%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP306-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:33:22 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 48
% Syntax : Number of formulae : 241 ( 15 unt; 23 def)
% Number of atoms : 776 ( 277 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1009 ( 474 ~; 512 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 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_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X3) != X4
| multiply(X3,X4) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f50,plain,
! [X5] :
( inverse(X5) != sk_c8
| ! [X2] :
( multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| ! [X4] :
( multiply(X4,sk_c7) != sk_c8
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f54,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f52,f55]) ).
fof(f59,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f52,f59]) ).
fof(f63,definition,
( sQ3_spl
<=> multiply(sk_c8,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f52,f63]) ).
fof(f67,definition,
( sQ4_spl
<=> multiply(sk_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ4_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f52,f67]) ).
fof(f71,definition,
( sQ5_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f52,f71]) ).
fof(f75,definition,
( sQ6_spl
<=> multiply(sk_c1,sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f35,f75,f55]) ).
fof(f79,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f36,f75,f59]) ).
fof(f80,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f37,f75,f63]) ).
fof(f81,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f75,f67]) ).
fof(f82,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f75,f71]) ).
fof(f83,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f83,f55]) ).
fof(f87,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f83,f59]) ).
fof(f88,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f83,f63]) ).
fof(f89,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f83,f67]) ).
fof(f90,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f83,f71]) ).
fof(f91,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f91,f55]) ).
fof(f95,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f91,f59]) ).
fof(f96,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f91,f63]) ).
fof(f97,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f91,f67]) ).
fof(f98,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f91,f71]) ).
fof(f99,definition,
( sQ9_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ9_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
! [X0,X1] :
( sQ10_spl
<=> ( multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f103,plain,
! [X0,X1] :
( ~ sQ10_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
! [X2] :
( sQ11_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f106,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
! [X3,X4] :
( sQ12_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f109,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl
| ~ sQ0_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f99,f52,f102,f105,f108]) ).
fof(f112,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f109]) ).
fof(f119,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f53,f27]) ).
fof(f120,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f60,f27]) ).
fof(f121,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f72,f27]) ).
fof(f122,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f84,f27]) ).
fof(f123,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f124,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f26,f123]) ).
fof(f125,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f76,f28]) ).
fof(f128,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f56,f28]) ).
fof(f129,plain,
! [X0] :
( ~ sQ0_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f119,f28]) ).
fof(f130,plain,
! [X0] :
( ~ sQ0_spl
| X0 = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f26,f129]) ).
fof(f131,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f120,f28]) ).
fof(f132,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c8,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f26,f131]) ).
fof(f133,plain,
! [X0] :
( ~ sQ5_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f121,f28]) ).
fof(f134,plain,
! [X0] :
( ~ sQ5_spl
| X0 = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f26,f133]) ).
fof(f135,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c6) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f119,f112]) ).
fof(f136,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f56,f112]) ).
fof(f137,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f68,f112]) ).
fof(f138,plain,
( ~ sQ12_spl
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f27,f112]) ).
fof(f139,plain,
( ~ sQ12_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f26,f112]) ).
fof(f141,definition,
( sQ13_spl
<=> multiply(sk_c8,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ13_spl
| multiply(sk_c8,identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ14_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ14_spl
| inverse(sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f135,f141,f144,f108,f52]) ).
fof(f148,definition,
( sQ15_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ15_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f136,f148,f59,f108,f55]) ).
fof(f152,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f137,f63,f71,f108,f67]) ).
fof(f153,definition,
( sQ16_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f138,f141,f153,f108]) ).
fof(f157,definition,
( sQ17_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f160,definition,
( sQ18_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( sQ18_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f139,f157,f160,f108]) ).
fof(f165,plain,
( sQ15_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f29,f150]) ).
fof(f166,plain,
! [X0] :
( ~ sQ10_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f103]) ).
fof(f167,plain,
( sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f29,f101]) ).
fof(f168,plain,
( sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f167]) ).
fof(f169,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ sQ11_spl
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f27,f106]) ).
fof(f172,plain,
( ~ sQ11_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f26,f106]) ).
fof(f174,definition,
( sQ19_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ19_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f178,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f171,f174,f153,f105]) ).
fof(f179,definition,
( sQ20_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ20_spl
| sk_c8 = sk_c7 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( sQ20_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f172,f179,f160,f105]) ).
fof(f183,plain,
( ~ sQ10_spl
| multiply(inverse(identity),sk_c7) != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f26,f166]) ).
fof(f185,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c8
| multiply(sk_c1,sk_c2) != sk_c8 ),
inference(paramodulation,[status(thm)],[f84,f166]) ).
fof(f186,definition,
( sQ21_spl
<=> multiply(inverse(identity),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ21_spl
| multiply(inverse(identity),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ sQ10_spl
| ~ sQ21_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f183,f160,f186,f102]) ).
fof(f190,definition,
( sQ22_spl
<=> multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ22_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ22_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f185,f75,f190,f102,f83]) ).
fof(f194,plain,
( sQ22_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f84,f192]) ).
fof(f195,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f92,f194]) ).
fof(f196,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f195]) ).
fof(f197,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f210,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c7) = multiply(sk_c1,sk_c8) ),
inference(paramodulation,[status(thm)],[f92,f125]) ).
fof(f213,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c1,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f29,f210]) ).
fof(f231,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f56,f132]) ).
fof(f239,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f245,f54]) ).
fof(f241,plain,
( sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f245,f165]) ).
fof(f245,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f29,f231]) ).
fof(f259,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(paramodulation,[status(thm)],[f68,f134]) ).
fof(f260,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c7,multiply(sk_c4,X0)) = multiply(sk_c3,X0) ),
inference(paramodulation,[status(thm)],[f134,f128]) ).
fof(f262,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f64,f259]) ).
fof(f263,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f181]) ).
fof(f264,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f276,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c8,multiply(sk_c4,X0)) = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f262,f260]) ).
fof(f283,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(inverse(identity),sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f262,f188]) ).
fof(f285,plain,
( sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f241,f179,f59,f55,f148]) ).
fof(f291,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| X0 = multiply(sk_c8,X0) ),
inference(backward_demodulation,[status(thm)],[f293,f132]) ).
fof(f293,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f134,f276]) ).
fof(f305,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f291,f121]) ).
fof(f306,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f291,f120]) ).
fof(f316,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f305,f162]) ).
fof(f317,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f305,f27]) ).
fof(f319,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(inverse(sk_c4),sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f305,f283]) ).
fof(f324,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f305,f306]) ).
fof(f335,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f72,f316]) ).
fof(f336,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f335]) ).
fof(f337,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f338,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f324,f317]) ).
fof(f340,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(inverse(sk_c3),sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f324,f319]) ).
fof(f341,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f60,f340]) ).
fof(f342,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f291,f341]) ).
fof(f343,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f342]) ).
fof(f344,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f360,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f124,f124]) ).
fof(f361,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| X0 = multiply(inverse(inverse(X0)),sk_c3) ),
inference(paramodulation,[status(thm)],[f338,f124]) ).
fof(f366,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| X0 = multiply(X0,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f360,f361]) ).
fof(f421,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f27,f124]) ).
fof(f424,plain,
( sQ13_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f425,f143]) ).
fof(f425,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f360,f421]) ).
fof(f427,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f92,f124]) ).
fof(f429,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c2),identity) ),
inference(paramodulation,[status(thm)],[f122,f124]) ).
fof(f431,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f432,f427]) ).
fof(f432,plain,
( ~ sQ7_spl
| sk_c1 = inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f425,f429]) ).
fof(f441,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f443,f130]) ).
fof(f443,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f213,f431]) ).
fof(f450,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f432,f27]) ).
fof(f451,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f432,f124]) ).
fof(f455,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f460,f162]) ).
fof(f456,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f460,f176]) ).
fof(f458,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(X0,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f460,f425]) ).
fof(f460,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f450]) ).
fof(f464,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c7,X0) ),
inference(backward_demodulation,[status(thm)],[f467,f441]) ).
fof(f467,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f125,f451]) ).
fof(f487,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(paramodulation,[status(thm)],[f458,f464]) ).
fof(f488,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = sk_c8 ),
inference(paramodulation,[status(thm)],[f464,f458]) ).
fof(f491,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f424]) ).
fof(f492,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f493,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f488,f179,f75,f83,f91,f52]) ).
fof(f498,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f443,f245]) ).
fof(f502,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f458,f56]) ).
fof(f504,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f498,f502]) ).
fof(f522,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ8_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f504,f60]) ).
fof(f532,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(X0) != sk_c8
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f458,f106]) ).
fof(f533,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| X0 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f498,f532]) ).
fof(f534,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| inverse(sk_c8) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f533]) ).
fof(f535,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f522]) ).
fof(f536,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f632,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = sk_c3 ),
inference(paramodulation,[status(thm)],[f291,f366]) ).
fof(f642,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f632,f60]) ).
fof(f651,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f642,f239]) ).
fof(f652,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f653,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f456,f179,f75,f83,f174]) ).
fof(f656,plain,
( sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c7) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f443,f146]) ).
fof(f688,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c8) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f443,f53]) ).
fof(f690,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f180,f688]) ).
fof(f699,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ20_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f690,f455]) ).
fof(f700,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f699]) ).
fof(f701,plain,
( sQ18_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f742,plain,
( sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f180,f656]) ).
fof(f743,plain,
( sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f690,f742]) ).
fof(f744,plain,
( sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f743]) ).
fof(f745,plain,
( sQ14_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f746,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f62,f66,f70,f74,f78,f79,f80,f81,f82,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f111,f147,f151,f152,f156,f163,f169,f178,f182,f189,f193,f197,f264,f285,f337,f344,f492,f493,f536,f652,f653,f701,f745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP306-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 20:08:58 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.062976 seconds
% 0.12/0.43 % CPU time: 0.242355 seconds
% 0.12/0.43 % Total memory used: 105.616 MB
% 0.12/0.43 % Net memory used: 105.229 MB
%------------------------------------------------------------------------------