%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP287-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:19 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 50
% Syntax : Number of formulae : 280 ( 10 unt; 21 def)
% Number of atoms : 1007 ( 307 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1375 ( 648 ~; 706 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/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,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c6
| 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,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c6
| 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,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c6
| 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_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
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
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c6
| multiply(X4,sk_c6) != 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,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( inverse(sk_c3) = sk_c6
| 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,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c6
| 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,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( inverse(sk_c3) = sk_c6
| 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_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != 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
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != 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
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c6) = 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
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c6 ),
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_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f101,plain,
( sQ8_spl
| multiply(sk_c2,sk_c6) != 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_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c6 ),
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_c6
| multiply(X1,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != 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(f134,plain,
( ~ sQ3_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f72,f31]) ).
fof(f135,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f76,f31]) ).
fof(f136,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f92,f31]) ).
fof(f137,plain,
( ~ sQ9_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f138,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f139,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f138]) ).
fof(f140,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f80,f32]) ).
fof(f141,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f68,f32]) ).
fof(f142,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f125,f80]) ).
fof(f144,plain,
( ~ sQ13_spl
| identity != sk_c6
| inverse(inverse(sk_c5)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f31,f125]) ).
fof(f147,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f76,f142]) ).
fof(f148,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f147]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c5,X0) = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f61,f32]) ).
fof(f151,plain,
! [X0] :
( ~ sQ3_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f134,f32]) ).
fof(f152,plain,
! [X0] :
( ~ sQ3_spl
| X0 = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f151]) ).
fof(f155,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f122,f68]) ).
fof(f161,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c6
| sk_c5 != sk_c7 ),
inference(paramodulation,[status(thm)],[f100,f122]) ).
fof(f162,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f72,f155]) ).
fof(f163,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f162]) ).
fof(f164,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f119,f100]) ).
fof(f168,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c6
| sk_c7 != sk_c5 ),
inference(paramodulation,[status(thm)],[f68,f119]) ).
fof(f173,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f108,f166]) ).
fof(f174,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f173]) ).
fof(f175,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f176,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f116,f84]) ).
fof(f178,plain,
( ~ sQ10_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f30,f116]) ).
fof(f181,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f92,f176]) ).
fof(f182,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f181]) ).
fof(f183,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,definition,
( sQ14_spl
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( sQ14_spl
| identity != sk_c6 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f191,definition,
( sQ16_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ16_spl
| sk_c7 = sk_c6 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f193,plain,
( sQ16_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,definition,
( sQ17_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( ~ sQ17_spl
| inverse(identity) = sk_c7 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f196,plain,
( sQ17_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f178,f191,f194,f115]) ).
fof(f198,definition,
( sQ18_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ18_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f202,plain,
( sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f200]) ).
fof(f203,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f206,plain,
! [X0] :
( ~ sQ9_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f137,f32]) ).
fof(f207,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c6,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f206]) ).
fof(f209,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f64,f32]) ).
fof(f210,definition,
( sQ19_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( ~ sQ19_spl
| sk_c5 = sk_c6 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f212,plain,
( sQ19_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f220,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f141]) ).
fof(f231,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c4) = multiply(sk_c3,identity) ),
inference(paramodulation,[status(thm)],[f135,f141]) ).
fof(f232,plain,
! [X0] :
( ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f135,f32]) ).
fof(f233,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f232]) ).
fof(f238,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f141,f152]) ).
fof(f239,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(paramodulation,[status(thm)],[f68,f152]) ).
fof(f242,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(backward_demodulation,[status(thm)],[f245,f209]) ).
fof(f243,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c6,X0)) ),
inference(backward_demodulation,[status(thm)],[f245,f140]) ).
fof(f245,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f209,f238]) ).
fof(f246,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f64,f239]) ).
fof(f247,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f246,f212]) ).
fof(f248,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f251,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f246,f62]) ).
fof(f253,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c2,sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f246,f101]) ).
fof(f254,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f246,f80]) ).
fof(f264,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f254,f233]) ).
fof(f265,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c7,multiply(sk_c4,X0)) = multiply(sk_c3,X0) ),
inference(paramodulation,[status(thm)],[f233,f141]) ).
fof(f268,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c6) = multiply(sk_c3,sk_c6) ),
inference(paramodulation,[status(thm)],[f264,f141]) ).
fof(f270,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f271,f251]) ).
fof(f271,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f268]) ).
fof(f273,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramodulation,[status(thm)],[f271,f242]) ).
fof(f277,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f264,f273]) ).
fof(f283,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,multiply(sk_c4,X0)) = multiply(sk_c4,X0) ),
inference(paramodulation,[status(thm)],[f233,f243]) ).
fof(f295,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(sk_c6,X0) ),
inference(backward_demodulation,[status(thm)],[f297,f233]) ).
fof(f296,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,X0) = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f297,f265]) ).
fof(f297,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f233,f283]) ).
fof(f306,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c7,X0) ),
inference(backward_demodulation,[status(thm)],[f295,f242]) ).
fof(f307,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f295,f207]) ).
fof(f309,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f295,f135]) ).
fof(f310,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f295,f134]) ).
fof(f313,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f295,f277]) ).
fof(f316,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f296,f68]) ).
fof(f317,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c4) = multiply(sk_c7,identity) ),
inference(backward_demodulation,[status(thm)],[f296,f231]) ).
fof(f325,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f295,f306]) ).
fof(f326,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f307,f253]) ).
fof(f333,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f309,f310]) ).
fof(f340,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f270]) ).
fof(f341,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f325,f316]) ).
fof(f344,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c4 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f325,f317]) ).
fof(f345,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c3 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f333,f344]) ).
fof(f346,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f325,f345]) ).
fof(f353,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f326,f198,f79,f75,f107,f63,f71,f67,f99]) ).
fof(f358,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f343,f193]) ).
fof(f359,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f358]) ).
fof(f360,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f374,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f84,f139]) ).
fof(f375,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f100,f139]) ).
fof(f376,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(inverse(sk_c7),multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f150,f139]) ).
fof(f377,plain,
( ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c5) ),
inference(paramodulation,[status(thm)],[f61,f139]) ).
fof(f380,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f92,f374]) ).
fof(f383,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f387,f65]) ).
fof(f387,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f61,f380]) ).
fof(f388,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f108,f375]) ).
fof(f389,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f387,f388]) ).
fof(f390,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(inverse(sk_c7),multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f387,f376]) ).
fof(f391,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f398,f389]) ).
fof(f392,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f398,f137]) ).
fof(f398,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f139,f390]) ).
fof(f399,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(forward_demodulation,[status(thm)],[f387,f377]) ).
fof(f400,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f399]) ).
fof(f401,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f186]) ).
fof(f402,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f404,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f398,f383]) ).
fof(f405,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f404]) ).
fof(f406,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f410,plain,
( sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(identity) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f391,f196]) ).
fof(f416,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f391,f387]) ).
fof(f418,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f391,f136]) ).
fof(f429,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c6 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f392,f400]) ).
fof(f445,definition,
( sQ21_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ21_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f464,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f161,f445,f107,f121,f99]) ).
fof(f465,plain,
( sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f392,f410]) ).
fof(f466,plain,
( sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f108,f465]) ).
fof(f467,plain,
( sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f466]) ).
fof(f468,plain,
( sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f472,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f398,f418]) ).
fof(f474,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f416,f447]) ).
fof(f475,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f391,f474]) ).
fof(f476,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f475]) ).
fof(f477,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f476]) ).
fof(f488,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f472,f392]) ).
fof(f493,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f496,f472]) ).
fof(f496,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c6 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f488,f429]) ).
fof(f513,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f211,f220]) ).
fof(f514,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ19_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f211,f140]) ).
fof(f539,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c4,X0) ),
inference(backward_demodulation,[status(thm)],[f295,f514]) ).
fof(f554,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(identity) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f313,f196]) ).
fof(f630,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f295,f539]) ).
fof(f631,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f333,f630]) ).
fof(f644,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(sk_c3) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f346,f554]) ).
fof(f645,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f72,f644]) ).
fof(f646,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f645]) ).
fof(f647,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f655,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f493,f195]) ).
fof(f657,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f391,f655]) ).
fof(f678,definition,
( sQ26_spl
<=> inverse(inverse(sk_c5)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f680,plain,
( sQ26_spl
| inverse(inverse(sk_c5)) != sk_c6 ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f144,f678,f184,f124]) ).
fof(f718,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f416,f680]) ).
fof(f719,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f657,f718]) ).
fof(f720,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f657,f719]) ).
fof(f721,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f720]) ).
fof(f722,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f721]) ).
fof(f761,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ16_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c3,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f192,f513]) ).
fof(f762,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ16_spl
| sk_c5 = multiply(sk_c3,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f64,f761]) ).
fof(f763,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f631,f762]) ).
fof(f809,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f168,f445,f71,f118,f67]) ).
fof(f869,plain,
( sQ21_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f763,f447]) ).
fof(f870,plain,
( sQ21_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f192,f869]) ).
fof(f871,plain,
( sQ21_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f870]) ).
fof(f872,plain,
( sQ21_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f871]) ).
fof(f873,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,f149,f164,f175,f183,f197,f203,f248,f341,f353,f360,f402,f406,f464,f468,f477,f647,f681,f722,f809,f872]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP287-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:11:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.45 % Elapsed time: 0.080071 seconds
% 0.15/0.45 % CPU time: 0.273700 seconds
% 0.15/0.45 % Total memory used: 76.273 MB
% 0.15/0.45 % Net memory used: 76.058 MB
%------------------------------------------------------------------------------