%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP284-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:33:18 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 47
% Syntax : Number of formulae : 268 ( 13 unt; 18 def)
% Number of atoms : 1018 ( 311 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1442 ( 692 ~; 732 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/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_c7
| multiply(X4,sk_c7) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
( 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(f36,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
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(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
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_c7
| multiply(X4,sk_c7) != sk_c5
| ! [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_c7
| multiply(X1,sk_c7) != sk_c5
| 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(f78,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f60,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(f82,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f60,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_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f101,plain,
( sQ8_spl
| multiply(sk_c2,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f99,f63]) ).
fof(f103,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f99,f67]) ).
fof(f104,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f99,f71]) ).
fof(f105,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f99,f75]) ).
fof(f106,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f99,f79]) ).
fof(f107,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f107,f63]) ).
fof(f111,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f107,f67]) ).
fof(f112,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f107,f71]) ).
fof(f113,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f107,f75]) ).
fof(f114,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f107,f79]) ).
fof(f115,definition,
! [X0] :
( 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_c7
| multiply(X1,sk_c7) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c5 ),
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,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f76,f128]) ).
fof(f131,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f122,f72]) ).
fof(f136,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f133]) ).
fof(f137,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f136]) ).
fof(f138,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f119,f100]) ).
fof(f142,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f108,f139]) ).
fof(f143,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f142]) ).
fof(f144,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f143]) ).
fof(f147,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f80,f32]) ).
fof(f151,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f116,f84]) ).
fof(f154,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f92,f151]) ).
fof(f155,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f157,definition,
( sQ14_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( sQ14_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f161,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f159]) ).
fof(f162,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f174,plain,
( ~ sQ9_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f176,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f184,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f176]) ).
fof(f186,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f64,f32]) ).
fof(f198,plain,
! [X0] :
( ~ sQ9_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f174,f32]) ).
fof(f199,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f198]) ).
fof(f210,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f108,f184]) ).
fof(f214,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f184]) ).
fof(f217,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f30,f184]) ).
fof(f220,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f184]) ).
fof(f222,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f80,f184]) ).
fof(f225,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f220]) ).
fof(f227,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f76,f222]) ).
fof(f248,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c5,multiply(sk_c2,X0)) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f199,f186]) ).
fof(f250,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f225,f186]) ).
fof(f251,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c2) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f174,f186]) ).
fof(f256,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f227,f250]) ).
fof(f265,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c5) ),
inference(paramodulation,[status(thm)],[f256,f147]) ).
fof(f266,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f256,f184]) ).
fof(f268,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c4,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f64,f265]) ).
fof(f269,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f80,f268]) ).
fof(f272,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f266]) ).
fof(f277,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f272,f31]) ).
fof(f278,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f272,f30]) ).
fof(f282,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c7,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f269,f225]) ).
fof(f285,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f269,f62]) ).
fof(f288,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f269,f72]) ).
fof(f291,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f278,f199]) ).
fof(f296,plain,
( sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f291,f101]) ).
fof(f304,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c3) = sk_c7 ),
inference(paramodulation,[status(thm)],[f68,f277]) ).
fof(f305,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c2) = sk_c7 ),
inference(paramodulation,[status(thm)],[f108,f277]) ).
fof(f308,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f278,f304]) ).
fof(f309,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f278,f305]) ).
fof(f311,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f278,f285]) ).
fof(f312,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f311]) ).
fof(f313,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f312]) ).
fof(f319,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f269,f116]) ).
fof(f322,plain,
( sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f308,f296]) ).
fof(f324,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f308,f272]) ).
fof(f328,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c2 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f330,f308]) ).
fof(f330,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f308,f309]) ).
fof(f331,plain,
( sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f330,f322]) ).
fof(f354,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f328,f282]) ).
fof(f355,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f291,f354]) ).
fof(f356,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c5 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f328,f355]) ).
fof(f357,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f331]) ).
fof(f358,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f362,definition,
( sQ22_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ22_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f367,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c5,X0) = multiply(sk_c2,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f100,f32]) ).
fof(f376,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f184,f217]) ).
fof(f398,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f92,f31]) ).
fof(f415,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c5) ),
inference(paramodulation,[status(thm)],[f100,f210]) ).
fof(f419,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f415,f184]) ).
fof(f421,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f419]) ).
fof(f422,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c1) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f421,f398]) ).
fof(f423,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f421,f31]) ).
fof(f426,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f421,f174]) ).
fof(f427,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f421,f376]) ).
fof(f428,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(inverse(sk_c5),X0) ),
inference(backward_demodulation,[status(thm)],[f421,f217]) ).
fof(f480,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c2,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f427,f367]) ).
fof(f481,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sk_c2 = multiply(sk_c2,sk_c5) ),
inference(paramodulation,[status(thm)],[f426,f480]) ).
fof(f483,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = multiply(sk_c2,sk_c5) ),
inference(paramodulation,[status(thm)],[f422,f480]) ).
fof(f509,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f510,f84]) ).
fof(f510,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f481,f483]) ).
fof(f512,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f100,f509]) ).
fof(f519,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,sk_c7) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f512,f65]) ).
fof(f522,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f512,f61]) ).
fof(f529,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f427,f519]) ).
fof(f530,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f415,f522]) ).
fof(f531,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f364]) ).
fof(f532,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f534,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f529,f362,f107,f99,f91,f83,f63]) ).
fof(f535,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c5) ),
inference(forward_demodulation,[status(thm)],[f512,f214]) ).
fof(f536,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f428,f535]) ).
fof(f537,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| multiply(sk_c2,X0) = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f427,f248]) ).
fof(f538,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,X0) = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f512,f537]) ).
fof(f539,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f427,f538]) ).
fof(f540,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| sk_c2 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f427,f251]) ).
fof(f541,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f512,f540]) ).
fof(f542,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f427,f541]) ).
fof(f543,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f421,f542]) ).
fof(f553,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c5) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f512,f122]) ).
fof(f611,definition,
( sQ24_spl
<=> inverse(sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( sQ24_spl
| inverse(sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,definition,
( sQ25_spl
<=> sk_c2 = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( sQ25_spl
| sk_c2 != sk_c2 ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f618,plain,
( sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f616]) ).
fof(f619,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f625,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f543,f536]) ).
fof(f632,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f543,f512]) ).
fof(f642,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(X0,sk_c5) != sk_c7
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f625,f553]) ).
fof(f643,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(X0,sk_c2) != sk_c7
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f543,f642]) ).
fof(f644,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f625,f643]) ).
fof(f646,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ12_spl
| sk_c2 != sk_c2
| inverse(sk_c2) != sk_c2 ),
inference(paramodulation,[status(thm)],[f539,f644]) ).
fof(f648,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f646,f611,f614,f121,f91,f83,f99,f63,f107]) ).
fof(f649,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f625,f108]) ).
fof(f650,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f649,f613]) ).
fof(f651,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f652,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f319,f118,f75,f79,f63,f67,f71,f115]) ).
fof(f660,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f625,f108]) ).
fof(f664,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f543,f423]) ).
fof(f710,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f632,f125]) ).
fof(f711,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(X0,sk_c2) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f543,f710]) ).
fof(f712,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f632,f711]) ).
fof(f713,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| inverse(inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f712,f664]) ).
fof(f720,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f660,f713]) ).
fof(f721,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f660,f720]) ).
fof(f722,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f721]) ).
fof(f723,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f731,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f324,f376]) ).
fof(f743,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f269,f76]) ).
fof(f749,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f324,f31]) ).
fof(f755,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f731,f288]) ).
fof(f757,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f759,f743]) ).
fof(f759,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f308,f755]) ).
fof(f767,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c4) = sk_c3 ),
inference(paramodulation,[status(thm)],[f757,f749]) ).
fof(f769,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f731,f767]) ).
fof(f771,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f769,f757]) ).
fof(f774,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f769,f759]) ).
fof(f775,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f769,f749]) ).
fof(f779,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f769,f308]) ).
fof(f783,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f774,f119]) ).
fof(f785,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c7) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f779,f783]) ).
fof(f786,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f779,f785]) ).
fof(f838,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(inverse(sk_c4)) != sk_c4 ),
inference(resolution,[status(thm)],[f786,f775]) ).
fof(f843,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f771,f838]) ).
fof(f844,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f771,f843]) ).
fof(f845,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f844]) ).
fof(f846,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f845]) ).
fof(f847,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f78,f82,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f102,f103,f104,f105,f106,f110,f111,f112,f113,f114,f127,f132,f138,f144,f156,f162,f313,f358,f532,f534,f619,f648,f651,f652,f723,f846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP284-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:08:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.040560 seconds
% 0.15/0.42 % CPU time: 0.153275 seconds
% 0.15/0.42 % Total memory used: 37.731 MB
% 0.15/0.42 % Net memory used: 37.637 MB
%------------------------------------------------------------------------------