%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP333-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:26 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 43
% Syntax : Number of formulae : 201 ( 14 unt; 22 def)
% Number of atoms : 618 ( 221 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 787 ( 370 ~; 395 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 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,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
! [X3,X4,X1,X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f29,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f42,plain,
! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| ! [X4] :
( multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f26,f44,f47]) ).
fof(f51,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f27,f44,f51]) ).
fof(f55,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f44,f55]) ).
fof(f59,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f44,f59]) ).
fof(f63,definition,
( sQ5_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ5_spl
| inverse(sk_c1) = sk_c6 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f30,f63,f47]) ).
fof(f67,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f31,f63,f51]) ).
fof(f68,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f32,f63,f55]) ).
fof(f69,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f33,f63,f59]) ).
fof(f70,definition,
( sQ6_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ6_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f34,f70,f47]) ).
fof(f74,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f35,f70,f51]) ).
fof(f75,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f36,f70,f55]) ).
fof(f76,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f37,f70,f59]) ).
fof(f77,definition,
( sQ7_spl
<=> multiply(sk_c2,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f38,f77,f47]) ).
fof(f81,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f39,f77,f51]) ).
fof(f82,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f77,f55]) ).
fof(f83,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f77,f59]) ).
fof(f84,definition,
( sQ8_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ8_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
! [X0] :
( sQ9_spl
<=> ( inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f88,plain,
! [X0] :
( ~ sQ9_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
! [X1] :
( sQ10_spl
<=> ( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f91,plain,
! [X0] :
( ~ sQ10_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
! [X2] :
( sQ11_spl
<=> ( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f94,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
! [X3] :
( sQ12_spl
<=> ( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f97,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f43,f84,f87,f90,f93,f96]) ).
fof(f100,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f97,f56]) ).
fof(f102,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c6
| sk_c7 != sk_c5 ),
inference(paramodulation,[status(thm)],[f45,f97]) ).
fof(f103,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f60,f100]) ).
fof(f104,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f103]) ).
fof(f105,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ8_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f25,f86]) ).
fof(f107,plain,
( sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f106]) ).
fof(f108,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f107]) ).
fof(f109,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f94,f48]) ).
fof(f112,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f52,f109]) ).
fof(f113,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f112]) ).
fof(f114,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f91,f78]) ).
fof(f117,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f115]) ).
fof(f118,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f117]) ).
fof(f119,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f128,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| inverse(sk_c4) != sk_c6
| sk_c5 != sk_c7 ),
inference(paramodulation,[status(thm)],[f56,f88]) ).
fof(f129,definition,
( sQ13_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ13_spl
| sk_c5 = sk_c7 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( sQ13_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f128,f129,f59,f87,f55]) ).
fof(f135,definition,
( sQ14_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ14_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f145,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f153,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f22,f145]) ).
fof(f165,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c6) ),
inference(paramodulation,[status(thm)],[f48,f153]) ).
fof(f166,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f56,f153]) ).
fof(f171,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f52,f165]) ).
fof(f172,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f60,f166]) ).
fof(f186,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f171,f88]) ).
fof(f187,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f171,f153]) ).
fof(f189,definition,
( sQ19_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ19_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ20_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f186,f189,f192,f87,f51,f47]) ).
fof(f196,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f23,f187]) ).
fof(f197,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f191]) ).
fof(f198,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f203,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f196,f23]) ).
fof(f204,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f196,f22]) ).
fof(f205,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f204,f25]) ).
fof(f209,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f131]) ).
fof(f210,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,definition,
( sQ21_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ21_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f215,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(paramodulation,[status(thm)],[f60,f203]) ).
fof(f219,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f204,f215]) ).
fof(f227,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| sk_c6 != sk_c6
| inverse(inverse(sk_c5)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f203,f91]) ).
fof(f230,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| sk_c5 != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f204,f91]) ).
fof(f231,definition,
( sQ22_spl
<=> inverse(inverse(sk_c5)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f227,f231,f211,f90,f51,f47]) ).
fof(f236,definition,
( sQ23_spl
<=> inverse(sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( sQ23_spl
| inverse(sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,definition,
( sQ24_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ24_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f230,f236,f239,f90,f51,f47]) ).
fof(f245,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f219,f204]) ).
fof(f247,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f219,f60]) ).
fof(f253,plain,
( sQ23_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f219,f238]) ).
fof(f254,plain,
( sQ23_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f219,f253]) ).
fof(f261,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f247,f254]) ).
fof(f262,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f263,plain,
( sQ24_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f219,f241]) ).
fof(f268,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f219,f172]) ).
fof(f269,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c4,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f219,f268]) ).
fof(f270,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f245,f269]) ).
fof(f271,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f263]) ).
fof(f272,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f271]) ).
fof(f273,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f213]) ).
fof(f274,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f280,plain,
( ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f45,f153]) ).
fof(f282,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f64,f280]) ).
fof(f288,plain,
( ~ sQ7_spl
| sk_c5 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f78,f153]) ).
fof(f290,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f71,f288]) ).
fof(f298,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f71,f23]) ).
fof(f305,plain,
( ~ sQ11_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f22,f94]) ).
fof(f310,definition,
( sQ26_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( sQ26_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,plain,
( ~ sQ11_spl
| ~ sQ26_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f305,f135,f310,f93]) ).
fof(f325,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c6 ),
inference(resolution,[status(thm)],[f88,f45]) ).
fof(f332,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f64,f325]) ).
fof(f333,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f332]) ).
fof(f334,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f344,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f25,f282]) ).
fof(f347,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f129,f63,f96,f44]) ).
fof(f348,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f344,f25]) ).
fof(f350,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f344,f71]) ).
fof(f360,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f344,f290]) ).
fof(f361,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f344,f360]) ).
fof(f362,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f361,f153]) ).
fof(f364,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f23,f362]) ).
fof(f367,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f364,f22]) ).
fof(f371,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f344,f298]) ).
fof(f372,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f367,f371]) ).
fof(f373,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f380,f367]) ).
fof(f374,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f380,f364]) ).
fof(f376,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ7_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f380,f350]) ).
fof(f377,plain,
( sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sk_c2 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f380,f131]) ).
fof(f379,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f380,f344]) ).
fof(f380,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f364,f372]) ).
fof(f401,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f380,f348]) ).
fof(f402,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f373,f401]) ).
fof(f403,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f380,f402]) ).
fof(f404,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f377]) ).
fof(f405,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f406,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f379,f137]) ).
fof(f417,plain,
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f380,f130]) ).
fof(f419,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f406]) ).
fof(f420,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f421,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| inverse(sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f374,f312]) ).
fof(f422,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f376,f421]) ).
fof(f428,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ13_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f417,f422]) ).
fof(f429,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f428]) ).
fof(f430,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f431,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f54,f58,f62,f66,f67,f68,f69,f73,f74,f75,f76,f80,f81,f82,f83,f99,f105,f108,f114,f119,f132,f195,f198,f210,f234,f242,f262,f272,f274,f313,f334,f347,f405,f420,f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP333-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:04:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.053088 seconds
% 0.13/0.41 % CPU time: 0.105104 seconds
% 0.13/0.41 % Total memory used: 23.095 MB
% 0.13/0.41 % Net memory used: 23.068 MB
%------------------------------------------------------------------------------