%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP390-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:33:36 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.62s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 55
% Syntax : Number of formulae : 278 ( 13 unt; 28 def)
% Number of atoms : 913 ( 311 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1200 ( 565 ~; 607 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 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_c4,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(X6,sk_c7) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f42,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f54,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f60,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f68,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f74,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f77,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f80,plain,
! [X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X6] :
( multiply(X6,sk_c7) != sk_c8
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| ! [X4] :
( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c8) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5] :
( multiply(X5,sk_c8) != sk_c9
| inverse(X5) != sk_c9
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| inverse(sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f82,f85]) ).
fof(f89,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f82,f89]) ).
fof(f93,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f82,f93]) ).
fof(f97,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f82,f97]) ).
fof(f101,definition,
( sQ5_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f105,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f109,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f109,f85]) ).
fof(f113,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f109,f89]) ).
fof(f116,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f109,f101]) ).
fof(f117,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f109,f105]) ).
fof(f118,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f118,f85]) ).
fof(f122,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f118,f89]) ).
fof(f125,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f118,f101]) ).
fof(f126,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f118,f105]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f127,f85]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f127,f89]) ).
fof(f132,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f127,f93]) ).
fof(f133,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f97]) ).
fof(f136,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f136,f85]) ).
fof(f140,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f136,f89]) ).
fof(f141,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f136,f93]) ).
fof(f142,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f136,f97]) ).
fof(f145,definition,
( sQ11_spl
<=> multiply(sk_c3,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ11_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f145,f85]) ).
fof(f149,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f145,f89]) ).
fof(f151,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f145,f97]) ).
fof(f154,definition,
! [X0] :
( sQ12_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X1,X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c7) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
! [X4] :
( sQ15_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f157,f160,f163]) ).
fof(f167,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f164,f94]) ).
fof(f171,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f167]) ).
fof(f172,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f171]) ).
fof(f173,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f158]) ).
fof(f175,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c9 ),
inference(resolution,[status(thm)],[f161,f86]) ).
fof(f177,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f90,f175]) ).
fof(f178,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f177]) ).
fof(f179,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f184,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f119,f43]) ).
fof(f189,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(sk_c8,inverse(sk_c8)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f83,f174]) ).
fof(f192,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c7) != sk_c8
| multiply(sk_c2,inverse(sk_c2)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f137,f174]) ).
fof(f193,definition,
( sQ16_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ16_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ17_spl
<=> multiply(sk_c7,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f189,f193,f196,f157,f82]) ).
fof(f211,definition,
( sQ21_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ21_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c8 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f192,f211,f145,f157,f136]) ).
fof(f215,plain,
( sQ21_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c3) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f137,f213]) ).
fof(f216,plain,
( sQ21_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f128,f215]) ).
fof(f217,plain,
( sQ21_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f216]) ).
fof(f218,plain,
( sQ21_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f221,plain,
( sQ16_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f83,f195]) ).
fof(f226,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f110,f42]) ).
fof(f228,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f229,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f228]) ).
fof(f234,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f226,f43]) ).
fof(f235,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c9,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f234]) ).
fof(f247,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f41,f229]) ).
fof(f249,plain,
( ~ sQ1_spl
| sk_c9 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f86,f229]) ).
fof(f253,plain,
( ~ sQ9_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f128,f229]) ).
fof(f259,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = multiply(sk_c3,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f137,f253]) ).
fof(f269,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| inverse(sk_c6) != sk_c9 ),
inference(resolution,[status(thm)],[f155,f106]) ).
fof(f270,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f155,f119]) ).
fof(f279,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ5_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f102,f269]) ).
fof(f280,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f279]) ).
fof(f281,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f282,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ7_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f110,f270]) ).
fof(f283,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f282]) ).
fof(f284,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f285,definition,
( sQ22_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ22_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f290,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f98,f42]) ).
fof(f300,plain,
( ~ sQ13_spl
| sk_c7 != sk_c8
| multiply(identity,inverse(identity)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f247,f174]) ).
fof(f301,plain,
( ~ sQ13_spl
| identity != sk_c8
| multiply(sk_c7,inverse(sk_c7)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f42,f174]) ).
fof(f307,definition,
( sQ23_spl
<=> multiply(identity,inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ23_spl
| multiply(identity,inverse(identity)) != sk_c8 ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,definition,
( sQ24_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ24_spl
| sk_c7 = sk_c8 ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f312,plain,
( sQ24_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,plain,
( ~ sQ13_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f300,f307,f310,f157]) ).
fof(f314,definition,
( sQ25_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f317,definition,
( sQ26_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( ~ sQ26_spl
| identity = sk_c8 ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f319,plain,
( sQ26_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f301,f314,f317,f157]) ).
fof(f335,plain,
( sQ23_spl
| inverse(identity) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f41,f309]) ).
fof(f392,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f287]) ).
fof(f393,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f397,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(paramodulation,[status(thm)],[f119,f235]) ).
fof(f436,definition,
( sQ35_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ35_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f454,plain,
( ~ sQ15_spl
| inverse(inverse(identity)) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f247,f164]) ).
fof(f456,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f41,f164]) ).
fof(f467,definition,
( sQ40_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ40_spl
| inverse(inverse(identity)) != sk_c8 ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( ~ sQ15_spl
| ~ sQ40_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f454,f310,f467,f163]) ).
fof(f475,definition,
( sQ42_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ42_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,plain,
( ~ sQ15_spl
| ~ sQ42_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f456,f310,f475,f163]) ).
fof(f534,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f90,f249]) ).
fof(f536,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f534,f229]) ).
fof(f539,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f536]) ).
fof(f540,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f319]) ).
fof(f541,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f548,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f259,f229]) ).
fof(f550,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f548]) ).
fof(f554,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(inverse(sk_c8),X0) ),
inference(backward_demodulation,[status(thm)],[f550,f247]) ).
fof(f556,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f550,f42]) ).
fof(f558,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f83,f554]) ).
fof(f561,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c7),X0) ),
inference(paramodulation,[status(thm)],[f558,f229]) ).
fof(f613,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c7 = sk_c8 ),
inference(paramodulation,[status(thm)],[f556,f561]) ).
fof(f615,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c7 = sk_c8 ),
inference(paramodulation,[status(thm)],[f561,f556]) ).
fof(f619,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f312]) ).
fof(f620,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f628,plain,
( sQ42_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f550,f477]) ).
fof(f629,plain,
( sQ42_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f83,f628]) ).
fof(f639,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f615,f550]) ).
fof(f653,plain,
( sQ42_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f615,f629]) ).
fof(f654,plain,
( sQ42_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f653]) ).
fof(f655,plain,
( sQ42_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f656,plain,
( sQ35_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f438]) ).
fof(f657,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f660,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f539,f335]) ).
fof(f679,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f539,f290]) ).
fof(f693,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f696,f679]) ).
fof(f696,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f539,f41]) ).
fof(f699,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f693,f696]) ).
fof(f712,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f693,f94]) ).
fof(f713,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f693,f98]) ).
fof(f714,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c8) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f693,f660]) ).
fof(f719,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f693,f539]) ).
fof(f722,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f693,f714]) ).
fof(f728,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f713,f722]) ).
fof(f729,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f728]) ).
fof(f730,plain,
( sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f776,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f693,f83]) ).
fof(f777,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f713,f776]) ).
fof(f794,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f693,f221]) ).
fof(f795,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f699,f794]) ).
fof(f796,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f693,f795]) ).
fof(f800,plain,
( sQ24_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f693,f312]) ).
fof(f805,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f777,f796]) ).
fof(f806,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f805]) ).
fof(f825,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f550,f317,f136,f127]) ).
fof(f829,plain,
( ~ sQ0_spl
| ~ sQ24_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f311,f83]) ).
fof(f835,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ24_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f311,f161]) ).
fof(f842,plain,
( ~ sQ11_spl
| ~ sQ24_spl
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f311,f146]) ).
fof(f844,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ24_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f842,f43]) ).
fof(f845,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ24_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f558,f844]) ).
fof(f846,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ24_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f558,f845]) ).
fof(f861,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f639,f42]) ).
fof(f863,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c2) = sk_c7 ),
inference(paramodulation,[status(thm)],[f137,f861]) ).
fof(f869,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f846,f863]) ).
fof(f873,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f869,f835]) ).
fof(f875,plain,
( ~ sQ0_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| inverse(sk_c7) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f869,f829]) ).
fof(f876,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f869,f639]) ).
fof(f878,plain,
( ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f869,f311]) ).
fof(f879,plain,
( ~ sQ0_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f869,f875]) ).
fof(f880,plain,
( ~ sQ0_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f137,f879]) ).
fof(f881,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f880,f869]) ).
fof(f883,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f880,f876]) ).
fof(f885,plain,
( ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f880,f878]) ).
fof(f905,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f885,f397]) ).
fof(f954,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f880,f873]) ).
fof(f961,definition,
( sQ49_spl
<=> sk_c3 = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f963,plain,
( sQ49_spl
| sk_c3 != sk_c3 ),
inference(component_clause,[status(thm)],[f961]) ).
fof(f970,plain,
( sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f963]) ).
fof(f971,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f970]) ).
fof(f981,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| ~ sQ26_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f318,f883]) ).
fof(f988,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f881,f639]) ).
fof(f996,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f988,f41]) ).
fof(f1115,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| ~ sQ26_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f981,f184]) ).
fof(f1116,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ26_spl
| sk_c3 = multiply(sk_c1,sk_c9) ),
inference(backward_demodulation,[status(thm)],[f1118,f905]) ).
fof(f1118,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ24_spl
| ~ sQ26_spl
| multiply(sk_c9,X0) = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f996,f1115]) ).
fof(f1129,plain,
( ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ26_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f1116,f954]) ).
fof(f1133,plain,
( ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ26_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f110,f1129]) ).
fof(f1134,plain,
( ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1133]) ).
fof(f1135,plain,
( ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1134]) ).
fof(f1145,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f719,f41]) ).
fof(f1162,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f693,f84]) ).
fof(f1163,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f713,f1162]) ).
fof(f1187,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(inverse(sk_c5)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f719,f469]) ).
fof(f1188,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f713,f1187]) ).
fof(f1189,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f713,f1188]) ).
fof(f1190,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f693,f1189]) ).
fof(f1191,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1190]) ).
fof(f1192,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1191]) ).
fof(f1196,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1145,f712]) ).
fof(f1197,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1196,f800]) ).
fof(f1198,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f1197]) ).
fof(f1219,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1196,f1163]) ).
fof(f1220,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1219]) ).
fof(f1221,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1220]) ).
fof(f1222,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f92,f96,f100,f112,f113,f116,f117,f121,f122,f125,f126,f130,f131,f132,f133,f139,f140,f141,f142,f148,f149,f151,f166,f173,f179,f199,f214,f218,f281,f284,f313,f320,f393,f470,f478,f541,f620,f655,f657,f730,f806,f825,f971,f1135,f1192,f1198,f1221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP390-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n017.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sun Sep 20 20:06:12 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.57 % Drodi V4.1.1
% 0.13/0.62 % Refutation found
% 0.13/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.63 % Elapsed time: 0.069759 seconds
% 0.13/0.63 % CPU time: 0.283598 seconds
% 0.13/0.63 % Total memory used: 107.093 MB
% 0.13/0.63 % Net memory used: 106.848 MB
%------------------------------------------------------------------------------