%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP351-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:33:29 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 53
% Syntax : Number of formulae : 249 ( 12 unt; 24 def)
% Number of atoms : 847 ( 276 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1123 ( 525 ~; 574 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 43 ( 43 !; 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,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| 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
| 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_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| 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_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| 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_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| 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_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X3,X4,X1,X2] :
( multiply(X2,sk_c6) != sk_c5
| inverse(X2) != sk_c5
| 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_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,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
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_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| 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_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| 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_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| 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_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X2] :
( multiply(X2,sk_c6) != sk_c5
| inverse(X2) != sk_c5
| ! [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_c6,sk_c5) != sk_c7 ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c6) != sk_c5
| inverse(X3) != sk_c5
| 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_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
<=> 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_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c5 ),
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_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c6) = sk_c5 ),
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(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_c6) != sk_c5
| inverse(X3) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f125,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c6) != sk_c5
| inverse(X0) != sk_c5 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ13_spl
| sQ12_spl
| ~ sQ1_spl
| sQ11_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f60,f115,f118,f63,f121,f124]) ).
fof(f128,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c5 ),
inference(resolution,[status(thm)],[f125,f80]) ).
fof(f129,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c5 ),
inference(resolution,[status(thm)],[f125,f100]) ).
fof(f130,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| sk_c7 != sk_c5
| inverse(sk_c3) != sk_c5 ),
inference(paramodulation,[status(thm)],[f68,f125]) ).
fof(f132,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| sk_c5 != sk_c5
| inverse(sk_c2) != sk_c5 ),
inference(paramodulation,[status(thm)],[f100,f125]) ).
fof(f133,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f76,f128]) ).
fof(f134,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f136,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f122,f68]) ).
fof(f139,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c6
| sk_c5 != sk_c7 ),
inference(paramodulation,[status(thm)],[f100,f122]) ).
fof(f140,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f72,f136]) ).
fof(f141,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f140]) ).
fof(f142,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f119,f100]) ).
fof(f145,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c6
| sk_c7 != sk_c5 ),
inference(paramodulation,[status(thm)],[f68,f119]) ).
fof(f148,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f108,f144]) ).
fof(f149,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f148]) ).
fof(f150,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f157,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f116,f84]) ).
fof(f160,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f92,f157]) ).
fof(f161,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f160]) ).
fof(f162,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,definition,
( sQ14_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ14_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f167,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f165]) ).
fof(f168,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( ~ sQ10_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f30,f116]) ).
fof(f171,definition,
( sQ15_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ15_spl
| sk_c7 = sk_c6 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f173,plain,
( sQ15_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ16_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ16_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f169,f171,f174,f115]) ).
fof(f182,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f190,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f182]) ).
fof(f191,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| inverse(sk_c6) != sk_c7
| sk_c5 != sk_c6 ),
inference(paramodulation,[status(thm)],[f64,f116]) ).
fof(f193,definition,
( sQ19_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ19_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ20_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f191,f193,f196,f115,f63]) ).
fof(f230,plain,
( ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f68,f190]) ).
fof(f232,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f80,f190]) ).
fof(f235,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f72,f230]) ).
fof(f236,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f64,f235]) ).
fof(f237,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f195]) ).
fof(f238,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f76,f232]) ).
fof(f244,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c5) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f236,f62]) ).
fof(f249,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f236,f72]) ).
fof(f250,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f236,f68]) ).
fof(f257,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f236,f240]) ).
fof(f258,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f257,f190]) ).
fof(f260,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f258]) ).
fof(f261,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f257,f244]) ).
fof(f263,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f260,f31]) ).
fof(f264,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f260,f30]) ).
fof(f308,definition,
( sQ21_spl
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( ~ sQ21_spl
| sk_c7 = sk_c5 ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f310,plain,
( sQ21_spl
| sk_c7 != sk_c5 ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f145,f308,f71,f118,f67]) ).
fof(f312,definition,
( sQ22_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ22_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f332,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f139,f308,f107,f121,f99]) ).
fof(f333,definition,
( sQ24_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ24_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f337,plain,
( sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f335]) ).
fof(f338,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f343,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f100,f190]) ).
fof(f345,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f108,f343]) ).
fof(f346,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f84,f190]) ).
fof(f348,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f92,f346]) ).
fof(f388,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f61,f345]) ).
fof(f389,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f173]) ).
fof(f390,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f391,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| identity = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f31,f263]) ).
fof(f393,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f314]) ).
fof(f394,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f393]) ).
fof(f397,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f391,f31]) ).
fof(f399,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f391,f30]) ).
fof(f413,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f250,f190]) ).
fof(f415,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f249,f413]) ).
fof(f416,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f264,f415]) ).
fof(f417,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f310]) ).
fof(f418,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f417]) ).
fof(f419,definition,
( sQ29_spl
<=> inverse(sk_c3) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ21_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f130,f419,f308,f124,f67]) ).
fof(f423,definition,
( sQ30_spl
<=> inverse(sk_c2) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ30_spl
| inverse(sk_c2) != sk_c5 ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ22_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f132,f423,f312,f124,f99]) ).
fof(f433,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f388,f108]) ).
fof(f435,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f433,f129]) ).
fof(f436,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f433,f425]) ).
fof(f441,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f388,f348]) ).
fof(f447,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f388,f64]) ).
fof(f448,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f441,f447]) ).
fof(f449,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f448,f310]) ).
fof(f450,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f451,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f436,f308,f60,f99,f107,f423]) ).
fof(f452,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f435,f308,f60,f107,f124,f99]) ).
fof(f453,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f261,f308,f75,f79,f63,f71,f67,f60]) ).
fof(f456,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| identity = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f309,f391]) ).
fof(f457,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f309,f236]) ).
fof(f458,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f456,f31]) ).
fof(f470,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f457,f173]) ).
fof(f471,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f470]) ).
fof(f472,plain,
( sQ15_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f473,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f456,f176]) ).
fof(f481,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f309,f399]) ).
fof(f484,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| inverse(sk_c3) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f309,f249]) ).
fof(f485,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c3) = sk_c7 ),
inference(paramodulation,[status(thm)],[f484,f458]) ).
fof(f487,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f481,f485]) ).
fof(f489,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f487,f484]) ).
fof(f497,plain,
( ~ sQ21_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f487,f309]) ).
fof(f500,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f497,f264]) ).
fof(f505,plain,
( ~ sQ4_spl
| ~ sQ21_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f497,f76]) ).
fof(f513,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f497,f397]) ).
fof(f514,plain,
( ~ sQ4_spl
| ~ sQ21_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c4) = sk_c3 ),
inference(paramodulation,[status(thm)],[f505,f513]) ).
fof(f517,plain,
( ~ sQ4_spl
| ~ sQ21_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f500,f514]) ).
fof(f526,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f517,f487]) ).
fof(f531,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| inverse(sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f526,f473]) ).
fof(f532,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ21_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f526,f531]) ).
fof(f534,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f517,f489]) ).
fof(f535,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f517,f534]) ).
fof(f536,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f532]) ).
fof(f537,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f540,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| multiply(sk_c7,sk_c5) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f172,f61]) ).
fof(f546,plain,
( sQ1_spl
| ~ sQ15_spl
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f172,f65]) ).
fof(f567,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f441,f546]) ).
fof(f568,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f441,f190]) ).
fof(f570,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f568]) ).
fof(f574,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f570,f30]) ).
fof(f576,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f574,f540]) ).
fof(f579,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f576,f308,f107,f99,f91,f83,f171,f60]) ).
fof(f580,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f567,f308,f60,f107,f99,f91,f83,f171,f63]) ).
fof(f582,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,f135,f142,f150,f162,f168,f177,f199,f238,f311,f332,f338,f390,f394,f418,f422,f426,f450,f451,f452,f453,f472,f537,f579,f580]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP351-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:09:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.076379 seconds
% 0.14/0.46 % CPU time: 0.291856 seconds
% 0.14/0.46 % Total memory used: 101.480 MB
% 0.14/0.46 % Net memory used: 101.252 MB
%------------------------------------------------------------------------------