%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP211-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:33:06 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 46
% Syntax : Number of formulae : 182 ( 12 unt; 17 def)
% Number of atoms : 544 ( 236 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 659 ( 297 ~; 345 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 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_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(X6,sk_c7) != sk_c8
| inverse(X6) != sk_c8
| multiply(X5,sk_c7) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X3] :
( inverse(X3) != sk_c8
| ! [X2] :
( multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| ! [X6] :
( multiply(X6,sk_c7) != sk_c8
| inverse(X6) != sk_c8
| ! [X5] :
( multiply(X5,sk_c7) != sk_c8
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c8 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f60,f63]) ).
fof(f67,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f60,f67]) ).
fof(f71,definition,
( sQ3_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f60,f71]) ).
fof(f75,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f60,f75]) ).
fof(f79,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f60,f79]) ).
fof(f83,definition,
( sQ6_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f83,f63]) ).
fof(f87,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f83,f67]) ).
fof(f88,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f40,f83,f71]) ).
fof(f89,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f41,f83,f75]) ).
fof(f90,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f42,f83,f79]) ).
fof(f91,definition,
( sQ7_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f91,f63]) ).
fof(f95,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f91,f67]) ).
fof(f96,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f91,f71]) ).
fof(f97,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f91,f75]) ).
fof(f98,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f91,f79]) ).
fof(f99,definition,
( sQ8_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f99,f63]) ).
fof(f103,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f99,f67]) ).
fof(f104,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f99,f71]) ).
fof(f105,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f99,f75]) ).
fof(f106,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f99,f79]) ).
fof(f107,definition,
( sQ9_spl
<=> multiply(sk_c3,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f107,f63]) ).
fof(f111,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f107,f67]) ).
fof(f112,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f107,f71]) ).
fof(f113,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f107,f75]) ).
fof(f114,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f107,f79]) ).
fof(f115,definition,
! [X0,X1] :
( sQ10_spl
<=> ( multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0,X1] :
( ~ sQ10_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X2] :
( sQ11_spl
<=> ( multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X4,X5] :
( sQ12_spl
<=> ( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f115,f118,f121]) ).
fof(f125,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f122]) ).
fof(f155,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f76,f125]) ).
fof(f163,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f155,f71,f79,f121,f75]) ).
fof(f164,plain,
! [X0] :
( ~ sQ10_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f116]) ).
fof(f165,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f119,f68]) ).
fof(f167,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f119,f108]) ).
fof(f172,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f64,f165]) ).
fof(f173,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f172]) ).
fof(f174,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f179,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f180,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f179]) ).
fof(f202,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f76,f180]) ).
fof(f204,plain,
( ~ sQ0_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f61,f180]) ).
fof(f207,plain,
( ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f108,f180]) ).
fof(f210,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f80,f202]) ).
fof(f212,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = multiply(sk_c2,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f84,f204]) ).
fof(f213,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f100,f207]) ).
fof(f237,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c7) != sk_c8
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f84,f164]) ).
fof(f246,definition,
( sQ17_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ17_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f237,f246,f91,f115,f83]) ).
fof(f255,plain,
( sQ17_spl
| ~ sQ6_spl
| multiply(sk_c1,sk_c2) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f84,f248]) ).
fof(f256,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f61,f255]) ).
fof(f257,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f256]) ).
fof(f258,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f263,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f264,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f180,f263]) ).
fof(f270,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f212,f180]) ).
fof(f273,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f270]) ).
fof(f274,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f273,f30]) ).
fof(f280,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f290,f273]) ).
fof(f289,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f290,f100]) ).
fof(f290,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f274,f213]) ).
fof(f293,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f280,f264]) ).
fof(f298,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f289,f180]) ).
fof(f299,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f293,f298]) ).
fof(f313,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c8
| multiply(sk_c7,multiply(X0,sk_c8)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f290,f125]) ).
fof(f314,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f293,f313]) ).
fof(f315,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f290,f314]) ).
fof(f316,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f290,f315]) ).
fof(f318,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f316,f299]) ).
fof(f324,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ12_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f289,f318]) ).
fof(f325,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f324]) ).
fof(f326,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f325]) ).
fof(f330,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f289,f167]) ).
fof(f331,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f290,f330]) ).
fof(f332,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f331]) ).
fof(f333,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f368,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f371,f64]) ).
fof(f370,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f371,f68]) ).
fof(f371,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f210,f72]) ).
fof(f373,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f371,f164]) ).
fof(f374,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),sk_c7) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f371,f373]) ).
fof(f382,definition,
( sQ20_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( sQ20_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f394,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f384]) ).
fof(f395,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f404,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f368,f374]) ).
fof(f407,definition,
( sQ23_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( sQ23_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,definition,
( sQ24_spl
<=> multiply(sk_c7,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ24_spl
| multiply(sk_c7,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f404,f407,f410,f115,f79,f75,f71,f63]) ).
fof(f414,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f368,f409]) ).
fof(f424,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f370,f180]) ).
fof(f426,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f368,f424]) ).
fof(f439,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f370,f414]) ).
fof(f440,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f439]) ).
fof(f441,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f440]) ).
fof(f459,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f412]) ).
fof(f460,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f461,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f78,f82,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f102,f103,f104,f105,f106,f110,f111,f112,f113,f114,f124,f163,f174,f249,f258,f326,f333,f395,f413,f441,f460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP211-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n012.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:06:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.41 % Elapsed time: 0.049756 seconds
% 0.08/0.41 % CPU time: 0.139779 seconds
% 0.08/0.41 % Total memory used: 103.486 MB
% 0.08/0.41 % Net memory used: 103.224 MB
%------------------------------------------------------------------------------