%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP327-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:33:25 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 56
% Syntax : Number of formulae : 257 ( 17 unt; 21 def)
% Number of atoms : 833 ( 305 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1066 ( 490 ~; 555 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
multiply(sk_c7,sk_c8) = sk_c6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f37,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
multiply(sk_c7,sk_c8) = sk_c6,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f41,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f42,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f43,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f46,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f47,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f48,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f49,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f50,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f52,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f58,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f60,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f61,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f62,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f63,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f64,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f65,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f67,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f68,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f69,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f70,plain,
! [X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c7) != sk_c6
| ! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ1_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ1_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( sQ1_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f72,f75]) ).
fof(f79,definition,
( sQ2_spl
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ2_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( sQ2_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f72,f79]) ).
fof(f83,definition,
( sQ3_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ3_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f72,f83]) ).
fof(f87,definition,
( sQ4_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ4_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f72,f87]) ).
fof(f91,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f72,f91]) ).
fof(f95,definition,
( sQ6_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f72,f95]) ).
fof(f99,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f99,f75]) ).
fof(f103,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f99,f79]) ).
fof(f104,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f99,f83]) ).
fof(f105,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f99,f87]) ).
fof(f106,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f99,f91]) ).
fof(f107,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f99,f95]) ).
fof(f108,definition,
( sQ8_spl
<=> multiply(sk_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f108,f75]) ).
fof(f112,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f108,f79]) ).
fof(f113,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f108,f83]) ).
fof(f114,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f108,f87]) ).
fof(f115,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f108,f91]) ).
fof(f116,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f108,f95]) ).
fof(f117,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f117,f75]) ).
fof(f121,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f117,f79]) ).
fof(f122,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f117,f83]) ).
fof(f123,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f117,f87]) ).
fof(f124,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f117,f91]) ).
fof(f125,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f117,f95]) ).
fof(f126,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f126,f75]) ).
fof(f130,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f126,f79]) ).
fof(f131,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f126,f83]) ).
fof(f132,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f126,f87]) ).
fof(f133,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f126,f91]) ).
fof(f134,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f126,f95]) ).
fof(f135,definition,
( sQ11_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ11_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
! [X0] :
( sQ12_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f139,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
! [X1,X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f142,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
! [X3] :
( sQ14_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f145,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
! [X4] :
( sQ15_spl
<=> ( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f148,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f135,f138,f141,f75,f79,f144,f147]) ).
fof(f151,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f148,f96]) ).
fof(f153,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f92,f151]) ).
fof(f154,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f153]) ).
fof(f155,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f156,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f142]) ).
fof(f157,plain,
( sQ11_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f39,f137]) ).
fof(f158,plain,
( sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f157]) ).
fof(f159,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f160,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f145,f88]) ).
fof(f163,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sk_c8 != sk_c8
| inverse(sk_c1) != sk_c8 ),
inference(paramodulation,[status(thm)],[f73,f145]) ).
fof(f164,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f84,f160]) ).
fof(f165,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f164]) ).
fof(f166,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f167,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f139,f88]) ).
fof(f168,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f139,f73]) ).
fof(f171,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f100,f168]) ).
fof(f172,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f171]) ).
fof(f173,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f176,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f96,f38]) ).
fof(f179,plain,
! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)),
inference(paramodulation,[status(thm)],[f39,f38]) ).
fof(f183,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c8
| multiply(sk_c8,sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f118,f156]) ).
fof(f185,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f183,f108,f126,f141,f117]) ).
fof(f196,definition,
( sQ18_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ18_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f209,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f37,f38]) ).
fof(f217,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f36,f209]) ).
fof(f223,definition,
( sQ23_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ23_spl
| inverse(sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f239,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c5,sk_c7) ),
inference(paramodulation,[status(thm)],[f80,f176]) ).
fof(f241,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f39,f239]) ).
fof(f272,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f36,f217]) ).
fof(f275,plain,
( ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f88,f217]) ).
fof(f276,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f241,f217]) ).
fof(f280,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f118,f217]) ).
fof(f287,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f84,f275]) ).
fof(f288,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f198]) ).
fof(f289,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f92,f276]) ).
fof(f294,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f127,f280]) ).
fof(f305,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f272,f217]) ).
fof(f312,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f290,f217]) ).
fof(f315,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f37,f312]) ).
fof(f323,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f315,f37]) ).
fof(f325,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f315,f36]) ).
fof(f326,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f325,f80]) ).
fof(f329,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f325,f156]) ).
fof(f332,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ23_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f329,f196,f223,f141,f91,f95,f79]) ).
fof(f333,definition,
( sQ25_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ25_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f341,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f84,f167]) ).
fof(f342,plain,
( sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f335]) ).
fof(f343,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f349,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f326,f76]) ).
fof(f354,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f326,f341]) ).
fof(f355,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f354]) ).
fof(f356,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,definition,
( sQ27_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( ~ sQ27_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ27_spl
| inverse(sk_c1) != sk_c8 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ25_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f163,f357,f333,f144,f72]) ).
fof(f371,plain,
( sQ27_spl
| ~ sQ7_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f100,f359]) ).
fof(f372,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f109,f294]) ).
fof(f377,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f372,f100]) ).
fof(f378,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f372,f73]) ).
fof(f379,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f372,f109]) ).
fof(f380,plain,
( sQ27_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f372,f371]) ).
fof(f381,plain,
( sQ27_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f380]) ).
fof(f382,plain,
( sQ27_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f386,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f372,f39]) ).
fof(f408,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f372,f81]) ).
fof(f481,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f379,f217]) ).
fof(f483,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f37,f481]) ).
fof(f507,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f378,f217]) ).
fof(f509,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f377,f507]) ).
fof(f510,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f386,f509]) ).
fof(f524,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f510,f372]) ).
fof(f678,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(paramodulation,[status(thm)],[f349,f323]) ).
fof(f682,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f325,f678]) ).
fof(f693,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f510,f127]) ).
fof(f699,plain,
( ~ sQ27_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f510,f358]) ).
fof(f704,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f524,f77]) ).
fof(f716,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c6) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f524,f73]) ).
fof(f717,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f510,f716]) ).
fof(f744,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f524,f148]) ).
fof(f745,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X0,sk_c6) != sk_c6
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f524,f744]) ).
fof(f746,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c6 ),
inference(resolution,[status(thm)],[f745,f717]) ).
fof(f756,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ27_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f699,f746]) ).
fof(f757,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f756]) ).
fof(f758,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f757]) ).
fof(f772,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c3) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f510,f109]) ).
fof(f773,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c3) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f524,f772]) ).
fof(f794,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f524,f39]) ).
fof(f795,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f510,f794]) ).
fof(f798,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f483,f37]) ).
fof(f800,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c2) = sk_c3 ),
inference(paramodulation,[status(thm)],[f693,f798]) ).
fof(f817,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f510,f408]) ).
fof(f818,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f795,f817]) ).
fof(f819,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f510,f818]) ).
fof(f820,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f819]) ).
fof(f821,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f820]) ).
fof(f823,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f682,f225]) ).
fof(f842,definition,
( sQ28_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f844,plain,
( sQ28_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f849,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f844]) ).
fof(f850,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f849]) ).
fof(f856,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f682,f349]) ).
fof(f857,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f856,f823]) ).
fof(f858,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f857]) ).
fof(f937,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(inverse(inverse(sk_c3)),X0) ),
inference(forward_demodulation,[status(thm)],[f483,f305]) ).
fof(f940,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c3) = sk_c3 ),
inference(paramodulation,[status(thm)],[f798,f937]) ).
fof(f953,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f524,f179]) ).
fof(f954,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f510,f953]) ).
fof(f956,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c2) = multiply(sk_c6,sk_c3) ),
inference(paramodulation,[status(thm)],[f800,f954]) ).
fof(f962,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c3 = multiply(sk_c6,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f800,f956]) ).
fof(f963,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c3 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f773,f962]) ).
fof(f997,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c6) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f963,f704]) ).
fof(f1016,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f963,f997]) ).
fof(f1017,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f940,f1016]) ).
fof(f1018,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1017]) ).
fof(f1019,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1018]) ).
fof(f1020,plain,
$false,
inference(sat_refutation,[status(thm)],[f78,f82,f86,f90,f94,f98,f102,f103,f104,f105,f106,f107,f111,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f125,f129,f130,f131,f132,f133,f134,f150,f155,f159,f166,f173,f185,f289,f332,f343,f356,f360,f382,f758,f821,f850,f858,f1019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP327-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:09:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.064179 seconds
% 0.13/0.43 % CPU time: 0.300151 seconds
% 0.13/0.43 % Total memory used: 108.124 MB
% 0.13/0.43 % Net memory used: 107.754 MB
%------------------------------------------------------------------------------