%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP272-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:33:16 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 53
% Syntax : Number of formulae : 305 ( 13 unt; 24 def)
% Number of atoms : 1135 ( 327 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1576 ( 746 ~; 806 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/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_c6
| multiply(X4,sk_c6) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
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,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| 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,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| 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] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ) ) ) ),
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_c6
| multiply(X1,sk_c6) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
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
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| inverse(sk_c1) = sk_c7 ),
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_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f93,plain,
( sQ7_spl
| multiply(sk_c7,sk_c5) != 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_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(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
<=> ( 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
| ~ sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f115,f91,f118,f63,f121,f124]) ).
fof(f129,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f125,f80]) ).
fof(f130,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| sk_c6 != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f92,f125]) ).
fof(f132,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f76,f129]) ).
fof(f133,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f132]) ).
fof(f134,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f122,f72]) ).
fof(f137,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| sk_c5 != sk_c7
| inverse(sk_c2) != sk_c7 ),
inference(paramodulation,[status(thm)],[f100,f122]) ).
fof(f138,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f135]) ).
fof(f139,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f138]) ).
fof(f140,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f119,f100]) ).
fof(f142,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c6
| sk_c7 != sk_c5 ),
inference(paramodulation,[status(thm)],[f72,f119]) ).
fof(f144,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f108,f141]) ).
fof(f145,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f144]) ).
fof(f146,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f150,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f80,f32]) ).
fof(f153,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f116,f61]) ).
fof(f156,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f84,f153]) ).
fof(f157,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,definition,
( sQ14_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ14_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f163,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f161]) ).
fof(f164,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f165,plain,
( ~ sQ10_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f30,f116]) ).
fof(f167,definition,
( sQ15_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( sQ15_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,definition,
( sQ16_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ16_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f165,f167,f170,f115]) ).
fof(f174,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f76,f31]) ).
fof(f175,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f68,f31]) ).
fof(f176,plain,
( ~ sQ9_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f178,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f186,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f178]) ).
fof(f188,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f64,f32]) ).
fof(f189,definition,
( sQ19_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ19_spl
| sk_c5 = sk_c6 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f191,plain,
( sQ19_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f198,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f175,f32]) ).
fof(f199,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f198]) ).
fof(f223,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f186]) ).
fof(f225,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f80,f186]) ).
fof(f228,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f223]) ).
fof(f230,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f76,f225]) ).
fof(f253,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f228,f188]) ).
fof(f254,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c3) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f175,f188]) ).
fof(f258,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f230,f253]) ).
fof(f267,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)],[f258,f150]) ).
fof(f268,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f258,f186]) ).
fof(f270,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c4,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f64,f267]) ).
fof(f271,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f80,f270]) ).
fof(f272,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f191]) ).
fof(f273,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f272]) ).
fof(f274,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f268]) ).
fof(f278,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f274,f174]) ).
fof(f279,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f274,f31]) ).
fof(f280,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f274,f30]) ).
fof(f285,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c7,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f271,f228]) ).
fof(f288,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f271,f93]) ).
fof(f296,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f280,f199]) ).
fof(f311,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c3) = sk_c7 ),
inference(paramodulation,[status(thm)],[f68,f279]) ).
fof(f315,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f280,f311]) ).
fof(f317,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f280,f288]) ).
fof(f318,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f317]) ).
fof(f319,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f271,f169]) ).
fof(f330,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f315,f274]) ).
fof(f332,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f315,f68]) ).
fof(f333,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f321]) ).
fof(f346,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f271,f278]) ).
fof(f347,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f315,f346]) ).
fof(f353,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c3,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f315,f285]) ).
fof(f354,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f296,f353]) ).
fof(f355,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f315,f354]) ).
fof(f356,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f333]) ).
fof(f357,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f362,definition,
( sQ21_spl
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ21_spl
| sk_c7 != sk_c5 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,definition,
( sQ22_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ22_spl
| inverse(sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f367,plain,
( sQ22_spl
| inverse(sk_c3) != sk_c6 ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f142,f362,f365,f118,f71]) ).
fof(f369,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f315,f364]) ).
fof(f371,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f355,f347]) ).
fof(f375,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f355,f271]) ).
fof(f378,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f296,f371]) ).
fof(f380,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f355,f369]) ).
fof(f381,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f380]) ).
fof(f382,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f383,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f332,f367]) ).
fof(f397,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f378,f355]) ).
fof(f398,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f378,f332]) ).
fof(f399,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f378,f330]) ).
fof(f404,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f378,f398]) ).
fof(f407,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f375,f383]) ).
fof(f408,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f407]) ).
fof(f409,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f442,definition,
( sQ23_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ23_spl
| inverse(sk_c2) != sk_c7 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ21_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f137,f442,f362,f121,f99]) ).
fof(f447,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f30,f186]) ).
fof(f450,plain,
( sQ23_spl
| ~ sQ9_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f108,f444]) ).
fof(f451,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f100,f186]) ).
fof(f453,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f108,f451]) ).
fof(f472,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f61,f186]) ).
fof(f474,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f84,f472]) ).
fof(f493,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f453,f186]) ).
fof(f495,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f493]) ).
fof(f497,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f495,f31]) ).
fof(f498,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f495,f176]) ).
fof(f500,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f495,f30]) ).
fof(f518,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f500,f254]) ).
fof(f519,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f495,f518]) ).
fof(f520,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f453,f519]) ).
fof(f522,definition,
( sQ28_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ28_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f130,f522,f159,f124,f91]) ).
fof(f540,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(inverse(sk_c5),X0) ),
inference(forward_demodulation,[status(thm)],[f495,f447]) ).
fof(f551,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f520,f474]) ).
fof(f552,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f551,f186]) ).
fof(f554,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f497,f552]) ).
fof(f556,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| X0 = multiply(inverse(sk_c3),X0) ),
inference(backward_demodulation,[status(thm)],[f554,f540]) ).
fof(f560,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f556]) ).
fof(f602,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f560,f551]) ).
fof(f615,plain,
( ~ sQ22_spl
| ~ sQ2_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f68,f366]) ).
fof(f623,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f397,f190]) ).
fof(f624,plain,
( ~ sQ22_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f623,f615]) ).
fof(f642,definition,
( sQ32_spl
<=> sk_c4 = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ32_spl
| sk_c4 != sk_c4 ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f662,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f644]) ).
fof(f663,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f680,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f399,f172]) ).
fof(f681,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ22_spl
| ~ sQ19_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f624,f680]) ).
fof(f707,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ16_spl
| ~ sQ22_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f681]) ).
fof(f708,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ16_spl
| ~ sQ22_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f707]) ).
fof(f710,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f602,f169]) ).
fof(f711,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f520,f710]) ).
fof(f712,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f711]) ).
fof(f713,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f727,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f450,f167,f107,f442]) ).
fof(f734,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f495,f30]) ).
fof(f745,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f495,f31]) ).
fof(f748,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c2) = sk_c5 ),
inference(paramodulation,[status(thm)],[f108,f745]) ).
fof(f776,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f61,f186]) ).
fof(f778,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f84,f776]) ).
fof(f779,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f734,f188]) ).
fof(f786,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(paramodulation,[status(thm)],[f474,f779]) ).
fof(f788,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f474,f186]) ).
fof(f790,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f64,f786]) ).
fof(f794,definition,
( sQ37_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f796,plain,
( sQ37_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f798,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f745,f788]) ).
fof(f804,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f790,f498]) ).
fof(f806,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f790,f108]) ).
fof(f807,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f790,f169]) ).
fof(f808,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f790,f64]) ).
fof(f811,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f734,f804]) ).
fof(f812,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f734,f808]) ).
fof(f813,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f812,f364]) ).
fof(f814,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f813]) ).
fof(f815,plain,
( sQ28_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f790,f524]) ).
fof(f820,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f807,f362,f107,f99,f63,f83,f60,f167]) ).
fof(f830,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f811,f812]) ).
fof(f842,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f811,f806]) ).
fof(f845,plain,
( sQ28_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f830,f815]) ).
fof(f846,plain,
( sQ28_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f842,f845]) ).
fof(f847,plain,
( sQ28_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f811,f846]) ).
fof(f848,plain,
( sQ28_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f847]) ).
fof(f849,plain,
( sQ28_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f848]) ).
fof(f850,plain,
( sQ37_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f796]) ).
fof(f851,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f856,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f798,f108]) ).
fof(f857,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| X0 = multiply(sk_c5,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f856,f186]) ).
fof(f858,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f734,f857]) ).
fof(f872,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c2) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f798,f748]) ).
fof(f880,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f734,f872]) ).
fof(f889,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f858,f100]) ).
fof(f891,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f880,f889]) ).
fof(f898,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f891,f778]) ).
fof(f901,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f880,f92]) ).
fof(f902,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f898,f901]) ).
fof(f903,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f891,f902]) ).
fof(f927,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f891,f65]) ).
fof(f928,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f858,f927]) ).
fof(f929,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f903,f928]) ).
fof(f930,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f880,f929]) ).
fof(f931,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f930]) ).
fof(f932,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f931]) ).
fof(f933,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,f134,f140,f146,f158,f164,f173,f273,f319,f357,f368,f382,f409,f445,f525,f663,f708,f713,f727,f814,f820,f849,f851,f932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP272-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.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 20:06:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.066747 seconds
% 0.12/0.42 % CPU time: 0.195616 seconds
% 0.12/0.42 % Total memory used: 104.141 MB
% 0.12/0.42 % Net memory used: 103.864 MB
%------------------------------------------------------------------------------