%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP302-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:33:21 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.55s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 43
% Syntax : Number of formulae : 176 ( 16 unt; 23 def)
% Number of atoms : 444 ( 211 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 493 ( 225 ~; 245 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 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 : 47 ( 47 !; 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,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( multiply(X2,sk_c8) != X5
| inverse(X5) != sk_c8
| inverse(X2) != X5
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( inverse(sk_c5) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( multiply(sk_c5,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( inverse(sk_c5) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c5,sk_c8) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f52,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f58,plain,
! [X2,X5] :
( multiply(X2,sk_c8) != X5
| inverse(X5) != sk_c8
| inverse(X2) != X5
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| ! [X3] :
( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X3,sk_c8) != X4
| inverse(X4) != sk_c8
| inverse(X3) != X4
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ1_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f60,f63]) ).
fof(f67,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f60,f67]) ).
fof(f71,definition,
( sQ3_spl
<=> multiply(sk_c3,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f60,f71]) ).
fof(f75,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c4 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f60,f75]) ).
fof(f79,definition,
( sQ5_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f60,f79]) ).
fof(f83,definition,
( sQ6_spl
<=> multiply(sk_c5,sk_c8) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c8) = sk_c4 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f60,f83]) ).
fof(f87,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f91,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f87,f67]) ).
fof(f92,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f87,f71]) ).
fof(f93,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f87,f75]) ).
fof(f94,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f87,f79]) ).
fof(f95,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f87,f83]) ).
fof(f96,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f96,f63]) ).
fof(f100,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f96,f67]) ).
fof(f105,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f105,f63]) ).
fof(f109,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f105,f67]) ).
fof(f114,definition,
( sQ10_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( sQ10_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,definition,
! [X0] :
( sQ11_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f118,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
! [X1] :
( sQ12_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f121,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
! [X3,X4] :
( sQ13_spl
<=> ( multiply(X3,sk_c8) != X4
| inverse(X4) != sk_c8
| inverse(X3) != X4 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X0,sk_c8) != X1
| inverse(X1) != sk_c8
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f114,f117,f120,f63,f123]) ).
fof(f127,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f134,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f68,f31]) ).
fof(f136,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f80,f31]) ).
fof(f137,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f61,f31]) ).
fof(f138,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f106,f31]) ).
fof(f139,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f140,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f139]) ).
fof(f150,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| sk_c4 != inverse(sk_c5)
| inverse(inverse(sk_c5)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f84,f127]) ).
fof(f151,plain,
( ~ sQ13_spl
| identity != inverse(inverse(sk_c8))
| inverse(inverse(inverse(sk_c8))) != sk_c8 ),
inference(paramodulation,[status(thm)],[f31,f127]) ).
fof(f152,plain,
( ~ sQ13_spl
| sk_c8 != inverse(identity)
| inverse(inverse(identity)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f30,f127]) ).
fof(f155,definition,
( sQ14_spl
<=> inverse(inverse(sk_c5)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ14_spl
| inverse(inverse(sk_c5)) != sk_c8 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ4_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f150,f155,f75,f123,f83]) ).
fof(f159,definition,
( sQ15_spl
<=> inverse(inverse(inverse(sk_c8))) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f162,definition,
( sQ16_spl
<=> identity = inverse(inverse(sk_c8)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f151,f159,f162,f123]) ).
fof(f166,definition,
( sQ17_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f169,definition,
( sQ18_spl
<=> sk_c8 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f152,f166,f169,f123]) ).
fof(f182,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c8 ),
inference(resolution,[status(thm)],[f121,f97]) ).
fof(f183,plain,
( ~ sQ12_spl
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c6 ),
inference(paramodulation,[status(thm)],[f31,f121]) ).
fof(f187,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f106,f182]) ).
fof(f188,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f187]) ).
fof(f189,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f193,plain,
( sQ14_spl
| ~ sQ4_spl
| inverse(sk_c4) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f76,f157]) ).
fof(f194,plain,
( sQ14_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f80,f193]) ).
fof(f195,plain,
( sQ14_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f194]) ).
fof(f196,plain,
( sQ14_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f198,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f118,f72]) ).
fof(f199,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f118,f88]) ).
fof(f203,plain,
( ~ sQ11_spl
| sk_c7 != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f30,f118]) ).
fof(f206,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f68,f198]) ).
fof(f207,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f206]) ).
fof(f208,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f209,plain,
( sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f33,f116]) ).
fof(f210,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f209]) ).
fof(f211,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f212,definition,
( sQ21_spl
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ21_spl
| identity != sk_c6 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,definition,
( sQ22_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ22_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f183,f212,f215,f120]) ).
fof(f223,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f64,f31]) ).
fof(f225,plain,
! [X0] :
( ~ sQ9_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f138,f32]) ).
fof(f226,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c8,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f225]) ).
fof(f232,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c7) != sk_c8
| identity != sk_c6 ),
inference(paramodulation,[status(thm)],[f223,f121]) ).
fof(f237,definition,
( sQ24_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ24_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f232,f212,f237,f120,f63]) ).
fof(f256,plain,
! [X0] :
( ~ sQ0_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f137,f32]) ).
fof(f257,plain,
! [X0] :
( ~ sQ0_spl
| X0 = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f256]) ).
fof(f262,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(paramodulation,[status(thm)],[f97,f226]) ).
fof(f282,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(paramodulation,[status(thm)],[f88,f257]) ).
fof(f337,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f140,f140]) ).
fof(f338,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f31,f140]) ).
fof(f342,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f262,f140]) ).
fof(f343,plain,
( ~ sQ0_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f137,f140]) ).
fof(f350,plain,
( ~ sQ5_spl
| sk_c4 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f136,f140]) ).
fof(f351,plain,
( ~ sQ2_spl
| sk_c3 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f134,f140]) ).
fof(f352,plain,
sk_c7 = multiply(inverse(sk_c8),sk_c6),
inference(paramodulation,[status(thm)],[f33,f140]) ).
fof(f402,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f337,f338]) ).
fof(f410,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(X0,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f411,f402]) ).
fof(f411,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f342]) ).
fof(f413,plain,
( sQ22_spl
| ~ sQ0_spl
| inverse(sk_c1) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f417,f217]) ).
fof(f415,plain,
( sQ1_spl
| ~ sQ0_spl
| sk_c1 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f417,f65]) ).
fof(f417,plain,
( ~ sQ0_spl
| sk_c1 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f402,f343]) ).
fof(f432,plain,
( ~ sQ0_spl
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f417,f352]) ).
fof(f446,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f410,f432]) ).
fof(f449,plain,
( sQ22_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f61,f413]) ).
fof(f450,plain,
( sQ22_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f449]) ).
fof(f451,plain,
( sQ22_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f454,plain,
( ~ sQ2_spl
| sk_c3 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f402,f351]) ).
fof(f455,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f460,f68]) ).
fof(f456,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c7) = identity ),
inference(backward_demodulation,[status(thm)],[f460,f134]) ).
fof(f460,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f64,f454]) ).
fof(f462,plain,
( ~ sQ5_spl
| sk_c4 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f402,f350]) ).
fof(f463,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f470,f80]) ).
fof(f470,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| sk_c4 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f64,f462]) ).
fof(f475,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f33,f456]) ).
fof(f476,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f475,f214]) ).
fof(f477,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f476]) ).
fof(f490,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f415]) ).
fof(f491,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f631,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sk_c7 != inverse(sk_c8)
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f282,f127]) ).
fof(f634,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f631,f215,f63,f123,f60,f87]) ).
fof(f643,definition,
( sQ33_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f203,f169,f643,f117]) ).
fof(f651,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f199,f60,f117,f87]) ).
fof(f653,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f463,f237,f63,f79]) ).
fof(f683,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f455,f237,f63,f67]) ).
fof(f694,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f78,f82,f86,f91,f92,f93,f94,f95,f99,f100,f108,f109,f126,f158,f165,f172,f189,f196,f208,f211,f218,f240,f451,f477,f491,f634,f646,f651,f653,f683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP302-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.52 % Computer : n010.cluster.edu
% 0.12/0.52 % Model : x86_64 x86_64
% 0.12/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.52 % Memory : 8046.5625MB
% 0.12/0.52 % OS : Linux 6.8.0-71-generic
% 0.12/0.52 % CPULimit : 300
% 0.12/0.52 % WCLimit : 300
% 0.12/0.52 % DateTime : Sun Sep 20 20:09:10 UTC 2026
% 0.12/0.52 % CPUTime :
% 0.12/0.53 % Drodi V4.1.1
% 0.12/0.55 % Refutation found
% 0.12/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.58 % Elapsed time: 0.049078 seconds
% 0.15/0.58 % CPU time: 0.166126 seconds
% 0.15/0.58 % Total memory used: 75.427 MB
% 0.15/0.58 % Net memory used: 75.265 MB
%------------------------------------------------------------------------------