%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP314-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:33:23 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 53
% Syntax : Number of formulae : 258 ( 21 unt; 24 def)
% Number of atoms : 747 ( 297 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 918 ( 429 ~; 465 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 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_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,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
| inverse(X5) != sk_c7
| multiply(X5,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
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_c7,sk_c8) = sk_c6,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| ! [X5] :
( inverse(X5) != sk_c7
| multiply(X5,sk_c7) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,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
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f60,f63]) ).
fof(f67,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f60,f67]) ).
fof(f71,definition,
( sQ3_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| inverse(sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f60,f71]) ).
fof(f75,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f60,f75]) ).
fof(f79,definition,
( sQ5_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f38,f79,f63]) ).
fof(f83,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f39,f79,f67]) ).
fof(f84,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f40,f79,f71]) ).
fof(f85,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f41,f79,f75]) ).
fof(f86,definition,
( sQ6_spl
<=> multiply(sk_c2,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f42,f86,f63]) ).
fof(f90,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f86,f67]) ).
fof(f91,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f86,f71]) ).
fof(f92,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f45,f86,f75]) ).
fof(f93,definition,
( sQ7_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f93,f63]) ).
fof(f97,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f93,f67]) ).
fof(f98,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f93,f71]) ).
fof(f99,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f93,f75]) ).
fof(f100,definition,
( sQ8_spl
<=> multiply(sk_c3,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ8_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f100,f63]) ).
fof(f104,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f100,f67]) ).
fof(f105,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f100,f71]) ).
fof(f106,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f100,f75]) ).
fof(f107,definition,
( sQ9_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f107,f63]) ).
fof(f111,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f107,f67]) ).
fof(f112,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f107,f71]) ).
fof(f113,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f107,f75]) ).
fof(f114,definition,
( sQ10_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( sQ10_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f118,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
! [X1] :
( sQ12_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f121,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,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(f127,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,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(f130,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f114,f117,f120,f123,f126,f129]) ).
fof(f134,plain,
! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)),
inference(paramodulation,[status(thm)],[f33,f32]) ).
fof(f137,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f76,f32]) ).
fof(f139,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f80,f31]) ).
fof(f140,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f94,f31]) ).
fof(f141,plain,
( ~ sQ9_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f142,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f64,f31]) ).
fof(f143,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f72,f31]) ).
fof(f144,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f145,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f144]) ).
fof(f146,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f68,f32]) ).
fof(f147,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f101,f32]) ).
fof(f150,plain,
! [X0] :
( ~ sQ5_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f139,f32]) ).
fof(f151,plain,
! [X0] :
( ~ sQ5_spl
| X0 = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f150]) ).
fof(f152,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f140,f32]) ).
fof(f153,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f152]) ).
fof(f154,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f130,f76]) ).
fof(f159,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f72,f154]) ).
fof(f160,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f159]) ).
fof(f161,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f127,f68]) ).
fof(f165,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| sk_c8 != sk_c8
| inverse(sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f101,f127]) ).
fof(f171,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f64,f163]) ).
fof(f172,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f171]) ).
fof(f173,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f33,f116]) ).
fof(f175,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f174]) ).
fof(f176,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f124,f101]) ).
fof(f185,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f108,f177]) ).
fof(f186,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f185]) ).
fof(f187,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f186]) ).
fof(f188,plain,
! [X0] :
( ~ sQ9_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f141,f32]) ).
fof(f189,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f188]) ).
fof(f190,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f61,f151]) ).
fof(f193,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f190,f32]) ).
fof(f198,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(paramodulation,[status(thm)],[f101,f189]) ).
fof(f205,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f209,f121]) ).
fof(f209,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f33,f198]) ).
fof(f215,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f118,f61]) ).
fof(f217,plain,
( ~ sQ11_spl
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f31,f118]) ).
fof(f220,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f80,f215]) ).
fof(f221,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f220]) ).
fof(f222,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f228,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| inverse(sk_c3) != sk_c7
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f101,f205]) ).
fof(f233,definition,
( sQ16_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( sQ16_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f237,definition,
( sQ17_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ17_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f244,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f228,f237,f107,f120,f100]) ).
fof(f249,definition,
( sQ20_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( sQ20_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f260,definition,
( sQ23_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ23_spl
| inverse(sk_c2) != sk_c8 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f267,definition,
( sQ25_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ25_spl
| inverse(sk_c3) != sk_c8 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,definition,
( sQ26_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ26_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f165,f267,f270,f126,f100]) ).
fof(f285,plain,
( sQ23_spl
| ~ sQ7_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f94,f262]) ).
fof(f286,plain,
( sQ25_spl
| ~ sQ9_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f108,f269]) ).
fof(f290,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f190,f127]) ).
fof(f300,definition,
( sQ31_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f290,f300,f270,f126,f79,f60]) ).
fof(f307,plain,
( sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f272]) ).
fof(f308,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f309,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f235]) ).
fof(f310,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f325,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c8,multiply(sk_c3,X0)) = multiply(sk_c3,X0) ),
inference(paramodulation,[status(thm)],[f189,f147]) ).
fof(f329,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f147,f189]) ).
fof(f364,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c8,multiply(sk_c3,X0)) = multiply(sk_c8,X0) ),
inference(paramodulation,[status(thm)],[f189,f193]) ).
fof(f372,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| X0 = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f375,f189]) ).
fof(f375,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| multiply(sk_c3,X0) = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f325,f364]) ).
fof(f383,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f392,f153]) ).
fof(f389,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c7,X0) = multiply(sk_c8,X0) ),
inference(backward_demodulation,[status(thm)],[f392,f329]) ).
fof(f392,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f329,f372]) ).
fof(f406,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f408,f190]) ).
fof(f408,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f392,f389]) ).
fof(f418,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f406,f239]) ).
fof(f419,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f433,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f285,f237,f93,f260]) ).
fof(f434,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f286,f237,f107,f267]) ).
fof(f439,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c7) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f209,f130]) ).
fof(f455,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ15_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f439,f383]) ).
fof(f460,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ15_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f94,f455]) ).
fof(f461,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f460]) ).
fof(f462,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f461]) ).
fof(f464,definition,
( sQ35_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ35_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( ~ sQ11_spl
| ~ sQ35_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f217,f249,f464,f117]) ).
fof(f477,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f145,f145]) ).
fof(f478,plain,
( ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f68,f145]) ).
fof(f479,plain,
sk_c8 = multiply(inverse(sk_c7),sk_c6),
inference(paramodulation,[status(thm)],[f33,f145]) ).
fof(f483,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f64,f478]) ).
fof(f489,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f31,f145]) ).
fof(f492,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f477,f489]) ).
fof(f495,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f30,f145]) ).
fof(f498,plain,
( ~ sQ1_spl
| sk_c4 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f142,f145]) ).
fof(f502,plain,
( sQ35_spl
| ~ sQ1_spl
| inverse(sk_c4) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f503,f466]) ).
fof(f503,plain,
( ~ sQ1_spl
| sk_c4 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f492,f498]) ).
fof(f505,plain,
( sQ35_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f502,f63,f464]) ).
fof(f512,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c4) = multiply(sk_c7,identity) ),
inference(paramodulation,[status(thm)],[f142,f134]) ).
fof(f513,plain,
! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c7),multiply(sk_c6,X0)),
inference(paramodulation,[status(thm)],[f134,f145]) ).
fof(f515,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f492,f512]) ).
fof(f528,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c5) = multiply(sk_c4,identity) ),
inference(paramodulation,[status(thm)],[f143,f146]) ).
fof(f529,plain,
( ~ sQ3_spl
| sk_c5 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f143,f145]) ).
fof(f531,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c5) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f492,f528]) ).
fof(f535,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c8,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(backward_demodulation,[status(thm)],[f537,f513]) ).
fof(f536,plain,
( ~ sQ3_spl
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f537,f479]) ).
fof(f537,plain,
( ~ sQ3_spl
| sk_c5 = inverse(sk_c7) ),
inference(forward_demodulation,[status(thm)],[f492,f529]) ).
fof(f541,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f548,f142]) ).
fof(f544,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f548,f531]) ).
fof(f545,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f548,f483]) ).
fof(f548,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f137,f535]) ).
fof(f549,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f76,f536]) ).
fof(f550,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f549,f239]) ).
fof(f551,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f555,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c4 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f559,f251]) ).
fof(f557,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| X0 = multiply(inverse(sk_c4),X0) ),
inference(backward_demodulation,[status(thm)],[f559,f495]) ).
fof(f558,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| X0 = multiply(X0,sk_c4) ),
inference(backward_demodulation,[status(thm)],[f559,f492]) ).
fof(f559,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| identity = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f143,f544]) ).
fof(f564,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f567,f515]) ).
fof(f567,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f33,f545]) ).
fof(f574,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f567,f121]) ).
fof(f581,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f64,f557]) ).
fof(f583,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f548,f581]) ).
fof(f588,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| identity = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f541,f564]) ).
fof(f589,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f559,f588]) ).
fof(f590,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f555]) ).
fof(f591,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f609,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| X0 = multiply(X0,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f589,f558]) ).
fof(f669,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| X0 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f609,f574]) ).
fof(f673,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c7) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f669]) ).
fof(f674,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| X0 = multiply(inverse(sk_c7),X0) ),
inference(paramodulation,[status(thm)],[f583,f145]) ).
fof(f683,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = inverse(sk_c7) ),
inference(paramodulation,[status(thm)],[f609,f674]) ).
fof(f685,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c7 ),
inference(paramodulation,[status(thm)],[f674,f609]) ).
fof(f688,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f683,f673]) ).
fof(f689,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f692,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| X0 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f609,f124]) ).
fof(f693,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f549,f692]) ).
fof(f694,plain,
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c7) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f693]) ).
fof(f695,plain,
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f694,f685]) ).
fof(f696,plain,
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f695]) ).
fof(f697,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f78,f82,f83,f84,f85,f89,f90,f91,f92,f96,f97,f98,f99,f103,f104,f105,f106,f110,f111,f112,f113,f132,f161,f173,f176,f187,f222,f244,f273,f303,f308,f310,f419,f433,f434,f462,f467,f505,f551,f591,f689,f696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP314-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:08:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.056683 seconds
% 0.10/0.44 % CPU time: 0.196371 seconds
% 0.10/0.44 % Total memory used: 104.468 MB
% 0.10/0.44 % Net memory used: 104.210 MB
%------------------------------------------------------------------------------