demodulation,[status(thm)],[f276,f149]) ).
fof(f270,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c6) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f276,f51]) ).
fof(f271,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f276,f84]) ).
fof(f272,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f276,f55]) ).
fof(f273,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f276,f77]) ).
fof(f276,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f151,f168]) ).
fof(f277,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f26,f254]) ).
fof(f278,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f144,f264]) ).
fof(f280,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(identity) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f277,f239]) ).
fof(f285,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f277,f25]) ).
fof(f286,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f277,f280]) ).
fof(f292,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f278,f273]) ).
fof(f293,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f292,f136]) ).
fof(f295,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f271,f293]) ).
fof(f296,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f270,f295]) ).
fof(f299,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c4) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f296,f272]) ).
fof(f302,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c5 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f296,f276]) ).
fof(f306,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f296,f286]) ).
fof(f307,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f296,f306]) ).
fof(f309,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f296,f285]) ).
fof(f316,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f307,f299]) ).
fof(f317,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f316]) ).
fof(f318,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f309,f59]) ).
fof(f321,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f302,f320]) ).
fof(f322,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f296,f321]) ).
fof(f323,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f322]) ).
fof(f324,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f333,plain,
( ~ sQ2_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f58,f136]) ).
fof(f335,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f54,f333]) ).
fof(f343,plain,
( ~ sQ3_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f62,f26]) ).
fof(f358,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f335,f52]) ).
fof(f359,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f335,f136]) ).
fof(f361,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f26,f359]) ).
fof(f363,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f361,f26]) ).
fof(f365,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f361,f25]) ).
fof(f420,plain,
! [X0] :
( ~ sQ3_spl
| X0 = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f62,f136]) ).
fof(f421,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f365,f420]) ).
fof(f430,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f365,f343]) ).
fof(f432,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f436,f62]) ).
fof(f436,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f361,f430]) ).
fof(f440,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f436,f363]) ).
fof(f445,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f421,f66]) ).
fof(f447,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f450,f54]) ).
fof(f449,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c3 != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f450,f358]) ).
fof(f450,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f436,f445]) ).
fof(f454,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c4) = sk_c3 ),
inference(paramodulation,[status(thm)],[f447,f440]) ).
fof(f456,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f421,f454]) ).
fof(f457,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f449]) ).
fof(f458,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f511,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(X0,sk_c4) != sk_c5
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f450,f101]) ).
fof(f512,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(X0,sk_c4) != sk_c3
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f450,f511]) ).
fof(f578,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(X0,sk_c3) != sk_c3
| inverse(X0) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f456,f512]) ).
fof(f648,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ4_spl
| inverse(inverse(sk_c3)) != sk_c3 ),
inference(resolution,[status(thm)],[f578,f440]) ).
fof(f654,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ4_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f432,f648]) ).
fof(f655,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ4_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f432,f654]) ).
fof(f656,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f655]) ).
fof(f657,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f658,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,f103,f108,f118,f121,f318,f324,f458,f657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP348-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 20:10:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.40 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.043215 seconds
% 0.12/0.43 % CPU time: 0.089381 seconds
% 0.12/0.43 % Total memory used: 23.010 MB
% 0.12/0.43 % Net memory used: 22.969 MB
%------------------------------------------------------------------------------