%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP355-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:33:30 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 35
% Syntax : Number of formulae : 150 ( 10 unt; 14 def)
% Number of atoms : 451 ( 190 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 559 ( 258 ~; 287 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 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(f8,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [X2,X1,X3,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
file('/export/starexec/sandbox2/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(f33,plain,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f50,plain,
! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ) ) ) ) ),
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_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f54,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> multiply(sk_c2,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f59,definition,
( sQ2_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ2_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f63,definition,
( sQ3_spl
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f67,definition,
( sQ4_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f71,definition,
( sQ5_spl
<=> multiply(sk_c8,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f52,f71]) ).
fof(f75,definition,
( sQ6_spl
<=> multiply(sk_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ6_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f52,f75]) ).
fof(f79,definition,
( sQ7_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ7_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f52,f79]) ).
fof(f83,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f36,f83,f55]) ).
fof(f87,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f37,f83,f59]) ).
fof(f88,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f38,f83,f63]) ).
fof(f89,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f39,f83,f67]) ).
fof(f90,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f40,f83,f71]) ).
fof(f91,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f41,f83,f75]) ).
fof(f92,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f42,f83,f79]) ).
fof(f93,definition,
( sQ9_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f43,f93,f55]) ).
fof(f97,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f44,f93,f59]) ).
fof(f98,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f45,f93,f63]) ).
fof(f99,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f46,f93,f67]) ).
fof(f100,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f47,f93,f71]) ).
fof(f101,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f48,f93,f75]) ).
fof(f102,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f49,f93,f79]) ).
fof(f103,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(f104,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
! [X2] :
( sQ11_spl
<=> ( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f107,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
! [X3,X4] :
( sQ12_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f110,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f52,f103,f106,f109]) ).
fof(f113,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f110]) ).
fof(f132,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c6 ),
inference(paramodulation,[status(thm)],[f76,f113]) ).
fof(f133,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f84,f113]) ).
fof(f134,definition,
( sQ13_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( sQ13_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f138,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f132,f71,f79,f109,f75]) ).
fof(f139,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f133,f134,f93,f109,f83]) ).
fof(f140,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f107,f68]) ).
fof(f143,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f64,f140]) ).
fof(f144,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f143]) ).
fof(f145,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f149,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f150,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f26,f149]) ).
fof(f162,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f26,f150]) ).
fof(f165,plain,
( ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c8) ),
inference(paramodulation,[status(thm)],[f53,f150]) ).
fof(f166,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f84,f150]) ).
fof(f168,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f166]) ).
fof(f176,plain,
( sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f168,f136]) ).
fof(f177,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f168,f150]) ).
fof(f179,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f177]) ).
fof(f180,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(inverse(sk_c7),X0) ),
inference(backward_demodulation,[status(thm)],[f179,f162]) ).
fof(f184,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f179,f26]) ).
fof(f186,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f184,f53]) ).
fof(f189,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f176]) ).
fof(f190,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f191,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f184,f54]) ).
fof(f216,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f64,f150]) ).
fof(f218,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f216]) ).
fof(f228,plain,
( ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f76,f150]) ).
fof(f230,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f80,f228]) ).
fof(f231,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f72,f230]) ).
fof(f232,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f191]) ).
fof(f233,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f180,f165]) ).
fof(f238,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(resolution,[status(thm)],[f104,f60]) ).
fof(f239,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(resolution,[status(thm)],[f104,f94]) ).
fof(f242,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f56,f238]) ).
fof(f243,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f242]) ).
fof(f244,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f243]) ).
fof(f245,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f84,f239]) ).
fof(f246,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f245]) ).
fof(f247,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f257,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f231,f54]) ).
fof(f278,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f231,f218]) ).
fof(f279,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f231,f278]) ).
fof(f280,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f279,f150]) ).
fof(f282,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f280]) ).
fof(f286,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f231,f72]) ).
fof(f287,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c5 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f286,f150]) ).
fof(f289,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f287]) ).
fof(f297,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f282,f26]) ).
fof(f302,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f303,f257]) ).
fof(f303,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f282,f289]) ).
fof(f304,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f303,f297]) ).
fof(f348,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f304,f302]) ).
fof(f349,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f348]) ).
fof(f350,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f383,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f235,f107]) ).
fof(f384,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f235,f383]) ).
fof(f385,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(resolution,[status(thm)],[f384,f94]) ).
fof(f387,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f385,f83,f52,f106,f93]) ).
fof(f392,plain,
$false,
inference(sat_refutation,[status(thm)],[f74,f78,f82,f86,f87,f88,f89,f90,f91,f92,f96,f97,f98,f99,f100,f101,f102,f112,f138,f139,f145,f190,f233,f244,f247,f350,f387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP355-1 : 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 : n010.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 20:10:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.052155 seconds
% 0.12/0.41 % CPU time: 0.194738 seconds
% 0.12/0.41 % Total memory used: 91.601 MB
% 0.12/0.41 % Net memory used: 91.427 MB
%------------------------------------------------------------------------------