%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP360-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:31 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 45
% Syntax : Number of formulae : 262 ( 10 unt; 16 def)
% Number of atoms : 1077 ( 304 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 1562 ( 747 ~; 799 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 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_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = 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) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
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_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = 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
| ! [X3] :
( multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ) ) ) ),
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) != X0
| multiply(sk_c7,X0) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( sQ0_spl
| multiply(sk_c6,sk_c5) != sk_c7 ),
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(f81,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
<=> inverse(sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| inverse(sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ6_spl
| inverse(sk_c7) != sk_c5 ),
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
<=> multiply(sk_c7,sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c2) = sk_c6 ),
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_c1,sk_c7) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c7) = sk_c2 ),
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_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c1) = 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,X1] :
( sQ10_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0,X1] :
( ~ sQ10_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X2] :
( sQ11_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X3] :
( sQ12_spl
<=> ( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ12_spl
| sQ11_spl
| ~ sQ1_spl
| sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f60,f83,f115,f63,f118,f121]) ).
fof(f125,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f122,f80]) ).
fof(f126,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f61,f122]) ).
fof(f128,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f76,f125]) ).
fof(f129,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f128]) ).
fof(f130,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f116]) ).
fof(f132,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f119,f72]) ).
fof(f134,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f132]) ).
fof(f135,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f134]) ).
fof(f136,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f138,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f61,f32]) ).
fof(f140,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f80,f32]) ).
fof(f154,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7
| multiply(sk_c7,sk_c2) != sk_c6 ),
inference(paramodulation,[status(thm)],[f100,f131]) ).
fof(f155,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f154,f91,f107,f115,f99]) ).
fof(f159,plain,
( ~ sQ9_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f160,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f161,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f160]) ).
fof(f163,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f64,f32]) ).
fof(f181,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f161]) ).
fof(f185,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f161]) ).
fof(f186,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f80,f161]) ).
fof(f187,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f100,f161]) ).
fof(f190,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f185]) ).
fof(f191,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f76,f186]) ).
fof(f192,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f108,f187]) ).
fof(f206,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f192,f161]) ).
fof(f208,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f206]) ).
fof(f225,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f190,f163]) ).
fof(f232,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f191,f225]) ).
fof(f236,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c1) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f208,f159]) ).
fof(f239,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f208,f31]) ).
fof(f240,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f208,f30]) ).
fof(f250,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)],[f232,f140]) ).
fof(f251,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c5) ),
inference(paramodulation,[status(thm)],[f232,f138]) ).
fof(f254,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c4,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f64,f250]) ).
fof(f255,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f80,f254]) ).
fof(f256,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f190,f251]) ).
fof(f257,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f61,f256]) ).
fof(f269,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c6,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f255,f191]) ).
fof(f274,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f255,f72]) ).
fof(f276,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f255,f269]) ).
fof(f297,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f255,f62]) ).
fof(f298,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f274,f161]) ).
fof(f300,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f298]) ).
fof(f305,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f276,f297]) ).
fof(f327,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f192,f92]) ).
fof(f335,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f327,f76]) ).
fof(f338,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c5) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f327,f61]) ).
fof(f339,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f338,f161]) ).
fof(f341,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f239,f339]) ).
fof(f349,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c4,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f327,f81]) ).
fof(f350,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c2) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f341,f349]) ).
fof(f353,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f341,f84]) ).
fof(f354,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c2 ),
inference(paramodulation,[status(thm)],[f353,f239]) ).
fof(f355,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c2,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f353,f161]) ).
fof(f356,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f240,f354]) ).
fof(f357,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f240,f355]) ).
fof(f358,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f356,f353]) ).
fof(f361,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f356,f335]) ).
fof(f362,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c2 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f356,f327]) ).
fof(f363,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c1) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f356,f236]) ).
fof(f368,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f240,f363]) ).
fof(f370,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f368,f362]) ).
fof(f371,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f368,f356]) ).
fof(f372,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| sk_c5 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f368,f341]) ).
fof(f374,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f368,f239]) ).
fof(f376,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f368,f208]) ).
fof(f378,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(X0,sk_c1) != sk_c7
| inverse(X0) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f370,f119]) ).
fof(f379,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f371,f357]) ).
fof(f382,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f368,f358]) ).
fof(f383,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f368,f382]) ).
fof(f387,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f368,f361]) ).
fof(f388,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c1,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f387,f161]) ).
fof(f389,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f379,f388]) ).
fof(f391,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c4,sk_c1) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f368,f350]) ).
fof(f392,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c4,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f371,f391]) ).
fof(f396,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c1 != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f389,f392]) ).
fof(f399,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f396]) ).
fof(f400,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f465,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(X0,sk_c1) != sk_c7
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f371,f378]) ).
fof(f466,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(X0,sk_c1) != sk_c1
| inverse(X0) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f371,f465]) ).
fof(f467,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ11_spl
| inverse(inverse(sk_c1)) != sk_c1 ),
inference(resolution,[status(thm)],[f466,f374]) ).
fof(f474,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f383,f467]) ).
fof(f475,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ11_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f383,f474]) ).
fof(f476,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f475]) ).
fof(f477,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f476]) ).
fof(f481,definition,
( sQ14_spl
<=> inverse(sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ14_spl
| inverse(sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,definition,
( sQ15_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( sQ15_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f126,f481,f484,f121,f60]) ).
fof(f488,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c1) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f370,f483]) ).
fof(f489,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f383,f488]) ).
fof(f490,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f370,f489]) ).
fof(f491,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f490]) ).
fof(f492,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f493,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f371,f486]) ).
fof(f494,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f370,f493]) ).
fof(f495,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f494]) ).
fof(f496,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f497,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f257,f255]) ).
fof(f499,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f257,f76]) ).
fof(f507,plain,
( sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f497,f85]) ).
fof(f563,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c5) ),
inference(forward_demodulation,[status(thm)],[f257,f181]) ).
fof(f564,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(forward_demodulation,[status(thm)],[f497,f563]) ).
fof(f566,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f571,f31]) ).
fof(f570,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f571,f30]) ).
fof(f571,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f564]) ).
fof(f687,definition,
( sQ16_spl
<=> sk_c1 = sk_c1 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( sQ16_spl
| sk_c1 != sk_c1 ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f698,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f689]) ).
fof(f699,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f698]) ).
fof(f717,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| X0 = multiply(sk_c7,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f499,f161]) ).
fof(f718,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f570,f717]) ).
fof(f724,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f570,f131]) ).
fof(f725,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f257,f724]) ).
fof(f727,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f725,f718]) ).
fof(f731,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f499,f727]) ).
fof(f732,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f731]) ).
fof(f733,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f732]) ).
fof(f734,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c3) = sk_c7 ),
inference(paramodulation,[status(thm)],[f68,f566]) ).
fof(f735,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c4) = sk_c7 ),
inference(paramodulation,[status(thm)],[f499,f566]) ).
fof(f738,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f570,f734]) ).
fof(f739,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c4 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f570,f735]) ).
fof(f742,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f738,f68]) ).
fof(f748,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f749,f738]) ).
fof(f749,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f738,f739]) ).
fof(f754,plain,
( sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f748,f507]) ).
fof(f755,plain,
( sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f748,f754]) ).
fof(f756,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f749,f742]) ).
fof(f757,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f749,f756]) ).
fof(f758,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f757,f755]) ).
fof(f759,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f758]) ).
fof(f765,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c1,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f376,f30]) ).
fof(f789,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f370,f65]) ).
fof(f790,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f765,f789]) ).
fof(f791,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f371,f790]) ).
fof(f792,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f372,f791]) ).
fof(f793,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f792]) ).
fof(f794,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f793]) ).
fof(f815,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f232,f161]) ).
fof(f817,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f815]) ).
fof(f820,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f817,f30]) ).
fof(f825,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f820,f300]) ).
fof(f826,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f305]) ).
fof(f827,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f828,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,f124,f130,f136,f155,f400,f477,f487,f492,f496,f699,f733,f759,f794,f827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP360-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:05:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.084161 seconds
% 0.14/0.45 % CPU time: 0.406826 seconds
% 0.14/0.45 % Total memory used: 79.013 MB
% 0.14/0.45 % Net memory used: 78.733 MB
%------------------------------------------------------------------------------