%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP291-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:33:19 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 45
% Syntax : Number of formulae : 249 ( 13 unt; 20 def)
% Number of atoms : 956 ( 285 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1369 ( 662 ~; 687 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 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_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X3,X4,X1,X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c5
| multiply(X4,sk_c5) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox/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,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c5
| multiply(X4,sk_c5) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c5
| multiply(X1,sk_c5) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
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
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
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_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| multiply(sk_c3,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
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f79,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f83,definition,
( sQ6_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
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
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f91]) ).
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
<=> multiply(sk_c2,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f99]) ).
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
<=> inverse(sk_c2) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c5 ),
inference(component_clause,[status(thm)],[f107]) ).
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] :
( sQ10_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c5
| multiply(X1,sk_c5) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c7 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
! [X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f125,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ13_spl
| sQ12_spl
| ~ sQ1_spl
| sQ11_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f60,f115,f118,f63,f121,f124]) ).
fof(f128,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f125,f80]) ).
fof(f130,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| sk_c7 != sk_c6
| inverse(sk_c2) != sk_c6 ),
inference(paramodulation,[status(thm)],[f100,f125]) ).
fof(f131,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f76,f128]) ).
fof(f132,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f134,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f122,f72]) ).
fof(f135,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| sk_c5 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f61,f122]) ).
fof(f137,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f134]) ).
fof(f138,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f137]) ).
fof(f139,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f138]) ).
fof(f141,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c5,X0) = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f61,f32]) ).
fof(f142,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f72,f32]) ).
fof(f144,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f84,f32]) ).
fof(f148,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f119,f108]) ).
fof(f149,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| sk_c7 != sk_c5
| multiply(sk_c1,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f92,f119]) ).
fof(f151,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f100,f148]) ).
fof(f152,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f151]) ).
fof(f153,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f156,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f68,f31]) ).
fof(f157,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f92,f31]) ).
fof(f158,plain,
( ~ sQ9_spl
| multiply(sk_c5,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f159,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f160,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f159]) ).
fof(f164,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f156,f32]) ).
fof(f165,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f164]) ).
fof(f181,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f30,f160]) ).
fof(f183,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f160]) ).
fof(f184,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f80,f160]) ).
fof(f185,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f84,f160]) ).
fof(f187,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f183]) ).
fof(f188,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f76,f184]) ).
fof(f189,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f92,f185]) ).
fof(f198,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(resolution,[status(thm)],[f116,f92]) ).
fof(f203,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f84,f198]) ).
fof(f204,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f203]) ).
fof(f205,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f209,definition,
( sQ15_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ15_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f216,definition,
( sQ17_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ17_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f224,definition,
( sQ19_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ19_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f228,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f218]) ).
fof(f229,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f249,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c6) = multiply(sk_c3,sk_c5) ),
inference(paramodulation,[status(thm)],[f188,f142]) ).
fof(f251,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f142]) ).
fof(f255,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| sk_c5 = multiply(sk_c3,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f61,f249]) ).
fof(f256,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f187,f251]) ).
fof(f266,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c7,sk_c5) ),
inference(paramodulation,[status(thm)],[f255,f165]) ).
fof(f279,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f287,f84]) ).
fof(f281,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f287,f116]) ).
fof(f284,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f287,f76]) ).
fof(f285,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f287,f72]) ).
fof(f287,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f255,f256]) ).
fof(f289,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f255,f285]) ).
fof(f295,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f289,f68]) ).
fof(f300,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f289,f266]) ).
fof(f301,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f300,f160]) ).
fof(f303,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f301]) ).
fof(f312,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f279]) ).
fof(f318,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f281]) ).
fof(f319,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f318]) ).
fof(f320,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c5) != sk_c5 ),
inference(resolution,[status(thm)],[f319,f295]) ).
fof(f324,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f255,f320]) ).
fof(f325,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f324]) ).
fof(f326,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f325]) ).
fof(f340,definition,
( sQ20_spl
<=> multiply(sk_c1,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ20_spl
| multiply(sk_c1,sk_c5) != sk_c7 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f149,f340,f224,f118,f91]) ).
fof(f352,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f119]) ).
fof(f353,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f312,f342]) ).
fof(f354,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f353]) ).
fof(f355,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f354]) ).
fof(f356,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,definition,
( sQ21_spl
<=> inverse(sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f135,f357,f224,f121,f60]) ).
fof(f363,plain,
( ~ sQ8_spl
| sk_c5 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f100,f160]) ).
fof(f365,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f108,f363]) ).
fof(f372,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f160,f181]) ).
fof(f373,plain,
! [X0] : X0 = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f181,f160]) ).
fof(f381,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f189,f61]) ).
fof(f382,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f226]) ).
fof(f383,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f382]) ).
fof(f385,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f303,f372]) ).
fof(f387,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f303,f30]) ).
fof(f398,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f303,f31]) ).
fof(f399,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c3) = sk_c5 ),
inference(paramodulation,[status(thm)],[f295,f398]) ).
fof(f400,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(paramodulation,[status(thm)],[f284,f398]) ).
fof(f403,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f387,f399]) ).
fof(f404,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f387,f400]) ).
fof(f421,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f403,f289]) ).
fof(f424,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f425,f403]) ).
fof(f425,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f403,f404]) ).
fof(f427,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f425,f421]) ).
fof(f431,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f425,f68]) ).
fof(f432,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f427,f431]) ).
fof(f435,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f424,f385]) ).
fof(f475,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f424,f352]) ).
fof(f476,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f424,f475]) ).
fof(f477,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f424,f476]) ).
fof(f478,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f477,f432]) ).
fof(f480,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f435,f478]) ).
fof(f481,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f480]) ).
fof(f482,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f381,f211]) ).
fof(f499,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f381,f84]) ).
fof(f506,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f381,f365]) ).
fof(f514,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f381,f157]) ).
fof(f529,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f381,f65]) ).
fof(f535,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c5,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f381,f141]) ).
fof(f536,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(inverse(sk_c5),multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f535,f160]) ).
fof(f538,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f160,f536]) ).
fof(f541,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f381,f144]) ).
fof(f545,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c5) = multiply(sk_c1,sk_c5) ),
inference(paramodulation,[status(thm)],[f506,f541]) ).
fof(f550,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f499,f545]) ).
fof(f556,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f538,f529]) ).
fof(f561,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f556]) ).
fof(f562,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f561]) ).
fof(f566,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f381,f122]) ).
fof(f567,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(X0,sk_c6) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f381,f566]) ).
fof(f568,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f538,f550]) ).
fof(f569,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f568,f483]) ).
fof(f570,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f577,definition,
( sQ22_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( sQ22_spl
| inverse(sk_c2) != sk_c6 ),
inference(component_clause,[status(thm)],[f577]) ).
fof(f580,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f130,f577,f209,f124,f99]) ).
fof(f582,plain,
( sQ22_spl
| ~ sQ9_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f108,f579]) ).
fof(f583,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f568,f538]) ).
fof(f590,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f568,f582]) ).
fof(f591,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f590]) ).
fof(f592,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f593,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f568,f567]) ).
fof(f595,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f583,f514]) ).
fof(f596,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f583,f158]) ).
fof(f603,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c1,X0) ),
inference(backward_demodulation,[status(thm)],[f595,f373]) ).
fof(f607,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f595,f596]) ).
fof(f609,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f607,f603]) ).
fof(f614,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c5) != sk_c5 ),
inference(resolution,[status(thm)],[f593,f108]) ).
fof(f616,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f609,f614]) ).
fof(f617,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f616]) ).
fof(f618,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f647,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = multiply(inverse(sk_c3),sk_c6) ),
inference(paramodulation,[status(thm)],[f256,f160]) ).
fof(f649,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f68,f647]) ).
fof(f650,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f649,f62]) ).
fof(f651,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f652,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f103,f104,f105,f106,f111,f112,f113,f114,f127,f133,f139,f153,f205,f229,f326,f343,f356,f360,f383,f482,f562,f570,f580,f592,f618,f651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP291-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:13:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.049899 seconds
% 0.14/0.41 % CPU time: 0.174862 seconds
% 0.14/0.41 % Total memory used: 75.655 MB
% 0.14/0.41 % Net memory used: 75.517 MB
%------------------------------------------------------------------------------