%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP213-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:33:07 PM UTC 2026
% Result : Unsatisfiable 0.23s 5.71s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 47
% Syntax : Number of formulae : 225 ( 11 unt; 19 def)
% Number of atoms : 752 ( 267 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 993 ( 466 ~; 508 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 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,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f30,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f41,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f56,plain,
! [X3] :
( inverse(X3) != sk_c8
| ! [X2] :
( multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| ! [X5,X6] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ1_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ1_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f63,plain,
( sQ1_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f58,f61]) ).
fof(f65,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f58,f65]) ).
fof(f69,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f58,f69]) ).
fof(f73,definition,
( sQ4_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f58,f73]) ).
fof(f77,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f58,f77]) ).
fof(f81,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f58,f81]) ).
fof(f85,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f38,f85,f61]) ).
fof(f89,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f39,f85,f65]) ).
fof(f90,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f85,f69]) ).
fof(f91,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f85,f73]) ).
fof(f92,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f85,f77]) ).
fof(f93,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f85,f81]) ).
fof(f94,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f94,f61]) ).
fof(f98,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f94,f65]) ).
fof(f99,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f94,f69]) ).
fof(f100,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f94,f73]) ).
fof(f101,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f94,f77]) ).
fof(f102,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f94,f81]) ).
fof(f103,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f103,f61]) ).
fof(f107,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f103,f65]) ).
fof(f108,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f103,f69]) ).
fof(f109,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f103,f73]) ).
fof(f110,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f103,f77]) ).
fof(f111,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f103,f81]) ).
fof(f112,definition,
! [X0] :
( sQ10_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f113,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
! [X1,X2] :
( sQ11_spl
<=> ( inverse(X1) != X2
| multiply(X1,X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0,X1] :
( ~ sQ11_spl
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X3] :
( sQ12_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X4,X5] :
( sQ13_spl
<=> ( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ13_spl
| sQ12_spl
| ~ sQ1_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f57,f112,f115,f61,f118,f121]) ).
fof(f125,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f122]) ).
fof(f147,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f125]) ).
fof(f148,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f59,f125]) ).
fof(f156,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f147,f73,f81,f121,f77]) ).
fof(f157,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( sQ16_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f148,f157,f85,f121,f58]) ).
fof(f161,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f119,f70]) ).
fof(f164,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f66,f161]) ).
fof(f165,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f164]) ).
fof(f166,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f167,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f116]) ).
fof(f171,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f172,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f29,f171]) ).
fof(f173,plain,
( ~ sQ11_spl
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f29,f167]) ).
fof(f176,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f104,f167]) ).
fof(f178,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f95,f176]) ).
fof(f179,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f178]) ).
fof(f180,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f183,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f82,f30]) ).
fof(f187,plain,
( ~ sQ10_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f29,f113]) ).
fof(f196,definition,
( sQ19_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ19_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ20_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ20_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( ~ sQ10_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f187,f196,f199,f112]) ).
fof(f203,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| inverse(sk_c5) != sk_c8
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f113]) ).
fof(f205,definition,
( sQ21_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ21_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f203,f205,f81,f112,f77]) ).
fof(f213,definition,
( sQ22_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ22_spl
| inverse(sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( sQ22_spl
| inverse(sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f233,plain,
( ~ sQ6_spl
| sk_c5 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f183,f172]) ).
fof(f235,plain,
( ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f172]) ).
fof(f237,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f78,f172]) ).
fof(f241,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f29,f172]) ).
fof(f246,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f62,f233]) ).
fof(f248,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f62,f235]) ).
fof(f250,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f82,f237]) ).
fof(f251,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f250]) ).
fof(f261,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f251,f74]) ).
fof(f265,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f251,f66]) ).
fof(f266,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f251,f62]) ).
fof(f268,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f251,f70]) ).
fof(f269,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f251,f173]) ).
fof(f280,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f261,f172]) ).
fof(f282,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f30,f280]) ).
fof(f283,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f282,f269]) ).
fof(f292,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f282,f246]) ).
fof(f293,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f300,f283]) ).
fof(f294,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f300,f266]) ).
fof(f297,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f300,f265]) ).
fof(f300,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f261,f292]) ).
fof(f301,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f300,f294]) ).
fof(f311,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f300,f248]) ).
fof(f312,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c6 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f300,f311]) ).
fof(f320,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f300,f268]) ).
fof(f321,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f300,f320]) ).
fof(f322,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f321,f172]) ).
fof(f324,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f297,f322]) ).
fof(f325,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f312,f324]) ).
fof(f331,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f325,f293]) ).
fof(f334,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f301,f331]) ).
fof(f335,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f334]) ).
fof(f336,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f339,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f325,f207]) ).
fof(f340,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f300,f339]) ).
fof(f341,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f340]) ).
fof(f342,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f343,plain,
( ~ sQ8_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f95,f172]) ).
fof(f345,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = multiply(sk_c3,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f104,f343]) ).
fof(f348,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f172,f241]) ).
fof(f354,plain,
( ~ sQ0_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f59,f172]) ).
fof(f356,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f86,f354]) ).
fof(f374,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f345,f172]) ).
fof(f376,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f30,f374]) ).
fof(f378,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f376,f30]) ).
fof(f381,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f376,f348]) ).
fof(f383,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f376,f201]) ).
fof(f404,plain,
( sQ16_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f381,f159]) ).
fof(f409,plain,
( sQ16_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f404]) ).
fof(f410,plain,
( sQ16_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f416,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f381,f356]) ).
fof(f420,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f416,f383]) ).
fof(f421,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f416,f381]) ).
fof(f422,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f416,f378]) ).
fof(f429,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f416,f63]) ).
fof(f431,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f416,f86]) ).
fof(f434,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f416,f215]) ).
fof(f435,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f416,f420]) ).
fof(f475,plain,
( ~ sQ22_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f416,f214]) ).
fof(f481,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c1) = sk_c7 ),
inference(paramodulation,[status(thm)],[f431,f422]) ).
fof(f486,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f421,f481]) ).
fof(f488,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f486,f431]) ).
fof(f490,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f475,f435]) ).
fof(f491,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f490]) ).
fof(f492,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f493,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ22_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f475,f429]) ).
fof(f494,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f493]) ).
fof(f495,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f514,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f416,f198]) ).
fof(f515,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f514]) ).
fof(f516,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f521,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f488,f434]) ).
fof(f522,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f527,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f416,f119]) ).
fof(f528,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c7) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f416,f527]) ).
fof(f536,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| multiply(sk_c7,sk_c7) != sk_c7 ),
inference(resolution,[status(thm)],[f528,f488]) ).
fof(f539,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f421,f536]) ).
fof(f540,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f539]) ).
fof(f541,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
$false,
inference(sat_refutation,[status(thm)],[f64,f68,f72,f76,f80,f84,f88,f89,f90,f91,f92,f93,f97,f98,f99,f100,f101,f102,f106,f107,f108,f109,f110,f111,f124,f156,f160,f166,f180,f202,f208,f336,f342,f410,f492,f495,f516,f523,f541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP213-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.67 % Computer : n001.cluster.edu
% 0.19/5.67 % Model : x86_64 x86_64
% 0.19/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.67 % Memory : 8046.5625MB
% 0.19/5.67 % OS : Linux 6.8.0-71-generic
% 0.19/5.67 % CPULimit : 300
% 0.19/5.67 % WCLimit : 300
% 0.19/5.67 % DateTime : Sun Sep 20 20:12:03 UTC 2026
% 0.19/5.67 % CPUTime :
% 0.19/5.69 % Drodi V4.1.1
% 0.23/5.71 % Refutation found
% 0.23/5.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/5.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.74 % Elapsed time: 0.063845 seconds
% 0.23/5.74 % CPU time: 0.229204 seconds
% 0.23/5.74 % Total memory used: 84.634 MB
% 0.23/5.74 % Net memory used: 84.456 MB
%------------------------------------------------------------------------------